Feature-Curation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Engineering for LSTM Solar Flares Project\n",
    "\n",
    "The input features are time series of 25 magnetic parameters. 24 of them are defined in [Bobra and Couvidat 2015](https://ui.adsabs.harvard.edu/abs/2015ApJ...798..135B/abstract). Before diving into feature engineering, we first look at their definitions and Fischer ranking scores calculated by Bobra and Couvidat. The Fischer ranking score indicates how relevant a feature is to the binary classification. I copy its definition from Equation (1) of Bobra and Couvidat (2015) ommiting the index $i$ below\n",
    "\n",
    "$F = {(\\bar x^+ -\\bar x)^2 + (\\bar x^{-} -\\bar x)^2\\over {1\\over n^+ -1}\\Sigma_{k=1}^{n^+}(x_k^+ -\\bar x)^2 + {1\\over n^- -1}\\Sigma_{k=1}^{n^-}(x_k^- -\\bar x)^2}\\, ,$\n",
    "\n",
    "where $x$ is a feature, $x^{+}$ is the same feature in the positive-class sample, $x^{-}$ is the same feature in the negative-class sample, $n^{+}$ is the number of positive-class samples, $\\bar x$ is the mean of this feature in all samples, $\\bar x^{+}$ is the mean of this feature in positive-class samples, etc.\n",
    "\n",
    "## Magnetic Parameters:\n",
    "\n",
    "Copied from Table 1 in [Bobra & Couvidat 2015](https://ui.adsabs.harvard.edu/abs/2015ApJ...798..135B/abstract). The first number is the index in the list `feature_names`, the second number is the Fischer ranking score (F score) in Table 1 of Bobra & Couvidat (2015). We also calculated the F score in our data set which turn out to be much smaller than those in their paper, perhaps because the large data set brings in more scattering (variation). *Slanted* features are not used in the machine learning model of Bobra and Couvidat for they decide these features' F scores are too small.\n",
    "\n",
    "* 0, TOTUSJH, 3560, total unsigned current helicity, $H_{c_{total}}\\propto\\Sigma |B_z\\cdot J_z|$. \n",
    "* 1, TOTBSQ, 3051, total magnitude of Lorentz force, $F\\propto \\Sigma B^2$.\n",
    "* 2, TOTPOT, 2996, total photospheric magnetic free energy density, $\\rho_{tot}\\propto\\Sigma (\\mathbf{B}^{Obs}-\\mathbf{B}^{Pot})^2 dA $.\n",
    "* 3, TOTUSJZ, 2733, total unsigned vertical current, $J_{z_{total}}=\\Sigma |J_z| dA$.\n",
    "* 4, ABSNJZH, 2618, absolute value of the net current helicity, $H_{C_{abs}}\\propto |\\Sigma B_z\\cdot J_z|$.\n",
    "* 5, SAVNCPP, 2448, sum of the modulus of the net current per polarity, $J_{z_{sum}}\\propto |\\Sigma^{B_z^+}J_z dA|+|\\Sigma^{B_z^{-}}J_z dA|$.\n",
    "* 6, USFLUX, 2437, total unsigned flux, $\\Phi=\\Sigma |B_z|dA$.\n",
    "* 7, TOTFZ, 1371, sum of z-component of Lorentz force, $F_z\\propto \\Sigma (B_x^2 + B_y^2 -B_z^2) dA$.\n",
    "* 8, MEANPOT, 1064, mean photospheric magnetic free energy, $\\bar\\rho\\propto {1\\over N}\\Sigma(\\mathbf{B}^{Obs}-\\mathbf{B}^{Pot})^2$.\n",
    "* 9, EPSZ, 864.1, sum of z-component of normalized Lorentz force, $\\delta F_z\\propto {\\Sigma(B_x^2+B_y^2-B_z^2)\\over\\Sigma B^2}$.\n",
    "* 10, *MEANSHR*, 727.9, mean shear angle, $\\bar\\Gamma = {1\\over N}\\Sigma \\mathrm{arccos}\\left(\\mathbf{B}^{Obs}\\cdot\\mathbf{B}^{Pot}\\over|B^{Obs}||B^{Pot}|\\right)$.\n",
    "* 11, SHRGT45, 740.8, fraction of area with shear > 45 degrees, area with shear $>45^\\circ/$ total area.\n",
    "* 12, *MEANGAM*, 573.3, mean angle of field from radial, $\\bar\\gamma = {1\\over N}\\Sigma \\mathrm{arctan}\\left(B_h\\over B_z\\right)$.\n",
    "* 13, *MEANGBT*, 192.3, mean gradient of total field, $\\langle{|\\nabla B_{tot}|}\\rangle = {1\\over N}\\Sigma\\sqrt{\\left(\\partial B\\over\\partial x\\right)^2+\\left(\\partial B\\over\\partial y\\right)^2}$.\n",
    "* 14, *MEANGBZ*, 88.4, mean gradient of $B_z$, replacing $B_{tot}$ by $B_z$ in the formula above.\n",
    "* 15, *MEANGBH*, 79.4, mean gradient of horizontal field, replacing $B_{tot}$ by $B_h$ in the formula for *MEANGBT*.\n",
    "* 16, *MEANJZH*, 46.73, mean current helicity ($B_z$ contribution), $\\bar H_c \\propto {1\\over N} \\Sigma B_z\\cdot J_z$.\n",
    "* 17, *TOTFY*, 28.92, sum of y-component of Lorentz force, $F_y\\propto \\Sigma B_y B_z dA$.\n",
    "* 18, *MEANALP*, 17.44, mean vertical current density, $\\bar J_z\\propto {1\\over N} \\Sigma \\left({\\partial B_y\\over\\partial x}-{\\partial B_x\\over\\partial y}\\right)$.\n",
    "* 19, *MEANALP*, 10.41, mean characteristic twist parameter, $\\alpha$, $\\alpha_{total}\\propto{\\Sigma J_z\\cdot B_z\\over \\Sigma B_z^2}$.\n",
    "* 20, *TOTFX*, 6.147, sum of x-component of Lorentz force, $F_x \\propto -\\Sigma B_x B_z dA$.\n",
    "* 21, *EPSY*, 0.647, sum of y-component of normalized Lorentz force, $\\delta F_y\\propto {-\\Sigma B_y B_z\\over \\Sigma B^2}$.\n",
    "* 22, *EPSX*, 0.366, sum of x-component of normalized Lorentz force.\n",
    "* 23, R_VALUE, 1057, sum of flux near polarity inversion line, $\\Phi = \\Sigma |B_{LoS}|dA$ within R mask.\n",
    "* 24, XR_MAX, unfornately this parameter is not listed in Bodra & Couvidat 2015, the [IEEE competition website](http://dmlab.cs.gsu.edu/bigdata19/flare-comp/) which has a table for parameters is no longer accessible. Fortunately, as we will show below, its F score is very low, meaning it is not a relevant parameter, so we can disgard it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# libraries for read in data\n",
    "import numpy as np # linear algebra\n",
    "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "from json import JSONDecoder, JSONDecodeError  # for reading the JSON data files\n",
    "import re  # for regular expressions\n",
    "import os  # for os related operations\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decode_obj(line, pos=0, decoder=JSONDecoder()):\n",
    "    no_white_space_regex = re.compile(r'[^\\s]')\n",
    "    while True:\n",
    "        match = no_white_space_regex.search(line, pos) \n",
    "        # line is a long string with data type `str`\n",
    "        if not match:\n",
    "            # if the line is full of white space, get out of this func\n",
    "            return\n",
    "        # pos will be the position for the first non-white-space character in the `line`.\n",
    "        pos = match.start()\n",
    "        try:\n",
    "            # JSONDecoder().raw_decode(line,pos) would return a tuple (obj, pos)\n",
    "            # obj is a dict, and pos is an int\n",
    "            # not sure how the pos is counted in this case, but it is not used anyway.\n",
    "            obj, pos = decoder.raw_decode(line, pos)\n",
    "            # obj = {'id': 1, 'classNum': 1, 'values',feature_dic}\n",
    "            # here feature_dic is a dict with all features.\n",
    "            # its key is feature name as a str\n",
    "            # its value is a dict {\"0\": float, ..., \"59\": float}\n",
    "        except JSONDecodeError as err:\n",
    "            print('Oops! something went wrong. Error: {}'.format(err))\n",
    "            # read about difference between yield and return\n",
    "            # with `yield`, obj won't be assigned until it is used\n",
    "            # Once it is used, it is forgotten.\n",
    "        yield obj\n",
    "        \n",
    "\n",
    "def time_series_flattened(fname, feature):\n",
    "    '''\n",
    "    Given fname and feature name, return ts_combined (all time series combined in a flattened 1D\n",
    "    pd.Series), P_ts_combined (positive-class time series combined in a flattened 1D pd.Series)\n",
    "    and N_ts_combined (negative-class time series combined in a flattened 1D pd.Series)\n",
    "    '''\n",
    "    with open(fname, 'r') as infile:\n",
    "        all_time_series = [] # all time series corresponding to the specified feature\n",
    "        P_time_series = []\n",
    "        N_time_series = []\n",
    "        for line in infile:\n",
    "            obj = next(decode_obj(line))\n",
    "            class_label = obj['classNum'] # a number 1 or 0\n",
    "            value_dict = obj['values'] # e.g. value_dict={\"0\":78.8, ..., \"59\":75.9}\n",
    "            time_series = np.array(list(value_dict[feature].values())) # np.array([78.8,...,75.9])\n",
    "            all_time_series.append(time_series)\n",
    "            if class_label == 1:\n",
    "                P_time_series.append(time_series)\n",
    "            elif class_label == 0:\n",
    "                N_time_series.append(time_series)\n",
    "            else:\n",
    "                print('id={}: class_label is neither 1 nor 0.'.format(idx))\n",
    "        ts_combined = pd.Series(np.concatenate(all_time_series))\n",
    "        P_ts_combined = pd.Series(np.concatenate(P_time_series))\n",
    "        N_ts_combined = pd.Series(np.concatenate(N_time_series))\n",
    "        return ts_combined, P_ts_combined, N_ts_combined\n",
    "    \n",
    "    \n",
    "def fischer_ranking_score(x_all, x_P, x_N, median=False):\n",
    "    '''\n",
    "    x_all, x_P, and x_N are all pandas.Series. They contain all x's, \n",
    "    x's in the positive class, and x's in the negative class.\n",
    "    '''\n",
    "    if median: \n",
    "        # use median, robust to outliers\n",
    "        xbar = x_all.median()\n",
    "        xbar_P = x_P.median()\n",
    "        xbar_N = x_N.median()\n",
    "    else: \n",
    "        # use mean, the usual definition of Fischer ranking score\n",
    "        xbar = x_all.mean()\n",
    "        xbar_P = x_P.mean()\n",
    "        xbar_N = x_N.mean()\n",
    "    # the numbers of positive-class samples and negative-class samples\n",
    "    n_P = x_P.shape[0]\n",
    "    n_N = x_N.shape[0]\n",
    "    numerator = (xbar_P - xbar)**2.0 + (xbar_N - xbar)**2.0\n",
    "    denominator = ((x_P-xbar)**2.0).sum()/(n_P - 1) + ((x_N-xbar)**2.0).sum()/(n_N - 1)\n",
    "    fischer_score = numerator/denominator\n",
    "    return fischer_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# path_to_data = \"../input\"\n",
    "# file_name = \"fold3Training.json\"\n",
    "# fname = os.path.join(path_to_data,file_name)\n",
    "\n",
    "# # Get all the names for the 25 features and store them in a list\n",
    "# with open(fname, 'r') as infile: \n",
    "#     line_count = 0\n",
    "#     for line in infile:\n",
    "#         if line_count>0:\n",
    "#             break\n",
    "#         obj = next(decode_obj(line)) \n",
    "#         feature_names = list(obj['values'].keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = ['TOTUSJH', 'TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'ABSNJZH', 'SAVNCPP', 'USFLUX', 'TOTFZ', 'MEANPOT', 'EPSZ', 'MEANSHR', 'SHRGT45', 'MEANGAM', 'MEANGBT', 'MEANGBZ', 'MEANGBH', 'MEANJZH', 'TOTFY', 'MEANJZD', 'MEANALP', 'TOTFX', 'EPSY', 'EPSX', 'R_VALUE', 'XR_MAX']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # get all data points at every time step from all three .json files\n",
    "# # for a specified feature and put them in a 1D pd.Series\n",
    "# feature = feature_names[0]\n",
    "# path_to_data = \"../input\"\n",
    "# ts_combined= pd.Series()\n",
    "# P_ts_combined = pd.Series()\n",
    "# N_ts_combined = pd.Series()\n",
    "# for i in range(1,4):\n",
    "#     file_name = \"fold{}Training.json\".format(i)\n",
    "#     fname = os.path.join(path_to_data, file_name)\n",
    "#     ts_i, P_ts_i, N_ts_i = time_series_flattened(fname,feature)\n",
    "#     ts_combined = ts_combined.append(ts_i, ignore_index=True)\n",
    "#     P_ts_combined = P_ts_combined.append(P_ts_i, ignore_index=True)\n",
    "#     N_ts_combined = N_ts_combined.append(N_ts_i, ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # get all data points at every time step from all three .json files\n",
    "# # for a specified feature and put them in a 1D pd.Series\n",
    "# path_to_data = \"../input\"\n",
    "# feature_tss_dic = dict()\n",
    "# for feature in feature_names:\n",
    "#     ts_combined= pd.Series()\n",
    "#     P_ts_combined = pd.Series()\n",
    "#     N_ts_combined = pd.Series()\n",
    "#     for i in range(1,4):\n",
    "#         file_name = \"fold{}Training.json\".format(i)\n",
    "#         fname = os.path.join(path_to_data, file_name)\n",
    "#         ts_i, P_ts_i, N_ts_i = time_series_flattened(fname,feature)\n",
    "#         ts_combined = ts_combined.append(ts_i, ignore_index=True)\n",
    "#         P_ts_combined = P_ts_combined.append(P_ts_i, ignore_index=True)\n",
    "#         N_ts_combined = N_ts_combined.append(N_ts_i, ignore_index=True)\n",
    "#     feature_tss_dic[feature] = [ts_combined, P_ts_combined, N_ts_combined]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTUSJH\n",
      "fischer ranking score with mean:  0.36773246673505716\n",
      "fischer ranking score with median:  0.2590214764285473\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/numpy/lib/histograms.py:824: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  keep = (tmp_a >= first_edge)\n",
      "/anaconda3/lib/python3.6/site-packages/numpy/lib/histograms.py:825: RuntimeWarning: invalid value encountered in less_equal\n",
      "  keep &= (tmp_a <= last_edge)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTBSQ\n",
      "fischer ranking score with mean:  0.32482343884670983\n",
      "fischer ranking score with median:  0.22074868843684287\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTPOT\n",
      "fischer ranking score with mean:  0.1499514561251042\n",
      "fischer ranking score with median:  0.08843820489213812\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTUSJZ\n",
      "fischer ranking score with mean:  0.3922663624763004\n",
      "fischer ranking score with median:  0.2928397811172166\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ABSNJZH\n",
      "fischer ranking score with mean:  0.1904095563553693\n",
      "fischer ranking score with median:  0.05378188356844432\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SAVNCPP\n",
      "fischer ranking score with mean:  0.22439439478932718\n",
      "fischer ranking score with median:  0.0776089422410042\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "USFLUX\n",
      "fischer ranking score with mean:  0.37438402332935666\n",
      "fischer ranking score with median:  0.2751302550517006\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTFZ\n",
      "fischer ranking score with mean:  0.33428600877683995\n",
      "fischer ranking score with median:  0.23289152241180763\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANPOT\n",
      "fischer ranking score with mean:  7.57263385334421e-06\n",
      "fischer ranking score with median:  1.5021074553326917e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EPSZ\n",
      "fischer ranking score with mean:  0.35386942525619547\n",
      "fischer ranking score with median:  0.549247897618009\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANSHR\n",
      "fischer ranking score with mean:  0.3535024071496605\n",
      "fischer ranking score with median:  0.4794014189691481\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHRGT45\n",
      "fischer ranking score with mean:  0.34630559558934837\n",
      "fischer ranking score with median:  0.48680517722938377\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANGAM\n",
      "fischer ranking score with mean:  0.30204144687681833\n",
      "fischer ranking score with median:  0.42562774117475605\n"
     ]
    },
    {
     "data": {
      "image/png": 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0+Xrp4UvgQuCONM3z7DrJngNMlLQOmJiGO12GmfWNqh+4lPRh4EfAX0TEv3dx17hm2qM12sMg7q3AeiM9f/FZYEK6+wRd33auFN9KdgdqYLq6nS9fmleHpIHAR4BtmBknnXQSu6rd7pYvX77zu6T3AFIdvahS+YiYB8yrEF8FjKoQfxWYUCHe6TLMbO9VdeVb0vvIEu8fRsR9KdzTtmKFt0fzVTSzrqWeS64AzoyIt3OjFgNTJL0/9WLSAjxOdkWtRdJRkg4keyhzcTpYPwKck6Yvv4VdurV9DvBwdJZtmJmZ7eeq6e1EwFxgbUR8Jzeqp23F3B7NrB9NnTqVE088keeee46mpiaAw4CbgYOAVkltkv4eICJWA/cAa4ClwEUR8V66qn0xWX1eC9yTykKWxF8mqZ2sTffcFJ8LHJril7HrwWkzM7OGU02zk08BXwCekdSWYn9N1jbsHkkzgZeAc9O4JcDpZG3F3gYugKw9mqRSezTYsz3ancAHydqi5dujVb0MM+vcwoULdxuWtDUixnRWPiKuBa6tEF9CVgfL4y+Q9YZSHv8Vu+qumZlZQ+s2+Y6In1K5jTX0sK2Y26OZmZmZWSPzGy7NzMzMuuFODayv9KirQTMzMzMz6z0n32ZmZmZmBXHybWZmZmZWECffZmZmZmYFcfJtZmZmZlYQJ99mZmZmZgVx8m1mZmZmVhAn32ZmZmZmBXHybWZmZmZWECffZmZmZmYFcfJtZmZmZlYQJ99mZmZmZgVx8m1mZmZmVhAn32YNYsaMGQwdOpRRo0btjEkaLKlV0rr095AUl6SbJLVLelrScblppqXy6yRNy8WPl/RMmuYmSepqGWZmZo3IybdZg5g+fTpLly4tD88GlkdEC7A8DQOcBrSkzyzgVsgSaeAqYCxwAnBVLpm+NZUtTTepm2WYmZk1HCffZg3i5JNPZvDgweXhycD89H0+cFYuviAyK4GDJQ0HTgVaI2JbRGwHWoFJadygiPhZRASwoGxelZZhZmbWcJx8mzW2YRGxESD9HZriI4ANuXIdKdZVvKNCvKtl7EHSLEmrJK3asmVLrzfKzMysVjn5NrNKVCEWvYj3SETcFhFjImLMkCFDejq5mZlZzXPybdbYNqUmI6S/m1O8AzgiV64JeKWbeFOFeFfLMDMzazgD+3sFzKxfLQamAXPS3wdy8YslLSJ7uPL1iNgoaRnwzdxDlqcAV0bENklvSBoHPAacD3y3m2XUpebZD/X3KpiZWR1z8m3WIKZOncqKFSvYunUrTU1NAIeRJcT3SJoJvAScm4ovAU4H2oG3gQsAUpJ9DfBEKvf1iNiWvl8I3Al8EPhJ+tDFMszMzBqOk2+zBrFw4cLdhiVtjYhXgQnlZVOPJRdVmk9EzAPmVYivAkZViFdchtW3zu4ArJ9zRsFrYmZWX9zm28zMzMysIE6+zczM+kmlN89effXVjBgxgtGjRzN69GiWLFmyc5ykK9NbZJ+TdGouPinF2iXNzsWPkvRYesPs3ZIOTPH3p+H2NL65u2WYWd9w8m1mZtZPOnnzLJdeeiltbW20tbVx+umnAyDpaGAKcAzZG2S/J2mApAHALWRvpj0amJrKAnwLuD69YXY7MDPFZwLbI+JjwPWpXKfL6PstN2tcTr7NzMz6SSdvnu3MZGBRRPw6Il4keyD6hPRpj4gXIuIdYBEwWZKAzwD3punL32JbevPsvcCEVL6zZZhZH3HybWZmVmNuvvlmjj32WGbMmMH27dtL4Z6+efZQ4LWI2FEW321eafzrqXxn89qD30hr1jvdJt+S5knaLOnZXOxqSS9Lakuf03Pj3B7NzMysly688EKef/552traGD58OJdffnlpVF++eXav31brN9Ka9U41V77vJGv3Ve76iBidPkvA7dHMzMz21rBhwxgwYAAHHHAAX/ziF3n88cdLo3r65tmtwMGSBpbFd5tXGv8RYFsX8zKzPtJt8h0R/0JWIavh9mhmZmZ7YePGjTu/33///fmeUBYDU9Kd4aOAFuBxspdetaQ7yQeSXaBanPrrfwQ4J01f/hbbaen7OcDDqXxnyzCzPrI3L9m5WNL5wCrg8ojYTtYubGWuTL6tWHkbsrH0oD2apHx7tM6WsRtJs4BZAEceeWQvNtHMzGzfKX/z7N/+7d+yYsUK2trakERzczPf//73ufvuu4mI1ZLuAdYAO4CLIuI9AEkXA8uAAcC8iFidFnEFsEjSN4CngLkpPhe4S1I72QW2KUCXyzCzvtHb5PtW4BqydmDXANcBM+i8rVilK+yFtEcDbgMYM2ZMxTJmZmb9pfzNswAzZ86sUDITEdcC11aILwGWVIi/QIW7wxHxK+DcnizDzPpGr3o7iYhNEfFeRPwGuJ1dFdvt0czMzMzMOtGr5FvS8NzgHwOlnlDcHs3MzMzMrBPdNjuRtBAYDxwmqQO4ChgvaTRZc4/1wJeg67Zibo9mZmZmZo2u2+Q7IqZWCM+tECuVd3s0MzMzM7MK/IZLMzMzM7OCOPk2MzMzMyuIk28zQ9KlklZLelbSQkkfSA9IPyZpnaS708PSpIed75bUnsY35+ZzZYo/J+nUXHxSirVLml38FpqZmdUGJ99mDU7SCOArwJiIGEX2UPQU4FvA9RHRAmwHSp0PzwS2R8THgOtTOSQdnaY7BpgEfE/SAEkDgFuA04CjgamprJmZWcPZmzdc2j7WPPuh/l4FaxwDgQ9Kehf4LWAj8BngT9L4+cDVZC/Ympy+A9wL3CxJKb4oIn4NvJh6Kio9TN2eHq5G0qJUds0+3iYzs075GGv9xVe+zRpcRLwMfBt4iSzpfh14EngtInakYh3AiPR9BLAhTbsjlT80Hy+bprP4HiTNkrRK0qotW7bs/caZmZnVGCffZg1O0iFkV6KPAg4HPkTWRKRclCbpZFxP43sGI26LiDERMWbIkCHdrbqZmVndcfJtZv8VeDEitkTEu8B9wB8AB0sqNU1rAl5J3zuAIwDS+I+QvQhrZ7xsms7iZmZmDcfJt5m9BIyT9Fup7fYEsvbYjwDnpDLTgAfS98VpmDT+4YiIFJ+SekM5CmgBHgeeAFpS7ykHkj2UubiA7TIzM6s5fuDSrMFFxGOS7gV+DuwAngJuAx4CFkn6RoqV3mw7F7grPVC5jSyZJiJWS7qHLHHfAVwUEe8BSLoYWEbWk8q8iFhd1PaZmZnVEiffZkZEXAVcVRZ+gV29leTL/go4t5P5XAtcWyG+BFiy92tqta6zHiTWzzmj4DUxM6tNbnZiZmZmZlYQJ99mZmZmZgVx8m1mZmZmVhAn32ZmZmZmBXHybWZmZmZWECffZmZmZmYFcfJtZmZmZlYQJ99mZmZmZgVx8m1mZmZmVhAn32ZmZmZmBXHybWZmZmZWECffZmZmZmYFGdjfK2BmVouaZz/U36tgZmb7IV/5NjMzMzMriJNvMzOzfjJjxgyGDh3KqFGjdsa2bdvGxIkTaWlpYeLEiWzfvh0AZW6S1C7paUnHlaaRNE3SuvSZlosfL+mZNM1NkpTigyW1pvKtkg7pbhlm1jecfJsZkg6WdK+k/y1praQTe3Nw7mkCYNbopk+fztKlS3eLzZkzhwkTJrBu3TomTJjAnDlzSqNOA1rSZxZwK2SJNHAVMBY4AbiqVF9TmVm56Sal+GxgeUS0AMvTcKfLMLO+023yLWmepM2Sns3F9vlB2WflZoW6EVgaEb8PfAJYSw8Pzr1MAMwa2sknn8zgwYN3iz3wwANMm5YdJqdNm8aPf/zj0qjJwILIrAQOljQcOBVojYhtEbEdaAUmpXGDIuJnERHAAuCs3Lzmp+/zy+KVlmFmfaSaK993sueBsoiDss/KzQogaRBwMjAXICLeiYjX6PnBuTcJgJmV2bRpE8OHZ/nu8OHD2bx5c2nUCGBDrmhHinUV76gQBxgWERsB0t+h3SxjD5JmSVoladWWLVt6solmDa3b5Dsi/gXYVhYu4qDss3KzYnwU2AL8QNJTku6Q9CF6fnDuTQKwGx/MzbpUqblW9CLem2XsGYy4LSLGRMSYIUOGdDNbMyvpbZvvIg7KPis3K8ZA4Djg1oj4JPAWu+40VbLPEgAfzM1g2LBhbNy4EYCNGzcydGjp8EcHcESuaBPwSjfxpgpxgE2lC1fpb+nyemfzMrM+0tcPXPqs3Kz+dAAdEfFYGr6XLBnv6cG5NwmAmZU588wzmT8/u/E7f/58Jk+eXBq1GDg/Pfs0Dng9XZxaBpwi6ZDUpPMUYFka94akcel5qvOBB3LzKj1/Na0sXmkZZtZHept8F3FQ9lm5WQEi4pfABkm/l0ITgDX0/ODcmwTArKFNnTqVE088keeee46mpibmzp3L7NmzaW1tpaWlhdbWVmbP3nkjagnwAtAO3A58GSAitgHXAE+kz9dTDOBC4I40zfPAT1J8DjBR0jpgYhrudBlm1nd6+4bL0kF5DnselC+WtIjs4crXI2KjpGXAN3MPWZ4CXBkR2yS9kQ7gj5EdlL/bm2X0cjvMLPPnwA8lHUh24L2A7OT8HkkzgZeAc1PZJcDpZAfnt1NZUn0uJQCwZwJwJ/BBsoN/KQEwa2gLFy6sGF++fPkesfRs1EWVykfEPGBehfgqYFSF+KtkJ9pVL8PM+ka3ybekhcB44DBJHWS9lsxh3x+Ue7QMM+u9iGgDxlQY1aODc08TADMzs0bTbfIdEVM7GbVPD8o+K+87zbMfqhhfP+eMgtfEzMzMrLH5DZdmZmZmZgVx8m1mZmZmVhAn32ZmZmZmBXHybWZmZmZWECffZmZmZmYFcfJtZmZmZlYQJ99mZmZmZgVx8m1mZmZmVhAn32ZmZmZmBen2DZdmZmZmVlmlt0j7DdLWFSffZma2z1VKUMBJipk1Hjc7MTMzMzMriJNvMzMzM7OCOPk2MzMzMyuIk28zMzMzs4I4+TYzACQNkPSUpAfT8FGSHpO0TtLdkg5M8fen4fY0vjk3jytT/DlJp+bik1KsXdLsorfNzMysVjj5NrOSS4C1ueFvAddHRAuwHZiZ4jOB7RHxMeD6VA5JRwNTgGOAScD3UkI/ALgFOA04GpiaypqZmTUcJ99mhqQm4AzgjjQs4DPAvanIfOCs9H1yGiaNn5DKTwYWRcSvI+JFoB04IX3aI+KFiHgHWJTKmpmZNRz3821mADcAXwUOSsOHAq9FxI403AGMSN9HABsAImKHpNdT+RHAytw889NsKIuPrbQSkmYBswCOPPLIvdic6nXW/7SZmdm+4OS7gfmlFwYg6bPA5oh4UtL4UrhC0ehmXGfxSnfYokKMiLgNuA1gzJgxFcuYmZnVMyffZvYp4ExJpwMfAAaRXQk/WNLAdPW7CXglle8AjgA6JA0EPgJsy8VL8tN0FjczM2sobvNt1uAi4sqIaIqIZrIHJh+OiPOAR4BzUrFpwAPp++I0TBr/cEREik9JvaEcBbQAjwNPAC2p95QD0zIWF7BpZmZmNcdXvs2sM1cAiyR9A3gKmJvic4G7JLWTXfGeAhARqyXdA6wBdgAXRcR7AJIuBpYBA4B5EbG60C0xMzOrEU6+zWyniFgBrEjfXyDrqaS8zK+AczuZ/lrg2grxJcCSPlxVMzOzuuTk2/bgBzHNzMzM9g23+TYzMzMzK4iTbzMzsxrU3NzMxz/+cUaPHg0wEkDSYEmtktalv4ekuCTdJKld0tOSjivNR9K0VH6dpGm5+PGSnknT3JReltXpMsysb+xV8i1pfaq4bZJWpZh3DGZmZn3gkUceoa2tDWBtCs0GlkdEC7A8DQOcRtbDUAvZi6puhex4CVxF9mKrE4CrcsfMW1PZ0nSTulmGmfWBvmjz/emI2JobLlXaOZJmp+Er2H3HMJas0o/N7RjGkL1440lJiyNiO7t2DCvJHtaaBPyki2XYPuS24GZm/W4yMD59n0/2gPQVKb4gdfu5UtLBkoansq0RsQ1AUiswSdIKYFBE/CzFFwBnkR1jO1uGmfWBfdHsZDJZZSX9PSsXXxCZlWQv8BgOnEraMaSEu7RjGE7aMaSdyYKyeVVahpmZ2X5BEqeccgrHH388wGEpPCwiNgKkv0NTfASwITd5R4p1Fe+oEO9qGeXrN0vSKkmrtmzZ0ruNNGtAe3vlO8rJ2OAAABDoSURBVIB/khTA99OroXertJL2+Y4ht4y61NkVZTMza1yPPvoohx9+OJs3b2bYsGFDJZ3cRXFViEUv4lVLx/zbAMaMGdOjaYvkY6zVmr298v2piDiOrEnJRbW2Y/BZuZmZ1avDDz8cgKFDhwK8RtZme1O6M0z6uzkV7wCOyE3eBLzSTbypQpwulmFmfWCvrnxHxCvp72ZJ95PbMaQr0tXuGMaXxVdQxY6hwjLK168uzsrrnduCm5n1rbfeeovf/OY3HHTQQbz11lsAg4BngcXANGBO+vtAmmQxcLGkRWTPVb2ejpHLgG/mHrI8BbgyIrZJekPSOOAx4Hzgu7l5VVqGVcnHRetKr698S/qQpINK38kqdH7HAHvuGM5PvZ6MI+0YyF45fYqkQ9LO4RRgWRr3hqRxqZeT88vmVWkZZmZmdW/Tpk2cdNJJfOITn+CEE04AeC0ilpIlxBMlrQMmpmHIOiV4AWgHbge+DJAetLwGeCJ9vl56+BK4ELgjTfM82cOWdLEMM+sDe3Plexhwf+r9byDwDxGxVNITwD2SZgIvses11EuA08kq+dvABZDtGCSVdgyw547hTuCDZDuF/I6h0jLMzMzq3kc/+lF+8Ytf7ByW9EuAiHgVmFBePnVMcFGleUXEPGBehfgqYFSFeMVlmFnf6HXyHREvAJ+oEPeOwczMzMysAr/h0szMzMysIH3xkh2zivzAiZl1x/sJM2s0Tr7NzMzMCuCTTQMn32YNT9IRZG+Q/W3gN8BtEXGjpMHA3UAzsB74bxGxPfU+dCPZA9RvA9Mj4udpXtOAv0mz/kZEzE/x49n18PQS4JL0HIiZWcNzUt5YnHxb4byTqTk7gMsj4uep+9AnJbUC04HlETFH0mxgNnAF2Uu1WtJnLHArMDYl61cBY8heiPWkpMURsT2VmQWsJEu+J7Gr9yIzM7OG4QcuzRpcRGwsXbmOiDeAtcAIYDIwPxWbD5yVvk8GFkRmJXBwetnVqUBrRGxLCXcrMCmNGxQRP0tXuxfk5mVmZtZQnHyb2U6SmoFPkr3xblh62RXp79BUbASwITdZR4p1Fe+oEK+0/FmSVklatWXLlr3dHDMzs5rj5NvMAJD0YeBHwF9ExL93VbRCLHoR3zMYcVtEjImIMUOGDOlulc3MzOqO23xbzXBb8P4j6X1kifcPI+K+FN4kaXhEbExNRzaneAdwRG7yJuCVFB9fFl+R4k0VypuZWRd8XNw/+cq3WYNLvZfMBdZGxHdyoxYD09L3acADufj5yowDXk/NUpYBp0g6RNIhwCnAsjTuDUnj0rLOz83LzMysofjKt5l9CvgC8IykthT7a2AOcI+kmcBLwLlp3BKybgbbyboavAAgIrZJugZ4IpX7ekRsS98vZFdXgz+hH3o66ewKkpmZWZGcfJs1uIj4KZXbZQNMqFA+gIs6mdc8YF6F+Cpg1F6sppmZ2X7BybfVPLd5MzMz28XHxfrmNt9mZmZmZgVx8m1mZmZmVhA3OzEzMzPbD7g5Sn3wlW8zMzMzs4L4yreZmZnZfsxXxGuLr3ybmZmZmRXEV77NzMzMGpCviPcPJ99Wt7zTMDMzs3rjZidmZmZmZgVx8m1mZmZmVhAn32ZmZmZmBXHybWZmZmZWED9wafsdP4hpVv9cj836j+vfvuXku0Cd/Wc2MzOzveNjrNULJ99mZmZm1i1fEe8bdd3mW9IkSc9Japc0u7/Xx8w65/pqVj9cX832nbq98i1pAHALMBHoAJ6QtDgi1vTvmplZuSLrq289m+0dH1/N9q26Tb6BE4D2iHgBQNIiYDLgnYNV1JOkzLfQ+pzrq1n9cH21HunpRY9GP8bWc/I9AtiQG+4AxuYLSJoFzEqDb0p6rqB1q8ZhwNb+XokeaKj11bf6cE2qV/Rv/DsFLqvb+gp9Wmfr7f9rtRp+u/qpbvZWX/577c/1ta/VYz2pt3Wut2Nsf/y+ndbZek6+VSEWuw1E3AbcVszq9IykVRExpr/Xo1pe332vHte5B7qtr9B3dXZ//S29XfWljrer0Pra1+rxd6+3dfb67p16fuCyAzgiN9wEvNJP62JmXXN9Nasfrq9m+1A9J99PAC2SjpJ0IDAFWNzP62Rmlbm+mtUP11ezfahum51ExA5JFwPLgAHAvIhY3c+r1RM1d6uuG17ffa8e17kq/VBf99ff0ttVX+pyu3x87Rf1ts5e372giD2acZmZmZmZ2T5Qz81OzMzMzMzqipNvMzMzM7OCOPnexyQdIekRSWslrZZ0SYoPltQqaV36e0h/r2uepAGSnpL0YBo+StJjaX3vTg/h1AxJB0u6V9L/Tr/1ibX8G0u6NP1/eFbSQkkfqPXfuBbVa/2qVr3Vw2rVW32tlut18ep1H1BPdbse62ut10Un3/veDuDyiBgJjAMuknQ0MBtYHhEtwPI0XEsuAdbmhr8FXJ/Wdzsws1/WqnM3Aksj4veBT5Cte03+xpJGAF8BxkTEKLIHmqZQ+79xLarX+lWtequH1aqb+lot1+t+U6/7gHqq23VVX+uiLkaEPwV+gAeAicBzwPAUGw4819/rllvHJrLK9BngQbIXLmwFBqbxJwLL+ns9c+s7CHiR9ABxLl6TvzG73h43mKzHoQeBU2v5N66XTz3Urx5sS13Vwx5sV13V1x5sl+t1DXzqYR9QT3W7HutrPdRFX/kukKRm4JPAY8CwiNgIkP4O7b8128MNwFeB36ThQ4HXImJHGu4g+89dKz4KbAF+kG7j3SHpQ9TobxwRLwPfBl4CNgKvA09S279xzauj+lWtequH1aqr+lot1+v+V0f7gHqq23VXX+uhLjr5LoikDwM/Av4iIv69v9enM5I+C2yOiCfz4QpFa6mPyoHAccCtEfFJ4C1q6BZYudQ2bjJwFHA48CHgtApFa+k3rmn1Ur+qVaf1sFp1VV+r5Xrdv+plH1CHdbvu6ms91EUn3wWQ9D6yncIPI+K+FN4kaXgaPxzY3F/rV+ZTwJmS1gOLyG6L3QAcLKn0UqZae9VwB9AREY+l4XvJdha1+hv/V+DFiNgSEe8C9wF/QG3/xjWrzupXteqxHlar3uprtVyv+0md7QPqrW7XY32t+bro5HsfkyRgLrA2Ir6TG7UYmJa+TyNrp9bvIuLKiGiKiGayBxQejojzgEeAc1KxmllfgIj4JbBB0u+l0ARgDTX6G5PdChsn6bfS/4/S+tbsb1yr6q1+Vase62G16rC+Vsv1uh/U2z6g3up2ndbXmq+LfsPlPibpJOBfgWfY1b7rr8napN0DHEn2H+XciNjWLyvZCUnjgb+MiM9K+ijZWfpg4CngTyPi1/25fnmSRgN3AAcCLwAXkJ1c1uRvLOlvgc+TPan/FPD/kLU/q9nfuBbVc/2qVj3Vw2rVW32tlut18ep5H1Avdbse62ut10Un32ZmZmZmBXGzEzMzMzOzgjj5NjMzMzMriJNvMzMzM7OCOPk2MzMzMyuIk28zMzMzs4I4+badJIWku3LDAyVtkfRgGp6ehttyn6Nz5S+V9CtJH8nFxqf5/lEu9mDqYqm0jG9KWpeb59fK1uuP0zx+PxdrTrFrcrHDJL0r6eY+/mnMzMzM+oSTb8t7Cxgl6YNpeCLwclmZuyNidO6zJjduKvAE8Mdl03QAX6Oyb5C9/vXjETEa+EPgfWVlpgI/JXshQd4LwGdzw+cCqztZjlm/aYQTW0lXS3o5LedZSWf24ncaI+mm3Pb9QW7cn0k6v6fzNKtGA9XRtyUNzcXe7MXP1SXX3e45+bZyPwHOSN+nAgurmUjS7wIfBv4mTZf3C+B1SRPLpvkt4IvAn0fErwAi4o2IuDpX5sNkr+OdyZ7J938AayWNScOfJ+v036zWNMqJ7fVpWecC8yT16BgTEasi4itpcDzZK6FL4/4+Ihb0ZH5mPdAodXQrcHkV5fbGeFx3u+Tk28otAqZI+gBwLNlbwvI+X3bmX9pRlRL1fwV+L39mnXyDLDHP+xjwUkS80cX6nAUsjYh/A7ZJOq6T9W0C3gNeqWIbzfpDw5zYRsRasjfLHSbpdyQtl/R0+ntkWv656Qr5LyT9S4qNT1cGm4E/Ay5N+5k/TFft/lLSSEmP57ajWdLT6fvxkv5Z0pOSlkkaXu06m9EYdXQe2XF8cIXt+FNJj6c6931JA1J8pqR/k7RC0u2lq+uS/kjSY5KekvS/JA1z3a2Ok2/bTUQ8DTST7UCWVChSfub/Hyk+BVgUEb8B7iM7C8/P918BJP1hZ8uWdEGqrBskHZHCU8kSbNLf8h3bUrIrFFOBu6vcTLP+0DAntpLGkr3qewtwM7AgIo4FfgjclIr9D+DUiPgEsFsTlYhYD/w96Up6af+Rxq0FDlT2Om5ISYek9wHfBc6JiOPJkoxrq11nMxqjjr5JVjcuyQcljSSrS59KV+HfA86TdDjw34FxZMfa389N9lNgXER8Mq3LV113q+Pk2ypZDHyb6s/6jwVagFZJ68kS8fIkGbLKlL/91g4cKekggIj4Qar0rwMDJB0KfAa4I833r8h2firNICLeAZ4ku432ox5so1mhGuTE9lJJbWT7j89HRAAnAv+Qxt8FnJS+PwrcKemLwIAq519yD/Df0vfPp/X7PWAU2X6ojSzZaerhfK2BNUgdhewEeJqkQbnYBOB44IlUfyYAHwVOAP45IrZFxLvAP+amaQKWSXqG7Ph8TBXLdt0FBvb3ClhNmge8HhHPKD0Y0o2pwNUR8T9LAUkvSvqdfKGI+CdlD4gcnobfljQXuFnSlyLiV+k214FpknPIrph9KTfffyY7eG/Izfo6sp3Dq7m83KwWlU5sxwOHdle47MQWsrrxAnBLWdHSie2ONLzzxDbdyv4B8ANJz7L7ie0oSUGW/Iakr5ZmGBHvSCqd2B4D/BHduz4ivt1NmUjz/7N0hfwMoE3S6CrmX3I38I+S7stmFeskfRxYHREn9mA+ZuX29zpKRLwm6R+AL+c3BZgfEVeWbV95G/a87wLfiYjFKVe4uorFu+7iK99WQUR0RMSNnYwuv+32B2Rn/feXlbufPduoQbYDyp/Rfg3YCDwr6Smy23bzyW6fTa0w3x8Bf1K2vqsjYn4Vm2bW3+YBX4+IZ6osXzqxbU6fw4ERlU5sgUOAT6Tht4HSie0HADo5sf2dNN8jgBfZdVW65Drgioh4tcdbusv/z659wXlkt6qR9LsR8VhE/A+yh8COKJvuDeCgSjOMiOfJbov/d3Zd8XsOGCLpxDT/90mq5kqcWV6j1NHvAF9i10XY5cA5pSYzkganbXgc+C+SDpE0EDg7N4+PsOuh1Gm5uOtuN3zl23aKiA9XiK0AVqTvdwJ3Vpj0qArTXZYbXJGLLyY7wy4NvwvMTp9y4yvM96bc4KgK4ztbR7N+FxEdQFcntvkD65fJktbTysqVTmzL26NeCzyQG/4acA3Zie0bZA9o5U9s55RNXzqx/VZufVez9913foWs55O/ImsDfkGK/52kFrL9wXKyB9P+S266/w+4V9Jk4M8rzPdu4O9I+590FfAc4CZl3b0NBG7og/W3BtIodTQitkq6H7g0Da+R9DfAPynrpehd4KKIWCnpm2lbXgHWkDUNhexK9z9KehlYya5cwHW3G8qa5JmZmZmZ7U7ShyPizXTl+35gXkSU35W2HnCzEzMzMzPrzNXpQchnyZq+/Lif16fu+cq3mZlVTdkb+M4tC/9jROzXXYOZ1QvX0drn5NvMzMzMrCBudmJmZmZmVhAn32ZmZmZmBXHybWZmZmZWECffZmZmZmYF+b+UxvqpvrRIlAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANGBT\n",
      "fischer ranking score with mean:  0.20139393684908496\n",
      "fischer ranking score with median:  0.24235853625218107\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANGBZ\n",
      "fischer ranking score with mean:  0.16150659054106076\n",
      "fischer ranking score with median:  0.18613773499670694\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANGBH\n",
      "fischer ranking score with mean:  0.014260107505483727\n",
      "fischer ranking score with median:  0.025084411183138575\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANJZH\n",
      "fischer ranking score with mean:  1.554600073688521e-06\n",
      "fischer ranking score with median:  0.00197986340292097\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTFY\n",
      "fischer ranking score with mean:  0.0003465144188979782\n",
      "fischer ranking score with median:  0.001032454640526456\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANJZD\n",
      "fischer ranking score with mean:  0.05188791382948918\n",
      "fischer ranking score with median:  0.015634807182532077\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEANALP\n",
      "fischer ranking score with mean:  8.068318407719482e-06\n",
      "fischer ranking score with median:  0.001523627722165576\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTFX\n",
      "fischer ranking score with mean:  2.8417658754857243e-06\n",
      "fischer ranking score with median:  0.0003244556731283395\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EPSY\n",
      "fischer ranking score with mean:  0.00047045785230618757\n",
      "fischer ranking score with median:  0.0013137677980803166\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EPSX\n",
      "fischer ranking score with mean:  9.019603779451062e-05\n",
      "fischer ranking score with median:  0.0003210085561443504\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R_VALUE\n",
      "fischer ranking score with mean:  0.5798349927896892\n",
      "fischer ranking score with median:  0.8323160451410178\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XR_MAX\n",
      "fischer ranking score with mean:  5.669262293286081e-08\n",
      "fischer ranking score with median:  5.314739175294073e-23\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "path_to_data = \"../input\"\n",
    "for feature in feature_names:\n",
    "    print(feature)\n",
    "    ts_combined= pd.Series()\n",
    "    P_ts_combined = pd.Series()\n",
    "    N_ts_combined = pd.Series()\n",
    "    for i in range(1,4):\n",
    "        file_name = \"fold{}Training.json\".format(i)\n",
    "        fname = os.path.join(path_to_data, file_name)\n",
    "        ts_i, P_ts_i, N_ts_i = time_series_flattened(fname,feature)\n",
    "        ts_combined = ts_combined.append(ts_i, ignore_index=True)\n",
    "        P_ts_combined = P_ts_combined.append(P_ts_i, ignore_index=True)\n",
    "        N_ts_combined = N_ts_combined.append(N_ts_i, ignore_index=True)\n",
    "    \n",
    "    print('fischer ranking score with mean: ',\n",
    "          fischer_ranking_score(ts_combined,\n",
    "                                P_ts_combined,\n",
    "                                N_ts_combined)\n",
    "         )\n",
    "    print('fischer ranking score with median: ',\n",
    "          fischer_ranking_score(ts_combined,\n",
    "                                P_ts_combined,\n",
    "                                N_ts_combined,median=True)\n",
    "         )\n",
    "    fig, axes = plt.subplots(1,3,figsize=(12,4)) # 1 row 3 columns\n",
    "    axes[0].hist(ts_combined, bins=30)\n",
    "    axes[0].set_xlabel(feature)\n",
    "    axes[1].hist(P_ts_combined, bins=30)\n",
    "    axes[1].set_xlabel(feature+'_Positive')\n",
    "    axes[2].hist(N_ts_combined, bins=30)\n",
    "    axes[2].set_xlabel(feature+'_Negative')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminary Observations and Understanding of Features\n",
    "\n",
    "According to the Fischer ranking scores and figures in the cell above, we make the following observations.\n",
    "\n",
    "* Parameters with Fischer ranking scores greater than $0.01$ are regarded as relevant parameters. This choice is mosty, although not completely, consistent with that in Table 1 of Bobra and Couvidat (2015). The relevant parameters are stored in the list `relevant_features_0`. \n",
    "    * `MEANPOT`, mean photospheric magnetic free energy has an Fischer ranking score $\\sim 10^{-6}$. But it is relevant in Bobra and Couvidat (2015). **We need a zoomed-in histogram to have a closer look.**  \n",
    "\n",
    "\n",
    "* Correlation among features: according to the definitions of these physical parameters, one can tell that the following groups of parameters should be correlated. **These speculated correlations need to be checked**.\n",
    "    * `EPSZ` $\\propto {TOTFZ\\over TOTBSQ}$, where `TOTFZ` is the total vertical Lorentz force and `TOTBSQ` is the total $B^2$. By definition, `EPSZ` is just the vertical Lorentz force normalized by the total $B^2$. I plan to delete `EPSZ` from the relevant feature list, because I think the other two parameters are easier to standardize given the simpler shapes of their histograms.\n",
    "    * `SHRGT45`, fraction of area with shear angle greater than 45 degrees, and `MEANSHR`(the mean shear angle), may be strongly positively correlated. The larger fraction of area with shear angle greater than 45 degrees, the greater the mean shear angle should be.\n",
    "    * `MEANGBT`, `MEANGBZ`, `MEANGBH` are the mean gradients of $B_{tot}$, $B_z$ and $B_h$ respectively. Because $B_{tot}^2 = B_z^2+B_h^2$, their gradients should also be correlated. I plan to delete `MEANGBH`, the one with the lowest F score of the three parameters.\n",
    "    * `R_VALUE` and `MEANGBZ` should be related, because `R_VALUE` is the absolute value of flux ($\\Sigma |B_{LoS}|dA$, where $LoS$ means line of separation) in the area along the polarity inversion line. The polarity inversion line is a line that separates areas with $B_z>0$ and $B_z<0$. For a large `R_VALUE`, it means the sign of $B_z$ must either change many times or change abruptly. Both cases shall lead to a large `MEANGBZ`, the mean horizontal gradient of $B_z$, i.e. ${1\\over N}\\Sigma |{\\partial B_z\\over\\partial h}|$, where $h$ means the horizontal direction. The Fischer ranking score of `R_VALUE` is 0.58 while that of `MEANGBZ` is 0.16. However, the histogram shape of `R_VALUE` is strange, which may make this parameter harder to standardize. **Need to further look into whether they do correlate with each other. If they correlate, which one should be dropped.**\n",
    "    \n",
    "* Most relevant features are positie and have their histograms right skewed, except for the following features.\n",
    "    * `TOTFZ` is mostly (but not always) negative, and its histogram is left skewed.\n",
    "    * `MEANGBT` is positive by definition and its histogram is *not* skewed, which is good.\n",
    "    * `R_VALUE` is positive by definition. Its histogram has a high and narrow spike near zero and low-height & wide hill. The hill component is slightly left skewed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "relevant_features_0 = ['TOTUSJH','TOTBSQ','TOTPOT','TOTUSJZ','ABSNJZH','SAVNCPP','USFLUX','TOTFZ',\n",
    "                     'EPSZ','MEANSHR','SHRGT45','MEANGAM','MEANGBT','MEANGBZ','MEANGBH','MEANJZD','R_VALUE']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlated Features I\n",
    "\n",
    "* `EPSZ` $\\propto {TOTFZ\\over TOTBSQ}$ according to their physical definitions.\n",
    "\n",
    "In order to check the correlations among different features, we first define a function that extract the features of interest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def feature_ts_all(fname, feature):\n",
    "    '''\n",
    "    Given fname and feature name, return ts_combined (all time series combined in a flattened 1D\n",
    "    pd.Series)\n",
    "    '''\n",
    "    with open(fname, 'r') as infile:\n",
    "        all_time_series = [] # all time series corresponding to the specified feature\n",
    "        for line in infile:\n",
    "            obj = next(decode_obj(line))\n",
    "            class_label = obj['classNum'] # a number 1 or 0\n",
    "            value_dict = obj['values'] # e.g. value_dict={\"0\":78.8, ..., \"59\":75.9}\n",
    "            time_series = np.array(list(value_dict[feature].values())) # np.array([78.8,...,75.9])\n",
    "            all_time_series.append(time_series)\n",
    "        ts_combined = pd.Series(np.concatenate(all_time_series))\n",
    "        return ts_combined\n",
    "    \n",
    "def extract_features(feature_list,path_to_data=\"../input\"):\n",
    "    '''\n",
    "    Given a list of features, return a pd.DataFrame, each column has label = feature and the \n",
    "    column is a 1D pd.Series containing all time series flattened from all 3 .json files.\n",
    "    '''\n",
    "    df_selected_features = pd.DataFrame()\n",
    "    for feature in feature_list:\n",
    "        ts_combined= pd.Series()\n",
    "        for i in range(1,4):\n",
    "            file_name = \"fold{}Training.json\".format(i)\n",
    "            fname = os.path.join(path_to_data, file_name)\n",
    "            ts_i = feature_ts_all(fname, feature)\n",
    "            ts_combined = ts_combined.append(ts_i, ignore_index=True)\n",
    "        df_selected_features[feature] = ts_combined\n",
    "    return df_selected_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['EPSZ','TOTFZ','TOTBSQ'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we take advantage of `pd.DataFrame.corr()` method to check the correlations among `EPSZ` (normalized vertical Lorentz force), `TOTFZ` (total vertical Lorentz force) and `TOTBSQ` (total magnetic field squared)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EPSZ</th>\n",
       "      <th>TOTFZ</th>\n",
       "      <th>TOTBSQ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>EPSZ</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.351938</td>\n",
       "      <td>0.574370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TOTFZ</td>\n",
       "      <td>-0.351938</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.823566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TOTBSQ</td>\n",
       "      <td>0.574370</td>\n",
       "      <td>-0.823566</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            EPSZ     TOTFZ    TOTBSQ\n",
       "EPSZ    1.000000 -0.351938  0.574370\n",
       "TOTFZ  -0.351938  1.000000 -0.823566\n",
       "TOTBSQ  0.574370 -0.823566  1.000000"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_selected_features.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `TOTFZ` strongly anti-correlates with `TOTBSQ`. Note that `TOTFZ` $\\propto \\Sigma B_x^2+B_y^2-B_z^2$ and `TOTBSQ` $\\propto \\Sigma B^2 =\\Sigma B_x^2 +B_y^2 -B_z^2$. The strong anti-correlation between `TOTFZ` and `TOTBSQ` must mean that $B_z^2$ dominates $B^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10772a5f8>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df_selected_features['TOTFZ'],df_selected_features['TOTBSQ'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, when you look at the scatter plot with x=`TOTFZ` and y=`TOTBSQ`, the lower boundary shows an anti-correlation, but the overall distribtuion does not really exhibit strong anti-correlation. So we shall include both `TOTFZ` and `TOTBSQ`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'EPSZ')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df_selected_features['TOTFZ'],df_selected_features['EPSZ'])\n",
    "plt.xlabel('TOTFZ')\n",
    "plt.ylabel('EPSZ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'EPSZ $\\\\propto$ 1/TOTBSQ')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df_selected_features['TOTBSQ'],df_selected_features['EPSZ'])\n",
    "plt.xlabel('TOTBSQ')\n",
    "plt.ylabel('EPSZ')\n",
    "plt.title('EPSZ $\\propto$ 1/TOTBSQ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observing the figures for `EPSZ` (normalized vertical Lorentz force) versus `TOTFZ` (the total vertical Lorentz force) & for `EPSZ` versus `TOTBSQ` (total Lorentz force proportional to $B^2$), we find that as `TOTFZ` (or `TOTBSQ`) approaches to zero `EPSZ` spans over the range $[-1,+1]$. I suspect that 0/0 is encountered and 0/0 can lead to a finite value. \n",
    "\n",
    "\n",
    "## Correlated Features II\n",
    "\n",
    "`SHRGT45`, fraction of area with shear angle greater than 45 degrees, and `MEANSHR`(the mean shear angle) should be positively correlated according to their definitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['SHRGT45','MEANSHR'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SHRGT45</th>\n",
       "      <th>MEANSHR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>SHRGT45</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.982111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANSHR</td>\n",
       "      <td>0.982111</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          SHRGT45   MEANSHR\n",
       "SHRGT45  1.000000  0.982111\n",
       "MEANSHR  0.982111  1.000000"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_selected_features.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the `SHRGT45` (fraction of area with shear angle greater than 45 degrees) is highly correlated with `MEANSHR` (mean shear angle). Let us look into their scattering figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119dc3ba8>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_selected_features.plot.scatter(x='SHRGT45',y='MEANSHR')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot also shows that `SHRGT45` and `MEANSHR` are highly correlated. Looking back at their histograms, I decide that the histogram of `MEANSHR` is always positive while the `SHRGT45` have many values cluster at zero. Both are right skewed. `MEANSHR` should be easier to standardize by using `log` first. So I decide to drop `SHRGT45` from the relevant features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['TOTUSJH', 'TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'ABSNJZH', 'SAVNCPP', 'USFLUX', 'TOTFZ', 'EPSZ', 'MEANSHR', 'MEANGAM', 'MEANGBT', 'MEANGBZ', 'MEANGBH', 'MEANJZD', 'R_VALUE']\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "relevant_features_0.remove('SHRGT45')\n",
    "print(relevant_features_0)\n",
    "print('SHRGT45' in relevant_features_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlated Features III\n",
    "\n",
    "`MEANGBT`, `MEANGBZ`, `MEANGBH` are the mean gradients of $B_{tot}$, $B_z$ and $B_h$ respectively. Because $B_{tot}^2 = B_z^2+B_h^2$, their gradients should also be correlated. I plan to delete `MEANGBH`, the one with the lowest F score of the three parameters. Before doing so, let us double check whether they indeed correlate with each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['MEANGBT','MEANGBZ','MEANGBH'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MEANGBT</th>\n",
       "      <th>MEANGBZ</th>\n",
       "      <th>MEANGBH</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>MEANGBT</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.991333</td>\n",
       "      <td>0.673467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANGBZ</td>\n",
       "      <td>0.991333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.689602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANGBH</td>\n",
       "      <td>0.673467</td>\n",
       "      <td>0.689602</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          MEANGBT   MEANGBZ   MEANGBH\n",
       "MEANGBT  1.000000  0.991333  0.673467\n",
       "MEANGBZ  0.991333  1.000000  0.689602\n",
       "MEANGBH  0.673467  0.689602  1.000000"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_selected_features.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting, I think the fact that `MEANGBT` and `MEANGBZ` are highly correlated with each other may due to the same reason for the strong anti-correlation between `TOTBSQ` and `TOTFZ`. The reason might be that $B_z^2$ dominates $B^2$ as I also mentioned in the section: \n",
    "Correlated Features I.\n",
    "\n",
    "However, a close-to-unity correlation coefficient does not necessarily mean a tight correlation. In the case for `TOTBSQ` and `TOTFZ`, their scatter plot shows a lot of scattering, indicating that their correlation is not as tight as one might speculate based solely on their correlation coefficient.\n",
    "\n",
    "Now let use look at the scatter plot between `MEANGBT` and `MEANGBZ`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119843a90>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FVx+pjFVR4+5WCQa7jWjpSJeRZhbtKaiMNO3l5b4dt10twZBOG9EAhhX2pKRfLz7224msy0gzjyYFlXHClWDozAdgOh06/91vDOeBy0YCdFhGqstKM4smBZVxYlWC4YJnl8YqpISb9fn/8R/nnkhhfl7AMtJY9KhUagmbFETkJGPMxhC3jTfGfOJMWEo5J9oSDO6GJmr3N1Kzt57PtnzJ4SPNrNnVwJTRA5mxZEu8wo2LHJeL2v2NAZvSYtWjUqklUk9hg4jMAm41xjQE3fY8MNaZsJRyjrcEQ7ix87mVO7hnThVHWto7PP65NEsIAC3t7Qzp1zOgTYvaZaZISWEdnsNvVonIdOvsZK9QFVCVSnqhSjBU19WzrHovP/nLBprbEhykA2ZcO4beuVm8/HENK7Z+Sc/cbFra221rGWlRu8wUKSm0GGMeEJEPgNkiMhN4zBjTTvosw1ZpwDvUE21dHuhYgiHcnoN08I0TCxlfWkTt/kZ+eYOnkx/u7yyaHpVKP1FNNBtjlopIOfBr4GMRucHZsJTqKNQHv3eoJ8fl8n3rvWLM4E797kzYc7B25wHGP7m4U39PWtQu80RKCr4hImPMAeB6EbkR+Bjo5WRgSvkL9cHvbmjyjf0fwTP+f9efVjNy0DGUFhdE/fvveHOVU6EnjQONnvEw79/T3XOqGF9aFLFnpUXtMkukHc2/DW4wxrwGfBP4kyMRKRXE/4O/vqmVIy3t3D2nytdzyHEF/jNubjNc8vwy5lXuiPo5qusOxzrspOddcaSUv7BJwRjz6+A2ESkCaowx/+FYVEr5sfvg936gDenXk5b2jiuEmluPJg5/t81ewakPvc9ts1cAR0tdnFFyjHMvIAFyo1gGYrfiSKlI+xTGAU8AXwKPArOAIsBlrUb6q/Mhqkxn98F/qKnVN7dw8oB8Knd81eFxR1raWfLFHs47eQCF+XkMu/c9323z1+5hvt/1dPGLa0YzYcQAavc3cuebf6d679Ee0KBjctnf2BowBBftpLzKHGJM6EVEIlIB3A/0AV4CLjbGLBeRk4HXjTFnxCdMe+Xl5aaioiKRIag4mVe5gx8EHVbTp0cWB49EXjfaI8fFyOLerKqtdyq8hMkG8nJdnD+iyPYQnEXrd7NgfR2TRxYzaeTALq3SUulHRFYaY8rtbos00ZxtjFlg/ZJHvPsUjDFfiOg2BRU/Xx1u7tAWTUIAT48hHRPC1igOv5k0ciCTRg70XS/Mz9NkoMKKNNHs32cPnpHSfQoqbuZW7erW47Nd6fMl5vLTBkSVEJTqikg9hdNF5Cs8S1N7WpexrvdwNDKl/EwZPYgVW/d3+fFZLqG1PfW/xzx+5WnccPbxiQ5DpbGwScEYkxWvQJQKZ9rXh/P0go0BQ0b5uUJDc3Qf9FeNHUy2S1J+g9qj767HtLXz0eZ9XDZqIFPHliQ6JJVmwk40d7izyGDAmyh2GmNaHYkqSjrRnHlmf1rD3KpdCPC3TvQcXpl+Jt+ZudK5wBJk0DG5fHb/hYkOQ6WYcBPNYecUROQ+EXnIr+kz4D1gAfBfsQsxc7kbmli9/UCH9fTK3rSvD+eei07qVEIY2q9HWiYEgF1fNfPOqu2JDkOlkUgTzd8Gfu533W2MGQWcCoSd6RKRV0Vkj4is9Wt7WER2iEil9ecSv9vuE5FqEdkoIhd14bWknLmVOxj/5GKmvfw5459c3KkduJlqbuUOrn5xeeQ7+tm2/4hD0TgnNwvOLT2WGdeOoUeOi4K87JBlid9dszuusan0FrEgnjHmkN/V56y2NhGJtBXyd8AvgZlB7c8aY37m3yAiI4Fr8SSb44CFIjLCGJOGxYs97Gr2RFuLJlN5/87SXfDKIm9l0zXb9/PgvPUd7n/ZqIEd2pTqqkg9hXwRyfFeMcb8DkBE8oCwdQGMMUvx7ISOxhTgj8aYJmNMDVANfC3Kx6akcKUbVEfuhiaueeFT20Nv0skFpwzoMJRYmJ/H6SV9uXj0cbaPmTBiQDxCUxkiUlJ4C3hRRHwVUUWkN/CCdVtXfF9EqqzhpX5W22DAf2C01mpLW3alG7QWjb25lTs487GF/GNf+hetW/zFnpBDibX7GynIC+zcF+Rl6xcJFVORksJ/A3uAbSKyUkRWAVuBOuu2zvoNcCIwBtjF0fkKu+FS22VRInKziFSISMXevXu7EEJyKMzP46mrRvvGi3vkuLQWjQ13QxM/DCpvkc7aDQFVYP3pFwkVD5H2KbQB94rIj4FSq7naGNOlrybGmDrvZRH5LfCudbUW8F9wPQTYGeJ3vISnDhPl5eUpvRvpijGDfePFWovGXu3+xozcOu8dSvT/N+H9InF30LkS+u9GxVKkKqkTbZrP8tY9suYNoiYig4wx3noFVwLelUnzgD+IyDN4JprLgL915nenKq1FY+/Bt1fz/ro6zhuRmecBh+oB6BcJ5bRIq4/s9iIY4HQ83+ZD7ngWkdeBc4EiEakF/gc4V0TGWL9jK3ALgDFmnYi8CawHWoFb03nlkQrPv8T1W3/vXs2jVJMlkJMdfihRv0goJ3V2R/M3gAeAfsDjxpj5TgUWDd3RnHr8SzfvP9RM5fYDjCnpS2lxAe6GJs58bGGiQ4y78uP78vUTizh9SB+KCnpoD0A5rjuls72/YBKeiWUD/MQY82EM41MZwv+c5cMtbbT5FaibUFrIx9XuBEaXONPOHqo1jFTSiDSncCmensFB4AFjzCdxiUqlHbvNev4yNSEMOiZXE4JKKpF6CvPxrAxyA/cEH6xjjLnCobhUmvFu1rNLCJngF9eMZsu+w0wsK6J2/2HeXbNbq5yqpBQpKZwXlyhUTMTjqMWuPofdGvtMMf2cwOGh8uGFmgxU0oq0T+F/7dpFpARPrSLb21X8+Y/Xe9evXzEmtpvCu/Mc3jX2//WWp3ZRU2v6J4grxxzHreeVUlpckOhQlIpapB3NPiJSJCL/KSJLgY+AYseiUp3iP15f39QackdsIp/D3dDE+2t309TanhEJAaDk2F6aEFTKiTTRXIBnk9n1wAjgz8AJxpghcYhNRcluvN5uR2winqOixs0vFm5m2T8ybyJ5YllmbrxTqS3SnMIePDuLHwSWGWOMiFzpfFiqM+JRE6crzzHt5eUsy4BVRa9MP5Mn//oFm/YcrTI/obSQ8uGFCYxKqa6JNHx0P9ADTyG7+0TkROdDUp0Vj+J6nX2O61/8JCMSwknFvZk0ciC3nl9GbpaL3CwhN8vFt8t1Ilmlpqh2NIvICcB1eCaXy/CUrPizMWaTs+GFpzuaA8Vj9ZH3jOQpowcx7evDbe/jX6YiHb0y/UwWrK9j8shiJo0ciLuhifFPLg4466FHjotP7jlfdyarpNTtHc3GmC3A48DjIjIKT4J4H08ZbJUknK6JM+4nH7L7q2YAVmzdz68+qu5waPwFP1vs2PMng8tPG8CkkQOZNPLoaWfxmNNRKl7CDh+JyMl+l/MAjDFrjDH3A9Mcjk0lkXdWbfclBK/gQ+PL7nuP6n3pfeDL89PO6tCm5xyodBJpTuEPfpc/C7rtVzGORSWxUIfDe9uf/WADLWl+8MHCO+wqyeuBSSq9RBo+khCX7a6rNHbZqIEs3LDHth3g1/+7Jd4hxVWPHBeX/XJZyA17es6BSheRegomxGW766oT3A1NrN5+IKYbzJw0dWwJg47JDWjzFnO7ZdYKWtJ8P9qRlvaIG/YK8/M4vaSvJgSV0iL1FIaIyAw8vQLvZazrsa2hkEHiUZLCCZ/dfyHvrNruK+ZWs7eB8T9dyI6DqZHYOis3S3C5JGBVkU4gq3TXmZPXgtd+6lrQLrArIX33nCrGlxalxAfN1LElTB1bQtl976X9HMKdF5Tx7OLqgDadQFbpLlJBvNfiFUimSIfli5kwqQywYtsBnrpqNHcH9epS5X1Sqisi1T6aF+52PU+h89Jh+eLcKvuVSKnq68P78mnNgQ7tl40aqBPIKuNEGj46B9gOvA58jq446jbv8sVU+fZpt0t6q/twgqOKrV49chl0TC67/PZh+J+I5vSmQKWSSaSkMBC4EM8O5uuB94DXjTHrnA4snaXKt0+7CfGlG+sSHVaXDczPZXdDc4f2y0YN5OUbzwqYRLc7BKe6rp7K7QcYU9JXS2KrtBVV7SPw7Wi+DngaeMQY87yTgUVDax85x93QxJmPLQxoy8sWmlpTdzJh7q3j+Y9ZKwJ6BMUFOXz+wOSIj33onTXMXL7Nd336OUN5ZMooR+JUymnhah9FPGRHRPJE5J+A2cCtwAzg7diGqJJNcEIAUjohuMQzn/PZ/Rcy7eyhCJDngoNH2phXuSPsY6vr6gMSAsDMz7ZRXVfvYMRKJUak2kevAZ8CY4EfG2POMsY8aowJ/79IpYwXl2zm4ueW8uKSzb6222avSGBEzrjh7BIK8/NwNzTx1qpaDNDUTlQnyFVu7zgJHa5dqVQWaU7hX4BDeE5d+4GIb55ZAGOMOcbB2FQMhCunfcqDf6HR+va/YVc9v1i0mQ2PXcLiTfsSEapjBuTn8OjU0UDXlgSPKenbqXalUlmkfQpRn+Gskk+4ndMvLtnsSwheja2GF5ds5vwRRcxf27HOUSrqmS387cGjcwZdWRJcWlzA9HOGMvOzwDkFnWxW6Ug/9NOU/87p+qbWDsMk71Ttsn3cO1W7bMtDp6rGVsPsT2t817ta0fSRKaNYeMdEfnb1aBbeMVEnmVXaiuqQHZV6Ig2TTB09iA27Ok6UTh09CPCcLvadmSvjFm935QAtIW6bW7Ur4JS4ri4JLi0u0N6BSnuO9RRE5FUR2SMia/3ajhWRD0Vks/Wzn9UuIjJDRKpFpEpExjoVV7p69oMNnPv0Ep79YAMQeZjklvPK6JkduBexZ7awdscBTn3ofR59d318Ao+BH04q5fVbxoW8fYqV6PxpRVOl7Dk5fPQ74FtBbfcCi4wxZcAi6zrAxXjOfi4DbgZ+42Bcaafsvvd4bskWtroP89ySLZTd915UwyQbHruE+y4awSmDCrjvohE0thrmr93DoeZ2tn6ZOieovbB0C8P75zOhtLDDbX16ZIU8S1op1ZFjw0fGmKUiMiyoeQpwrnX5NeAj4B6rfabx7KRbLiJ9RWSQMcZ+4Fv52BWnazGe9jsuOiXiMMkt55Vxy3llKb0M1TssNuumcVTUuHl+cTV7vmrkhrOP14SgVCfFe06h2PtBb4zZJSIDrPbBeGosedVabR2SgojcjKc3wdChQ52NNgWEKk43t2o3d1x0SlR1e9wNTXz4xV4nwosL/2Gx8uGFvPadjj0GpVR0kmX1kV2hPdvts8aYl4wx5caY8v79+zscVvKbMnpgp9qDza3cwfgnF3MkhXYrZ7sgL1vPQ1bKCfHuKdR5h4VEZBDgXQxfC/hXIBsC7IxzbCnpjotO4dcfbQkYQsoRT3sk/stWU8kz14xJiYKCSqWiePcU5gE3WpdvBOb6tU+3ViGNAw7qfEL0Nv/0Um4/7wSGFfbi9vNOYPNPL+1wn9mf1vDtFz4NWLPvXbaaSlY+eAFXjBmsq4eUckjUVVI7/YtFXsczqVwE1AH/A7wDvAkMBbYB3zbGfCme+hm/xLNa6TDwb8aYiOVPtUpqdE5/+K8cPNLmu96nRxarH/6WbSXUZDV++LH8/pZzqKhxs3TzPiaWFVE+XOcOlOqKcFVSnVx9dF2ImybZ3NfgqcCqYuzBt1cHJATwVAad/WlNyqzM6ZHjYsYNY5n28nKWVbsBmLG4mgmlhcy6KfT+BKVU5+mO5jRUXVfPK8u28PqK2pD3mVu1i/+el9wb1LIEcrI9E8k1ext8CcHr42o3FTVu7TEoFUOaFNLMLTMr+GB95NPRVmzdH4douuft7433TSQ/s2Cj7X2Wbt6nSUGpGEqtWUYV1j/9allUCSEVzLh2TMBE8sSyItv7hWpXSnWNJoU0UVHjZtX2g4kOI2aCD74pH17YoYzFhNJC7SUoFWM6fJQm3qlMr20ddgffeMtY6OojpZyjSSFF+Z+o9tzCTcz+fFvkB6WQUAfflA/X3oFSTtKkkIL8T1RrbmunqTW1diTbyckSXAK5WVm+U+J0Y5pS8adJIcX4l6bwP0An1WS7IMvlIjfr6FGhWrpCqcTTpJBiaitAQbkAABIiSURBVPc3kiV29QOTX06W0CM7K2wS0GSgVGJpUkgxa3cc5FBzW+Q7JqGhx/bkmWvO0CSgVBLTJakpxN3QxKPvJfcu5HD+sfcw++qPaCJQKolpUkghqVjVNNiCNNlcp1S6Su1PmAwzpF9PWtpTd3IZYPLI4kSHoJQKQ5NCEnM3NLF6+wHfzt7C/DwuSuEP1ZOKezNpZHQnwimlEkMnmpOU/14E72qdZdX7mLs6+c8eEjzfNvynw3OzhD9895wERaSUipb2FJKQ/16E+qZWjrS0c9efVvNmRehS2Mli8slFvHPreHrlBX7fyMvOonZ/Y4KiSj3BvUSl4kV7Cg7zL0cR7aob74Sy/+Y0z+F0zpySFyt9emTx0r+ejbuhqcPcR6iyFaoju17iFWMGJzoslSG0p+CguZU7GP/kYqa9/Dnjn1zMvModUT3ObkK5PcknmHNcsPrhbwGeuY+nrhpNjxwXBXnZ9MhxadmKKNn1EoMrxirlJO0pOMSuHMXdc6oYX1oU8cPR+6H6ozcr8ZU1EuGk4l5srDvkcORdU9grJ+D6FWMGa9mKLrDrJdpVjFXKKZoUHNKd/9zuhib69soly+Wi1eohtLSZpE0IAPU2u6wL8/P0g6yT7HqJOvSm4kmTgkO6+p/bO57sQlKq+umh5tSJNZl5e4l3B80paHJV8aJJwSFd+c/tP+SUim6bvYLnp52V6DBSng69qUTSpOCgzv7nthtyAuiZk0VjS/IXwVu8aV+iQ0gbOvSmEkVXHzmsMD8v4AB6f9V19bxVsZ3qunrAfsgpL1v4/nknxiXWcE4Z0Iveua6w/2DOH1EUt3iUUs7QpJAgD72zhgueXcpdb1VxwbNLufutStulnHdeeBKvflKT6HA568Qi1j1yMZeeNiDkfXToSKnUJ8Yk94aocMrLy01FRUWiw+i06rp6Lnh2aYf2+y8+mavOHMK6nQcBYc7K7UlV1mLhHRMpLS5g2L3vdbht6xOXJiAipVRXiMhKY0y53W06p5AAob75P/nXL3h6wUbysl00NrfRlmT5unL7AUqLC9j6xKXcNnsFizft4/wRRdpDUCqNJCQpiMhWoB5PzbRWY0y5iBwLvAEMA7YC1xhj9iciPie5G5qYs8p+Z3ObgbY2Q0tbck4qjynp67usiUCp9JTIOYXzjDFj/Low9wKLjDFlwCLretqp3d9IblbyT+UM6dsj4Po15YMpLS5IUDRKqXhJpk+nKcBr1uXXgKkJjMUxQ/r1pLkt+fch7Ks/QpZAlkvonZvFvNW7oq7dpJRKXYlKCgZYICIrReRmq63YGLMLwPppu8xFRG4WkQoRqdi7d2+cwu284NLH3usAZ5T0SWRoUTnSZg1ntRsONbdpYTalMkSiJprHG2N2isgA4EMR+SLaBxpjXgJeAs/qI6cC7I7g0sfXlA/hzYpaclwumtvaaEmyGeTcLDh98DH06d2DZZv2cCTElIYWZlMq/SUkKRhjdlo/94jIn4GvAXUiMsgYs0tEBgF7EhFbd9lVR5352TaADjuVk0VzG7ww/WsAjH9yMYQY3tLCbEqlv7gPH4lIbxEp8F4GJgNrgXnAjdbdbgTmxju2WPCWqkg13h6A/+a5bBfkZImeiaBUBklET6EY+LPnJDGygT8YY/4qIiuAN0XkO8A24NsJiK3bhvTrSWNLa6LDsDUwP4fdDS22t3l7AMH1mgAtzKZUBol7UjDGbAFOt2l3A5PiHU+0ojlW093QxLqdX3U4OjPLJWBMwjaj9emR5TsVzW438oxrxwS8puBibJoMlMocuqM5CtGcmeu9jxg6TiQnMCGcUNSLxXed57vu3Y28aOM+xpb05bnrx+qHvlLKR5NCBNEcqxnpHIRELjbasu8wFTVuyocX+tq6shs5mp6SUir1aVKIIJpjNWv3N9KcxAfjLN28LyApdFY0PSWlVHpIvWUycWZ3xkFzWxsHG5t9G7laWtuSYrHp7eedYNs+sazr5xz494Lqm1p1E5tSaU6TQgR2yzTbDdz6+78z/snFzKvcwVb34USHCUDF1gNMKA3sEUwoLexWL8Fuia23p6SUSj86fBQF7zLNdTu/4rszK2hqbaelzbPs9O45Vcz+968lOEKPyh0HWPfIxVTUuFm6eR8Ty4q6lRDAvqekm9iUSl/aU4hSYX4efXrmdKhwmuNycbilDZc4H0Okp/Aeh1k+vJAfTT6p2wkBOvaUdBObUulNewpRcjc0cbCxpUOFU8+3aKF3bjb1Tc5uWvNufwi1mMmpMw6CN7RpQlAqfWlSiIL/6pu29nZysoQe2Vm+lTinHndMXHYxt9tkg965rricfha8oU0plZ40KURgt08hLxt+dcMZnHpcHwrz83A3NHXYxRwPBXnZzL7pbE73OxFNKaW6Q5NCBHb7FHKzsujTM5f9h5qZv3onFVu/TEg5bJ3wVUrFmiaFCOxW3zS1tvLYe+tZsdWZI6RzssQ2ycy4dgx3B20i0yEdpVQsaVKIwLv6xvth3NDUSnMbjiWEbBe8/4MJlBYXcNvsFSzetC9gzkAnfJVSThJjkusUsM4oLy83FRUVcXkud0MTn/3Dzfdf/7ujz/P41NO4YdzxvucMlQC0FpFSqqtEZKUxptzuNu0pRKkwP48jLSHOqYyR//zmCb6EMLdyB3e/VUWWS2hrNzx99dF6Q6lUi0iTl1KpRZNCJwwr7OXY784WuGmCp3aRu6GJu/60OmBe4c4/rWZ8qWdzWqSqrckilZKXUsojI5NCuG+v1XX1VG4/wJiSvpQWF/iuf3momWcWbiJLOpbCzsKzGLU7RfGe+eejB92s23mww0RzS5th3c6D9OmZG7Fqa7RiWQ4jWDQlx5VSySfjkkK4b68PvbOGmcu3+e57UnFvNtYdivg724i+XsidF47g+rOHsmDdbtbtPMipx/Vh8qkDgz4o7QtafPYPNzdNOCEmtYimvbycZdVuAGYsrmZCaSGzbhrXqd8RTjQlx5VSySejah+FKwNdXVcfkBCAqBKCVzS9hLxsF9efPZTC/DyuO/t4HrtyNNedfXyHD8lTjzuGLJu88OonWwG6XYuoosbtSwheH1e7qahxh3hE52khPaVSU0b1FMJ9e91cV+/48z902cioPrwL8/P44QUj+PmHmwLac7M8sXa3FtHSzftCtsdqGCl4Ka/uq1AqNWRUUgj37bV3bpajz907L4vTBveJ+v7Xnz2UXy6ppqn1aLz+37S7U4toYlkRMxZX27bHkhbSUyr1ZNTwUbgy0KXFBUw/Z2jA/Uv6xe5DrK3d0Ds3i9XbD0R1allhfh5PX+1Myery4YUxP4wnlML8PE4v6asJQakUkZGb16JdfTRv9U7bb9TRcAG5OS7f0Mk1Zw7hzZW1nV6e6eQ6fydXHymlkle4zWsZmRSiVVHj5uoXl3f58Y9dMZJRJf3onZvFZb9cxpGWo0NBPXJcfHLP+foNWikVd+GSQkYNH3WW3TCLv0gnoX20eR+nl/TlUHObnnOslEoJGTXR3BWzbhoXMMzSt1eub3hp/a6v+NGblbSGWI962aiBgC7PVEqlDk0KUSgfHjgJW1pc4Ps5vrSIdTu/4vbXV7K/8WhtpEHH5DJ1bAmgyzOVUqkj6eYURORbwHN4qke8bIx5ItR941klNRrvrNrOu2t2c9mogb6E4E+LwymlkkHKTDSLSBawCbgQqAVWANcZY9bb3T/ZkoJSSqWCVJpo/hpQbYzZYoxpBv4ITElwTEoplTGSLSkMBrb7Xa+12nxE5GYRqRCRir1798Y1OKWUSnfJlhTsVnkGjG8ZY14yxpQbY8r79+8fp7CUUiozJFtSqAX8Z2iHADsTFItSSmWcZEsKK4AyERkuIrnAtcC8BMeklFIZI6lWHwGIyCXAL/AsSX3VGPN4mPvuBf6vE7++CLCvG5060uE1QHq8jnR4DaCvI5nE6zUcb4yxHX9PuqTgJBGpCLUMK1Wkw2uA9Hgd6fAaQF9HMkmG15Bsw0dKKaUSSJOCUkopn0xLCi8lOoAYSIfXAOnxOtLhNYC+jmSS8NeQUXMKSimlwsu0noJSSqkwNCkopZTyyYikICLfEpGNIlItIvcmOp7OEJGtIrJGRCpFpMJqO1ZEPhSRzdbPfomOM5iIvCoie0RkrV+bbdziMcN6f6pEZGziIj8qxGt4WER2WO9HpbWvxnvbfdZr2CgiFyUm6kAiUiIiS0Rkg4isE5HbrfZUey9CvY5Uez96iMjfRGS19Tp+bLUPF5HPrffjDWvzLiKSZ12vtm4f5niQxpi0/oNnE9w/gBOAXGA1MDLRcXUi/q1AUVDbU8C91uV7gScTHadN3BOBscDaSHEDlwDv46l9NQ74PNHxh3kNDwN32dx3pPVvKw8Ybv2by0qC1zAIGGtdLsBTmn5kCr4XoV5Hqr0fAuRbl3OAz62/5zeBa632F4D/tC5/D3jBunwt8IbTMWZCTyEdy3FPAV6zLr8GTE1gLLaMMUuBL4OaQ8U9BZhpPJYDfUVkUHwiDS3EawhlCvBHY0yTMaYGqMbzby+hjDG7jDGrrMv1wAY8lYdT7b0I9TpCSdb3wxhjGqyrOdYfA5wPvGW1B78f3vfpLWCSiEQ6Hr5bMiEpRCzHneQMsEBEVorIzVZbsTFmF3j+swADEhZd54SKO9Xeo+9bQyuv+g3dJf1rsIYezsDz7TRl34ug1wEp9n6ISJaIVAJ7gA/x9GIOGGNarbv4x+p7HdbtB4FCHJQJSSFiOe4kN94YMxa4GLhVRCYmOiAHpNJ79BvgRGAMsAv4udWe1K9BRPKBOcAPjTFfhburTVsyv46Uez+MMW3GmDF4qkB/DTjF7m7Wz7i/jkxICildjtsYs9P6uQf4M55/RHXeLr31c0/iIuyUUHGnzHtkjKmz/lO3A7/l6JBE0r4GEcnB80H6e2PM21Zzyr0Xdq8jFd8PL2PMAeAjPHMKfUUk27rJP1bf67Bu70P0Q5pdkglJIWXLcYtIbxEp8F4GJgNr8cR/o3W3G4G5iYmw00LFPQ+Ybq18GQcc9A5tJJug8fUr8bwf4HkN11qrRYYDZcDf4h1fMGv8+RVggzHmGb+bUuq9CPU6UvD96C8ifa3LPYEL8MyPLAGutu4W/H5436ergcXGmnV2TKJn4+PxB8+Kik14xu4eSHQ8nYj7BDwrKFYD67yx4xlTXARstn4em+hYbWJ/HU93vgXPt53vhIobTxf5V9b7swYoT3T8YV7DLCvGKjz/YQf53f8B6zVsBC5OdPxWTN/AM9xQBVRafy5Jwfci1OtItfdjNPB3K961wENW+wl4klY18Ccgz2rvYV2vtm4/wekYtcyFUkopn0wYPlJKKRUlTQpKKaV8NCkopZTy0aSglFLKR5OCUkopH00KKmOJiBGRWX7Xs0Vkr4i8a13/V+t6pd+fkX73v0NEjohIH7+2c63fe7lf27sicq7fc/zEqobp/Z0P+N23zWpbLSKrROTrIjLK775fikiNdXmhw39FKgNlR76LUmnrEHCaiPQ0xjQCFwI7gu7zhjHm+yEefx2ezZFXAr/za6/Fs0Z+vs1jHgMGAqOMMUeszYl3+t3eaDwlELDKPf/UGPNNPGUcEJHfAe8aY95CKQdoT0FluveBS63L1+HZsBaRiJwI5AMPWo/ztxo4KCIXBj2mF/Bd4DZjzBHwVPw0xjwc4mmOAfZHE49SsaJJQWW6P+Iph9ADz27Tz4Nu/+eg4aOeVrs3gXwMnCQiwZVqH8OTMPyVAtuMp/RzKD2t5/kCeBl4tAuvSaku06SgMpoxpgoYhudD/i82d3nDGDPG70+j1X4tnnr97cDbwLeDfu/HACIyIdRzi8i/WQlgu4h4i7c1Ws9zMvAtYKbT9fOV8qdJQSlPzZyfEf3Q0Wg8BdY+FJGteBJE8BASwON45ha8qoGh3iKHxpj/Z80fHMRzQmAAY8xnQBHQP+pXolQ3aVJQCl4FHjHGrIny/tcBDxtjhll/jgMGi8jx/ncyxiwA+gGnW9cP46n0+UtruAoRycJzTGwHInIynmTh7sJrUqpLdPWRynjGmFrguRA3/7OIfMPv+vfw9AwuDrrfn6324DmJxwksbf4AnnmCtSJSDzTiOW7RWz+/p3UqF3gqlt5ojGnrxMtRqlu0SqpSSikfHT5SSinlo0lBKaWUjyYFpZRSPpoUlFJK+WhSUEop5aNJQSmllI8mBaWUUj7/H10IaLKm9pBRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_selected_features.plot.scatter(x='MEANGBT',y='MEANGBZ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aha, tightly correlated, therefore I must drop one of them. Looking back at their histograms, both look like normal distributions to me, neither is skewed. So I guess it is okay to drop either parameter. I just drop `MEANGBZ`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['TOTUSJH', 'TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'ABSNJZH', 'SAVNCPP', 'USFLUX', 'TOTFZ', 'EPSZ', 'MEANSHR', 'MEANGAM', 'MEANGBT', 'MEANGBH', 'MEANJZD', 'R_VALUE']\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "relevant_features_0.remove('MEANGBZ')\n",
    "print(relevant_features_0)\n",
    "print('MEANGBZ' in relevant_features_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlated Features IV\n",
    "`R_VALUE` and `MEANGBZ` should be related, according to their definitions (see below). I have already dropped `MEANGBZ` since it highly correlated with `MEANGBT`. So I shall check whether `R_VALUE` correlates with `MEANGBT` to decide whether I shall further drop `R_VALUE`.\n",
    "\n",
    "To remind you, `R_VALUE` is the absolute value of flux ($\\Sigma |B_{LoS}|dA$, where $LoS$ means line of separation) in the area along the polarity inversion line. The polarity inversion line is a line that separates areas with $B_z>0$ and $B_z<0$. For a large `R_VALUE`, it means the sign of $B_z$ must either change many times or change abruptly. Both cases shall lead to a large `MEANGBZ`, the mean horizontal gradient of $B_z$, i.e. ${1\\over N}\\Sigma |{\\partial B_z\\over\\partial h}|$, where $h$ means the horizontal direction. The Fischer ranking score of `R_VALUE` is 0.58 while that of `MEANGBZ` is 0.16. However, the histogram shape of `R_VALUE` is strange, which may make this parameter harder to standardize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['R_VALUE','MEANGBT'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R_VALUE</th>\n",
       "      <th>MEANGBT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>R_VALUE</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.547618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANGBT</td>\n",
       "      <td>-0.547618</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          R_VALUE   MEANGBT\n",
       "R_VALUE  1.000000 -0.547618\n",
       "MEANGBT -0.547618  1.000000"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_selected_features.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting, I expect that `R_VALUE` should be positively correlated with `MEANGBT`. However, they are anti-correlated. Let us look into their scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11b959cc0>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OP0umvguPSK/Dv7Mz9Ji+yEwxXXj1E/asXGvdAYxTSvUC/qaUGq21rvG7fRGwCDyLhnQznqS2YOb5zB5fFraHyYPLt7HtM+k3Ljwi/aO4ekSJpXGI1BTJhddnMX6dKSDicQWt9VGl1HvAtUBNmN3T1tDSopANqowu0AoRiQ2fOO0OQSShSM7kQ63HF3KtPqVUX6DNm+B7AFcBj0YRX8aRi67CTFFeNm1uN9rtxmWwLnj9l62Uzatg38JpiQ9OJK3uzHjNB2aE+fEzgT8qpbLwjP+/rLV+LeooM4hcdBVGSgqyef57lzCgdw/mL68OWVN/z0sfSkml6BTVhVfvRdSpSqnFwKfAzaH211pXa60v0FqP0VqP1lov6E6wyc7Z7GLrgaM4m10x38fQ0iKGlfSMY1QiHUwc3pfZv93IIxXbw7Y4eOWfsmSkOEVpHf6yjlJqInALMA34AJgADNFan4hnMOXl5bqyMuQIUNJaUVXPfcuqyXE4aHO7AzoLRsPZ7KL8oXczs85URGzfwmmUL3iTwycMxm389hGZQSm1RWtdbnRb2DN5pVQdsBBYD4zUWt8AtMQ7wacyZ7OL+5ZVc7LNTZOrPaCzYLTqjrQQweRHkeHK5lWETPDgaVssRCTDNcuA/niGZmYopQrI0AlNZuqOtJDjCPxV5jgc1B2JvofbgN490Kq70xeEgNW7DtsdgkgCkbQ1uAsoA34JTAJ2AX2VUjcppQqtDS81DOjdgzZ34Jp9vpWBorWu9jAdbln/T3Tf5OF97A5BJIGIThm97QlWa61vw5PwbwG+BuyzLrTUUVyYx2M3jCE/x0FRXnbnaj/RLuvmG/aRNV5FPEgPegGRTYa6B3hJa30AQGvdBqwEVnpr3wVw/bj+TBjah7ojLTGv21l3pIVshzSTF/FRNq+CGbLgSMaL5Ey+P/APpdRapdR/KKU6PwPKwiGBigvzGDuwV8wLM9fUH6PZaJaLEDGSBUdEJGPyc4FBwE+BMUC1UuoNpdRspZR00YoTZ7OLBa9ttzsMkaa+suAtu0MQNolmTP7vWuv/AAbiWdd1LtBgZXCZpO5IC1lSVSMs4jzRTuXe8L1tHnhlK1/5+ds88MrWBEQlEiHaGa/nAwuAXwOtwI+tCCoTDejdgw4tV1yFddbuDl1SWTavgiUf1OE83saSD+pkmCdNRDIZaphS6qdKqR3AX4ATwBSt9SVa66csjzBDFBfm8fiNY8mWk3lhkWdX13aZIDVnyWaG/biCoSYJXc7oU18kKeUtIB+4WWt9vtb6Ya31HovjykjXj+vPph9fxbWjSu0ORaQhTeCF2LJ5FaysaaTNDe0mP/PGdhmRTXWRdKEcEskdKaU2aK0v7X5ImW1d7WFW7ZQ/LGGt8gVvRrTfVDnhSHnxHBzIj+N9ZSTfZKg2GZoXFgvX98bnoW+MtTgSYbV4JnnpZ9MNzmYXaz5qlMlQwnY9cxSzLh4gXSzTRHfXeBVx4GtTnKUUx1tlMpSwz+n5WWydf63dYYg4imeSl1PQGPi3KRbCbsdOyklGuol5uMa7StR3/Db9axziyThGbYqFsJOUTaaXSOrkT1NK3a+U+pVSaorymAPsAW7y7ae1rrEy0FQWallAozbFQthJyibTSyTDNX8CjgAbgFuBHwG5wEytdZWFsaWFcMsC+toU/9eL8qsUyUHKJtNLJOMEQ7TW39NaPwd8GygHpkuCDy/SZQGvH9efywb3silKIQKd1+80u0MQcRRJkm/zfaG17gD2aq2brAspfUSzLOBfvj8hUWEJEdIT73xsdwgijiJJ8mOVUl96/zUBY3xfK6W+tDrAVBbtsoD7Fk7jiqFnJCI0IUwdbemIqDlZqGtNInlE0k8+S2t9mvdfkdY62+9r+VwXQizLAg4rlRb9IjkEJ3r/pL6iqp4Jj65m1gubmPDoal6tqrcpShGOTIayWLTLAr5WczBBkQkR3gOvbOWhb4wNKCBo7ejAraGtQ3MSzyfVe5dVM2Fon5hXRRPWkQJtC/nOfICwywL69r3y3L6JCk+IsN7Y3tClgMDVrmnrCOxiYnatSdjP0jN5pdRAYDHQD3ADi7TWT1v5mMkiXOlkqH2FSBZTR5V2FhD4ztqNhLrWJOxl9Zl8O/BDrfUIYDxwh1JqpMWPabtISyfN9s2TlUNEknjoG2MNCwiyHZCXHfm1JmEfS8/ktdafA597v25SSu0E+gM7rHxcuxmd+fg+zgb/IRjtm5vl4PJhfXh3Z2PCYhZixugSTu+ZyxvbG5g6qrSzzbCvgODeoE+m0VxrEvZJ2IVXpVQZcAGwKWj77cDtAIMGDUpUOJaKpnTSbN9HbxjDsi11/OKNjyyNVQiAHtmKZ2ddBMBD3+h6u1kBgST35JeQcQGlVCGwDPiB1jqgtl5rvUhrXa61Lu/bNz0uOkZTOllcmMdN5QMCtt1UPoDiwjxu/+o5zLp4QJefESLeWto1z63ZHXKf+curueX5DcxfXp2gqEQ8KK2tXetDKZUDvAa8pbX+Zah9y8vLdWVlpaXxJJKz2RX242zlXiffen4j7X4n8/k5DtbfN5mn393F4o37ExStyHQjzizijbsm8uRbO1lRfZCZY/ox95oRQNeaeUAWFUkiSqktWutyo9usrq5RwG+BneESfKozSujFhXkhP84+uHybYRLPcTjY8IlTErxIqK+NOZNh91fQ5j3ve3rNHp5es4cZo0sM95+zZDMAq3cdZvLwPp3DPSK5WD0mPwFPn/ltSilfQ7Mfa61ft/hxEyqackmf2oYm0yTe5nZzWKaKiwSrqT/ameD9rawxLgDw376yppGV8yrk7D4JWTomr7Vep7VWWusxWutx3n9pleAjLZf0nxLubHbx6tbPDO8v2wGP3TCGLfu+SET4QnQyS+bR8J3di+QhbQ26KVS5pO/2mvpj/LxiBzkOByda20FBrsmC3S/eNp7BfQulv7xISa/XNPJshPvOWbJZhnoSQJJ8hMwuopqVQNbUH+PmRRsCFufufCPQ0OI2vuD9cUMz734k9fEiudw24WwOHmvpTMpgfObfgecibbhhG/8LuTLUYy1J8hEINebuK4FcvOHU+Pr1Y8/i5xU7Ylqc+6crajDJ/0LYwgH8ZMboLttXhmhHPGfJZtOzc7MhnVA/I2In8+fDCDfm7mx28XJlXcDP/O3DOrJNhmPCkQQvks03LjjTcHtWiJf46l2Ho74t1M+I2EmSDyPc6k5Gt7e5ocU7RCNEKgiVsN8xaK9R29BER4gTEt+QTjS3hfoZETtJ8mGEa1EwoHcPWju6JnSHQ5Gbpcjx/vXkZTvIdiiyFBTkZZGb7eDhr4/m4a+NJjdLUZCbRW6W9ccjhJHrRhnXwgNcPaLrbVXeFtpmQg27mN0mQzXWkCQfRrgWBcWFedw5aViXn8tyKNz6VN9tV7ubdrcmO8vB/37nK2yYN5nvXHI23xl/Nhvuv5K/3DaeF757EdmxjfIIEbNcQifYpf/8nFueWx+wbdxA44Xn+xbksPT748M+5r6F05gxuoSCXAczRpfIRVcLWd7WIBrJ3NYgVIsCZ7OLyxauxtUe/kJrUV42S269hLF+fyS1DU1UHThKWXFPZv3ugy4XbItyHTS1Sp95Yb8Zo0s6K2x6F+UHFBz4G9irB0/ePJbywcVh77Nyr5O1uw8zcVifiPYXXYVqayBJPk5erarvbMXq6nCjtMZlMGjp60vje6MIbm1w+dBiNn96BKU1rR2aOycNZfZlZXzloXcTdixCxMvlQ4v5063mZ/azXtjIulpnxPsLY7b1rkkVkTQSC+Y7+x43sBdDS4sCWrEW5GYx/VfrCL4ylZcdONRj1Nrg/VonS78/nhNtbkDTMyeLX7y+My7HKUSivV/rpHKv0/AMvXKvMyDBh9tfxCbjk3wsfWeCz75nXzqIBTPPD2hI5r/IQmtHB3dOGsYtlwwKeBMxu3j1yj/reeWf9XS4u66lKUSkZowuod/pPXit5iDTR/fjg31H2Fr/ZfgfjLO1uw8bJu21u41LJs32F7HJ6CTvXwMfyarzzmaXYXfIxRv2M3t8GUNLizq3mS2y4M/s4tWyD+sjGt8XIpRLhvRh1mWDOycyTXpslS1xTBxmXBo5cVgfnlldG/H+IjYZXV0Trgbe34qqeiY8upofvrzV8L5+v35fl23FhXmMHdjLdAhoaGkRsy8NXA3ruvNLyc3K6KdFxGhQr8DX2QOv7mDs/DcBTxuBvV+ctPTx+xbmUFKQG7Dt8qHFpmfl5YOLuXxoccT7i9hk9Jl8pMv0+Z/xm/nrlv3cPWV41MuhLZh5PrPHl3WO7/cuyOWyhaujug+RmRwKCnKzO4cZvzzRygOvBi6ffOxkB9Ofes/yWJZ+f3xnco6mWuZPt46X6hqLZXSSN1ugOJLFtoPlZWcbLtQdiaGlRQFDPXdOGsr/vLMr6vsRmcWtYcmtl3QOB37zN/8w3G/7weNh76tPzywOn4hslnZBroPJw/uYdpAsHxzd2Xi0+4voZHSSh8jGzo3O+IOZLdQdLJJKnlsuGcQv39mFXHIV4bzw992dSXb3QeML+aP6FVBjkOgHn5HPjHEDOs+gjZb4M3LCO2dj+4KpIfcLrkAT9pA6+Qj518G3ud3cVD6AlyvroqrK8a/kae1wc+ekoV0qbnwefm0Hz6/ba9XhiDRRkOtg+4Kppgn69Pwsts6/NuI1Wsc/9DYHm9sifnyzmapmFWjCGjIZKk6Cz8LDzYIN3nfCo6u7jOvnZSsev3Gs4RvEVf+zhtpDJyw9JpHaZowuYWvdMfYfNV4uclCvPNbOuwqIfJEOozcEBxgOVs4YXdLlvmobmrjqybVd9n137kQ5o7eITIaKk+CFuc0W6g6uvf/p9JHkZTkM2w+72nWXsk3fx9zfzCrnU+dx/n3xFusOSqS0Z2ddFHKYZf9RV+ciHpE2ANu3cFqXN4RRD77BcYPWGkbtgc3mf1QdOCpJ3gaS5MOIdjasUe39T/5WQ88ch3cWa1e+ss3iwrwuH3MvLjOupRcCYNj9FQzqlWd6Ju/zwCtbeegbYyO+3/lfG8Ot3tc9eNoAG60EZdQe2Gz+h9l2YS0pyA7BVxs/64VNTHh0Na9W1Yf9GaPae8A0wcOpi7ZGbQ4+2Be6pavIbG0avn5B6GtBAG9sb4j4Po1e99G0Bzaa/zH70kEpcxbvbHax9cDRzoWBUp0keRPhVoTy38//BRGuEqcgN4vvXDyIvGzVpXVxuB7dIjP52vKaWVF9kH0Lp3WZDOVv6qjSiB4r1Os+mvbAC2aez7tzJ/LEjWN4d+7ElLnoGsuJXbKT4RoTRrXx/sMqYN73xld7n+VQHHcF1h53aM3dU4Zz95ThXYaB5OOsCOZLpM/Ouoghb+3k6TV7uuwzc0w/wHNGv6L6IPucXS/WRzpUE+51H83CHsHzP5JdtG1OUoUkeRPhZsOGekH4197X1B/j5xU7DCdbBb9wfB9zzXp0i/SSmwXXjChh874jhmWLlw32vOn7LsTPGDeA//feHtr8CuJyFMy9ZgTD7q8I2A5QXJDD1FGlUY3FRzoLPB1FcmKXiiTJmwg3GzbcC8L3b+zAXlw7ul/EF2+D2xws3rgvIOmP7FfAjghmMIrklq1g18PTQlbG/GPvUS79xTt8/mVr57YJQ4oZ3KcH6z75gplj+jH3mhE8+dbOLgkeYNbFA5l7zYio4op0Fng6Stc3OEvr5JVSvwOmA41a69Hh9k/GOnmj6prKvU7e3N7A4g2f0tpx6kURvCBIvATPHIx0ZqJIblcMPYP3ar+I6Wf9Jxdd8fgawyGasuKevPejSTHdfyxrLKSD4EmPkUxyTAZ21sn/AfgVsNjix7FMcC188Eo2wU2iYvmDCPcHFTy2OWN0iWE5m0gtsSZ4CGxvPXNMv5Bj9bEwmwOS7iJpc5JqLK2u0VqvBWJ/JScZo5Vs3Bp+ct15rL9vckzv+LFczZdV7QWcmnQ095oR5ATNs/ON1YvohWsRnmpsL6FUSt2ulKpUSlUeOnTI7nBCMlvJ5rNjJ6N6QfjKLmsbmrqUq92ztJrahqaQPz9xoT2LP4jEO/O0XNPb/Kuxdj8yjbsmDaGsuCd3TRrC7kfMyxtFZrH9wqvWehGwCDxj8jaHE6J4gS4AABPMSURBVFI8VrLxL7v0Lfjtr7XdzXXPvM8T3zTuZ1Pb0MT+o9Yu/iASx1f/7mshcNfV5/HbdXvY5zzBzeUD+NqFA6ltaOJnK7azfs+pT5FGk4vmXjNCzt5FF7Yn+VTiW8nm/aDV5Xv1zGVp5YGwLVVrG5r40dJqWtvdIXvTt3Z07WfjM/flD7t/IMJSCiJuEx089Pbg8m383+Y6ADbs+YIPDxxlwczz+fPt46V1r4iJJHkvsz+g4IuiwSvZvLr1s4COe2YtVVdU1fOjv26lNWhh7vwcB+1uTXvQdrP63NoG6UqZ7MIleAcwzaR7Y6j1g1NtcpFIDpYmeaXU/wFXAH2UUnXAz7TWv7XyMWNh1vvabEarbyWbcH+UPr6JU8EJ3ufFWy/hlhc2BdxuVp87+qxCNu//sruHLGy0J6gdwD0vfcg7Oxs5p6TAcP9k6t4oS/WlHkuTvNb621befzyYJerrx5wVdopzpC1VzZYPzM329K0pH1zME98cG3YCypQn32NXg0yESmXB/V785zx8aPLmHe92F7EO+/iXDz+zupbLhxbzp1vHxzU2EX8ZP1yzrta4Ymbt7sNdEnOWUqz5qJFJ55VQXJgXcUvVgtwsXO2BPWxysxSvz/mXzj+ycPW5q3YclASfwowW17jnpfDXV+LdvTHWFZuMyoffr3VSudcpZ/RJzvYSSjutqKrnoYodhrdNHNanyxTn460dzF+5vbOePZKWqiuq6pn6zPsBQzE5WYqfXT+K460dAV0tQ9Xnvr0j8laxIvn4T16bs2Qzox58g+VVnxvuW5ibZUn3RrNPreFKdsG8fNhsu0geGXsm72x2ce/SatoNilxuKh9A+eDiU90kleJ4q+dMvNnbVdI3dBPcayZ4LP7epdW0BY3Fd3RoFqzcQW6W+dTp4Au+U0aW8lJlXZx/CyKR5izZHNFM5WtHlXBj+cC4P353VmyKR/lwomRqSwYzGZvk6460kGWwHF9etuI7l5wNnBpCWfNRI/NXbu9M8BBY/dK7IJdhpUX0LvBMXPG9yI61tBk+hhtwtbtxtXcd63c2u/jzpv38ek1tlzeBc0sL+FiGbFLW6xG2onji5gstefzurNhkVj6cbEM1ZsUSmSxjk/yA3j3ocBtXu/hXtRQX5jHpvBIeWFETsI+v+iX4RXXTVwbw8pY6chwOWjvctHeY18P7+N4w1tUe5t6lW3G1e+LyfxMYeeZpPHbjOPYeamLNx4dZsfWzWA9d2KQjzO0KWH7HBMse36iVdTRj/sHlw8mW4NO1H3x3ZWySLy7M4/Ebx/DDv27tHE7JdsDjN47t8oIwa78KdHlR+cY8fd/nZCmU1p3DQlkKHA4VMITT5nZTkJvFfcuqOxN8sOueeZ+87KzON5JsB4ZDTSJ5hWssl5fjiKmtbfCi26GEGl6MhK98OFn4D82kaz/47srYJA+nhmO2f3YMUIw66zTTF4NR9cvWA0cNSyP95Wdn8evvXOD9zvMY62sPd3nDON7aYXpfJ73rw7Z2tAN0uXgGkJcFrnCniiJh9i2cZph8Vxq0iS7Ki72LqX8J5sqaRlbOqwi5LB+k3opNZoI/Rf902si07AffXRmd5MFzlj5xuPn6mcH7+v8RhlvPFTwvslFnnR7wc0ZvGM5ml+F95WY5UGhcJhOpfCTBJ5eHV9YYnlUHJ//5XxsT80XCOUs2m25P906lRkMzP6/YwU+nj+TnrxmvxJapMj7Jd4fRMM5N5QN4ubIu7Iss+A0j+L5aOzq4c9Iwpo7ux/RfrYMwSV4kl9dqDvKTGYHr5Pgn9+0LpnZujzUJrd5lXL5otj0Rohk6imV/H7OhmdFnnc76+yZLdY0fS1eGilYyrgwVieCSre6UcBnd11827edXa3aTm5VFk6vdoqMQ8XTbhLMDkrzRal7hhlXCMSvJNJp4lQjRHmN3fifOZhcTHl3dOZQJ1q3MlgpCrQyV0ZOh4sU3iQlgq7cWOdZFB/zv65lVu7ls4SoWrd0DKG6fOIQp5yVfXbLo6vn1n3Z+PdhkuUaz4ZZImSXyRCf4OUs2MyTKY4x2ezDfJ9/8HAdFednk5zhkaMaEDNfESTzrc1dU1XPv0urOEkpXu+fs/dfv1bL+vsm8/dC7cYtbWGfOks1cMqSPaVfKeAyrmF3gTZRw6w1HO6QUze8kHZfqs4Ik+TiIZ32u775cBvWRvnIw/z/s461SR5msVu86zMHmNtPbJw+Pz6cyuy6yRnLWbXaMk4f3MRxqivZ3kqlr0UZDhmu6wbeM3/bPjpHjCPxV+hJytHwXlIz4l4M9O+si/nLbpRTlyft0spo8vA+b9x0xvT3VK2AiOeuOdkgp1X8nyUgyRIz8h2daOzoInjxrVp8b7qKsWVlmXrbqMuY4oHcPuRCbxPqdbl6f3d2LrsnA7GxcAdMjuPhr91BTppAkHwOj4ZlgZ5/RNYlHMm7ftZTSzZ2ThnLLJYO63N/i9Xvie2AiLkb3K+C1H1zBpY8YXzs583TP85jqCe7ZWRcZTu7aG8UbWCoed6qRJB8Ds0VA/H3ccDyg13Y04/aRXlBaUX0wTkck4iUbeO0HVwAwfXS/gCobn8+PuWKaqZps5izZTEGug6LcLJpaO1L2zSrdyZh8DCKZ6QqBvbaNxtpDjduH6i3vM3NMvwgjFlYZfEZ+wPft0FlO+FuDBB/K9KfeizkOX4/67pZlRqpsXgUraxo53urmYHMbx1vdkuCTlCT5GATX6OaY/Bb9e20bvTEEj9v7LuT6LyQSytxrRpDTtZOxSKC9X5zsss2NJ2FHW/dUc/A4Y+e/GXUM/gl3ZU1j2LLG7oq1xj3Rb0TCQ5J8jK4f15/1901mya2XsPHHV3H50MDOfMG9tkNN3nA2u7wTn1Yz64VNnStPmfF/M9j9yDSmnNeHbHkmk8r2g7H1/T92soMl/9gb8f5mCXP8Q2/H9PiRiKXGPdFvROIUaWsQR5H02g6urvFMfNrapcWw2RRt38Vb33RuB0R9xiisN7pfATUxJvpe+Q6q5k8NvyMw6sE3Qs6VsGKcP9p2CsnWfiEdSVuDBCkfXMzdU84N2W/bf6z91MSnrm+0vvH62oYmllYeoLahKeDirY8k+ORkluBnjC5hxugSCnIdFOYa/+zRk+6Iz3TDTR6yYmgk2hr3ZGyklkkkydso3MSnP2/6lKueXMs9S6u56sm1PLi8JiDBi9TiWzTEN2zR3Bp6/0gSdLgzYasS6b6F0zrfrGaMLgn5iSHUrFdhPUnyNjKf+OTg7quH83LQwt0VNVIymQqyTLZXRLjGq0+kCXrfwmn0K8wxvM3KRPrsrIvYvmBq2Dcamd1qL0nyRF/VEi/BF2PzshU/vHo4/5g3mTN6Gn+WH9gr33C7SB7XjTZehCbaz2DRJOiND0wx3J4siTSaM38RXxl/4TUZVnc3anVQ29DEVU+u7bLvu3MnGm4X9hvUK4+1864CwndnjEQs0/5TfRatiE2oC6+WJ3ml1LXA03g+xb6gtV5otm93krxZT5jahqaARYt9359sbWf1x4dY8/GhgFawDmD8kN60dmjKzujBqo8aaWl1c37/Ir5oaedIs4ssh4NmVxtuDVkOyHY46FuUT0tbB4ebXLS6Pf07sgFHFmQ5FCfakufNVAg79cp38OVJd8AnmxyguDCXxubWgO3n9OnJozeMAQhbuRYsksV7jCriurPoT6xW7TjI2zsamDKylCtHRj/J0bYkr5TKAnYBVwN1wGbg21rrHUb7x5rkzc7GH1y+LWDR63NLC/i4IbayNiFEcrh8aDF/unV8yH0i+YQ+64WNrKt1BtzvjeUDE/7JfsqT77HLLy+dW1rAW3OviOo+7CyhvBio1Vrv0Vq3Ai8CM+P5AP5lhU2udk62ubl3WTWVe50BCR6QBC9EGni/1knlXqfp7WY5wf+aW+VeZ0CC993vj/4a+ufibdWOgwEJHjx5atWO+BVZWJ3k+wMH/L6v827rpJS6XSlVqZSqPHToUNQPYNYTxr9vjBAivYT6+46kT5T5zweObMS6LkSk3t7RENX2WFid5I06qwT8FrXWi7TW5Vrr8r59+0b9AGY9Yfz7xggh0kuov+9I+kSZ/3xgyjJbFyJepowsjWp7LKxO8nXAQL/vBwCfxfMBzHrClA8uZvalgwL2Pbe0IJ4PLYSwQXBfqGCRLPJdPrjYsN/UE99M7OLgV47s1yUvnVtaENPFVzNWX3jNxnPh9UqgHs+F11u01tuN9k90dc26T5z07pnDOX0LcbW7OaMgl+OudtbVHqLZ1SHVNUJYQKprukrZ6hrvg18HPIWnhPJ3WuuHzfZN9QZlQghhh1BJ3vKVobTWrwOvW/04QgghupK2BkIIkcYkyQshRBqTJC+EEGlMkrwQQqSxpOpCqZQ6BESzxH0fIB2mtqbDcaTDMUB6HEc6HAOkx3Ek6hjO1lobziZNqiQfLaVUpVnZUCpJh+NIh2OA9DiOdDgGSI/jSIZjkOEaIYRIY5LkhRAijaV6kl9kdwBxkg7HkQ7HAOlxHOlwDJAex2H7MaT0mLwQQojQUv1MXgghRAiS5IUQIo2lbJJXSl2rlPpYKVWrlJpndzyRUkrtU0ptU0pVKaUqvdvOUEq9o5Ta7f2/t91xBlNK/U4p1aiUqvHbZhi38njG+9xUK6UutC/yU0yOYb5Sqt77fFR5u6b6brvfewwfK6WusSfqrpRSA5VSa5RSO5VS25VSd3m3p8zzEeIYUur5UErlK6U+UEpt9R7Hf3u3D1ZKbfI+Fy8ppXK92/O839d6by+zPEitdcr9w9O2+BNgCJALbAVG2h1XhLHvA/oEbXsMmOf9eh7wqN1xGsQ9EbgQqAkXN3Ad8AaetvrjgU12xx/iGOYD9xjsO9L7usoDBntfb1l2H4M3tjOBC71fF+FZs2FkKj0fIY4hpZ4P7++00Pt1DrDJ+zt+GfiWd/tvgP/wfv2fwG+8X38LeMnqGFP1TN7yBcITbCbwR+/XfwS+ZmMshrTWa4EvgjabxT0TWKw9NgK9lFJnJiZScybHYGYm8KLW2qW13gvU4nnd2U5r/bnW+kPv103ATjxrJ6fM8xHiGMwk5fPh/Z02e7/N8f7TwGRgqXd78HPhe46WAlcqpYyWSY2bVE3yYRcIT2IaeFsptUUpdbt3W6nW+nPwvPiBEtuii45Z3Kn2/NzpHcb4nd9QWUocg/fj/gV4ziBT8vkIOgZIsedDKZWllKoCGoF38HzKOKq1bvfu4h9r53F4bz8GRLbUVYxSNcmHXSA8iU3QWl8ITAXuUEpNtDsgC6TS8/O/wDnAOOBz4H+825P+GJRShcAy4Ada6y9D7WqwLSmOxeAYUu750Fp3aK3H4VnD+mJghNFu3v8TfhypmuQtXyDcKlrrz7z/NwJ/w/OiaPB9fPb+32hfhFExiztlnh+tdYP3j9QNPM+pIYCkPgalVA6e5PhnrfUr3s0p9XwYHUOqPh8AWuujwHt4xuR7ede4hsBYO4/De/vpRD6EGJNUTfKbgWHeK9i5eC5gvGpzTGEppQqUUkW+r4EpQA2e2L/r3e27wAp7IoyaWdyvArO9VR3jgWO+YYRkEzQ2/XU8zwd4juFb3mqIwcAw4INEx2fEO4b7W2Cn1vqXfjelzPNhdgyp9nwopfoqpXp5v+4BXIXn+sIa4EbvbsHPhe85uhFYrb1XYS1j99XpWP/hqRjYhWf86yd2xxNhzEPwVAhsBbb74sYzJrcK2O39/wy7YzWI/f/wfHxuw3M28u9mceP5SPpr73OzDSi3O/4Qx/Anb4zVeP4Az/Tb/yfeY/gYmGp3/H5x/Quej/jVQJX333Wp9HyEOIaUej6AMcA/vfHWAA96tw/B8yZUC/wVyPNuz/d+X+u9fYjVMUpbAyGESGOpOlwjhBAiApLkhRAijUmSF0KINCZJXggh0pgkeSGESGOS5EXaUEpppdSf/L7PVkodUkq95v3+e97vq/z+jfTbf65S6qRS6nS/bVd473eG37bXlFJX+D3GL7zdBn33+RO/fTu827YqpT5USl2mlDrfb98vlFJ7vV+/a/GvSGSg7PC7CJEyjgOjlVI9tNYtwNVAfdA+L2mt7zT5+W/jmWj3deAPftvr8NRorzT4mYeAfsD5WuuT3sluP/S7vUV7przjbY/7iNb6q3im7aOU+gPwmtZ6KUJYQM7kRbp5A5jm/frbeCZAhaWUOgcoBB7w/py/rcAxpdTVQT/TE7gNmKO1Pgmejopa6/kmD3MacCSSeISIF0nyIt28iGf6ez6e2Yibgm6/OWi4pod3u+8N4X3gXKVUcCfQh/C8AfgbCuzXnla5Znp4H+cj4AXg5zEckxAxkyQv0orWuhoow5O0XzfY5SWt9Ti/fy3e7d/C06/cDbwCfDPoft8HUEpdbvbYSql/8yb0A0opXzOtFu/jnAdcCyy2un+4EP4kyYt09CrwBJEP1YzB0/DqHaXUPjwJP3jIBuBhPGPzPrXAIF/TOa31773j78fwrF4WQGu9AegD9I34SIToJknyIh39Dligtd4W4f7fBuZrrcu8/84C+iulzvbfSWv9NtAbGOv9/gSeToq/8g4PoZTKwrMkZRdKqfPwJH9nDMckREykukakHa11HfC0yc03K6X+xe/7/8Rz5j41aL+/ebcHj+k/TGAr6J/gGWevUUo1AS14lnfz9Q/v4V01CDzdIL+rte6I4nCE6BbpQimEEGlMhmuEECKNSZIXQog0JkleCCHSmCR5IYRIY5LkhRAijUmSF0KINCZJXggh0tj/B06wvoqm3kzOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_selected_features.plot.scatter(x='MEANGBT',y='R_VALUE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, no clear correlation is presented between `R_VALUE` and `MEANGBT`. So I decide not to drop either parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling Features\n",
    "\n",
    "* Standardization means to convert the parameter's pdf into a normal (Gaussian with $\\mu=0$ and $\\sigma=1$) distribution. \n",
    "* Normalization means to apply the following operation to a feature x:\n",
    "    $ {x-x_\\mathrm{min}\\over x_\\mathrm{max}-x_\\mathrm{min}} $\n",
    "* For highly skewed probability distribution function (or histogram), I follow \n",
    "\n",
    "Most relevant features are positie and have their histograms right skewed (the tail is on the right), except for the following features.\n",
    "* `TOTFZ` is mostly (but not always) negative, and its histogram is left skewed.\n",
    "* `MEANGBT` is positive by definition and its histogram is *not* skewed, which is good.\n",
    "* `R_VALUE` is positive by definition. Its histogram has a high and narrow spike near zero and low-height & wide hill. The hill component is slightly left skewed. It ranges from zero to about six.\n",
    "\n",
    "\n",
    "\n",
    "### Right Skewed Features\n",
    "\n",
    "I plan to scale a feature, x, in the following two steps:\n",
    "* $ y = \\ln(x-x_\\mathrm{min} +1) $, where $x_\\mathrm{min}$ is the minimal value of this feature in the combined (training and validation) data. We will separate the data into training and validation later.\n",
    "* $ {y-\\bar y\\over \\sigma_y}$, where $\\bar y$ is the mean of $y$ in the combined (training & validation) data.\n",
    "\n",
    "We must find $x_\\mathrm{min}$, $\\bar y$ and $\\sigma_y$, so later we can use them to scale the same feature in the test data.\n",
    "\n",
    "Let us look at `TOTUSJH` (total unsigned current helicity) first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['TOTUSJH'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled TOTUSJH:\n",
      "            TOTUSJH\n",
      "count  1.173987e+07\n",
      "mean   8.600690e-13\n",
      "std    1.000000e+00\n",
      "min   -2.924703e+00\n",
      "25%   -7.751969e-01\n",
      "50%   -6.105436e-03\n",
      "75%    7.819727e-01\n",
      "max    2.586020e+00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c97b4240>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_min = df_selected_features.min() # pd.Series with index (label) = feature_name\n",
    "type(x_min)\n",
    "y_df = np.log(df_selected_features - x_min + 1) # pd.DataFrame, column=feature_name, row_index=0,1,2,etc\n",
    "y_mean = y_df.mean() # pd.Series\n",
    "y_std = y_df.std() # pd.Series\n",
    "x_scaled = (y_df - y_mean)/y_std\n",
    "\n",
    "print('Scaled TOTUSJH:')\n",
    "print(x_scaled.describe())\n",
    "x_scaled.hist(bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good, it seems to work. Let us design a function that takes in a feature name and output $x_\\mathrm{min}$, $y_\\mathrm{mean}$ and $\\sigma_y$. We will need these parameters to scale right skewed features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaling_params_right_skewed(feature_name):\n",
    "    df_selected_features = extract_features([feature_name])\n",
    "    # pd.Series with index (label) = feature_name\n",
    "    x_min = df_selected_features.min() \n",
    "    # pd.DataFrame, column=feature_name, row_index=0,1,2,etc\n",
    "    y_df = np.log(df_selected_features - x_min + 1) \n",
    "    y_mean = y_df.mean() # pd.Series\n",
    "    y_std = y_df.std() # pd.Series\n",
    "#     x_scaled = (y_df - y_mean)/y_std\n",
    "    return x_min[feature_name], y_mean[feature_name], y_std[feature_name]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will take use of the function `scaling_params_right_skewed` to calculate these three scaling parameters for all right skewed relevant parameters. In the following, \n",
    "\n",
    "* we first get a list of features names for these relevent right-skewed features. \n",
    "* then we obtain a pd.DataFrame with index = list('x_min','y_mean','y_std') and columns = list of feature names. This step takes a while. We do not want to redo it in the future. \n",
    "* So we then save the resulting dataframe as a .csv file. `pd.DataFrame.to_csv('file_name', index=True)`. When read the cvs file back in, use `df = pd.read_csv('file_name')`, then set the index using `df.set_index('Unnamed: 0',inplace=True)` to set the index back to list('x_min','y_mean','y_std')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get a list of feature names which are right skewed.\n",
    "right_skewed_features = [x for x in relevant_features_0 if x not in ['TOTFZ','MEANGBT','R_VALUE']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following two cells calculate the `x_min`, `y_mean` and `y_std` for the features in `right_skewed_features`, and save them in `scaling_params_df.csv` in the current dir. Both cells are commented, because they have been executed and they only need to be executed once. From now on, we can read in these scaling parameters from the csv file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scaling_params_df = pd.DataFrame(index=['x_min','y_mean','y_std'])\n",
    "# for feature in right_skewed_features:\n",
    "#     x_min, y_mean, y_std = scaling_params_right_skewed(feature)\n",
    "#     scaling_params_df[feature] = [x_min,y_mean,y_std]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scaling_params_df.to_csv('scaling_params_df.csv',index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We read the `x_min`, `y_mean`, `y_std` to a pandas.DataFrame called `right_skewed_scaling_params`. We will need these scaling parameters to scale the right skewed features in the list `right_skewed_features`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "right_skewed_scaling_params = pd.read_csv('scaling_params_df.csv')\n",
    "right_skewed_scaling_params.set_index('Unnamed: 0', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>x_min</th>\n",
       "      <th>y_mean</th>\n",
       "      <th>y_std</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>TOTUSJH</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.963492</td>\n",
       "      <td>1.697093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TOTBSQ</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>20.880991</td>\n",
       "      <td>2.738754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TOTPOT</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>50.436895</td>\n",
       "      <td>5.203139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TOTUSJZ</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>28.536669</td>\n",
       "      <td>3.114336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>ABSNJZH</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.614397</td>\n",
       "      <td>1.619750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>SAVNCPP</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>27.131898</td>\n",
       "      <td>3.029859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>USFLUX</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>48.717942</td>\n",
       "      <td>4.841408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>EPSZ</td>\n",
       "      <td>-0.990590</td>\n",
       "      <td>0.384481</td>\n",
       "      <td>0.114633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANSHR</td>\n",
       "      <td>1.821557</td>\n",
       "      <td>3.221742</td>\n",
       "      <td>0.280066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANGAM</td>\n",
       "      <td>8.056775</td>\n",
       "      <td>3.251750</td>\n",
       "      <td>0.303707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANGBH</td>\n",
       "      <td>4.735956</td>\n",
       "      <td>3.843436</td>\n",
       "      <td>0.284348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEANJZD</td>\n",
       "      <td>-52.278859</td>\n",
       "      <td>3.980520</td>\n",
       "      <td>0.012390</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Unnamed: 0      x_min     y_mean     y_std\n",
       "TOTUSJH      0.000000   4.963492  1.697093\n",
       "TOTBSQ       0.000000  20.880991  2.738754\n",
       "TOTPOT       0.000000  50.436895  5.203139\n",
       "TOTUSJZ      0.000000  28.536669  3.114336\n",
       "ABSNJZH      0.000000   2.614397  1.619750\n",
       "SAVNCPP      0.000000  27.131898  3.029859\n",
       "USFLUX       0.000000  48.717942  4.841408\n",
       "EPSZ        -0.990590   0.384481  0.114633\n",
       "MEANSHR      1.821557   3.221742  0.280066\n",
       "MEANGAM      8.056775   3.251750  0.303707\n",
       "MEANGBH      4.735956   3.843436  0.284348\n",
       "MEANJZD    -52.278859   3.980520  0.012390"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "right_skewed_scaling_params.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "right_skewed_scaling_params.loc['x_min','TOTUSJH']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let us take a look at the histograms of the scaled features for those in `right_skewed_features`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled TOTUSJH:\n",
      "            TOTUSJH\n",
      "count  1.173987e+07\n",
      "mean   8.600690e-13\n",
      "std    1.000000e+00\n",
      "min   -2.924703e+00\n",
      "25%   -7.751969e-01\n",
      "50%   -6.105436e-03\n",
      "75%    7.819727e-01\n",
      "max    2.586020e+00\n",
      "Scaled TOTBSQ:\n",
      "             TOTBSQ\n",
      "count  1.173987e+07\n",
      "mean   1.130803e-12\n",
      "std    1.000000e+00\n",
      "min   -7.624266e+00\n",
      "25%   -5.153206e-01\n",
      "50%    2.776891e-02\n",
      "75%    6.534680e-01\n",
      "max    1.754980e+00\n",
      "Scaled TOTPOT:\n",
      "             TOTPOT\n",
      "count  1.173987e+07\n",
      "mean  -9.289803e-13\n",
      "std    1.000000e+00\n",
      "min   -9.693551e+00\n",
      "25%   -2.658536e-01\n",
      "50%    2.605320e-02\n",
      "75%    4.513875e-01\n",
      "max    1.877541e+00\n",
      "Scaled TOTUSJZ:\n",
      "            TOTUSJZ\n",
      "count  1.173987e+07\n",
      "mean   8.616231e-13\n",
      "std    1.000000e+00\n",
      "min   -9.163004e+00\n",
      "25%   -3.475739e-01\n",
      "50%    6.497853e-02\n",
      "75%    4.917751e-01\n",
      "max    1.522380e+00\n",
      "Scaled ABSNJZH:\n",
      "            ABSNJZH\n",
      "count  1.173987e+07\n",
      "mean  -6.176045e-13\n",
      "std    1.000000e+00\n",
      "min   -1.614075e+00\n",
      "25%   -7.973506e-01\n",
      "50%   -1.472809e-01\n",
      "75%    7.152585e-01\n",
      "max    3.325014e+00\n",
      "Scaled SAVNCPP:\n",
      "            SAVNCPP\n",
      "count  1.173987e+07\n",
      "mean  -1.118555e-12\n",
      "std    1.000000e+00\n",
      "min   -8.954840e+00\n",
      "25%   -2.949705e-01\n",
      "50%    8.032835e-02\n",
      "75%    4.660450e-01\n",
      "max    1.711730e+00\n",
      "Scaled USFLUX:\n",
      "             USFLUX\n",
      "count  1.173987e+07\n",
      "mean  -1.199621e-12\n",
      "std    1.000000e+00\n",
      "min   -1.006276e+01\n",
      "25%   -1.961075e-01\n",
      "50%    8.558024e-02\n",
      "75%    3.670418e-01\n",
      "max    9.299757e-01\n",
      "Scaled EPSZ:\n",
      "               EPSZ\n",
      "count  1.163901e+07\n",
      "mean  -2.541795e-13\n",
      "std    1.000000e+00\n",
      "min   -3.353999e+00\n",
      "25%   -6.949311e-01\n",
      "50%   -3.228589e-01\n",
      "75%    7.010146e-01\n",
      "max    6.199984e+00\n",
      "Scaled MEANSHR:\n",
      "            MEANSHR\n",
      "count  1.163901e+07\n",
      "mean  -1.767046e-12\n",
      "std    1.000000e+00\n",
      "min   -1.150352e+01\n",
      "25%   -6.641953e-01\n",
      "50%   -3.329469e-01\n",
      "75%    6.826689e-01\n",
      "max    5.181374e+00\n",
      "Scaled MEANGAM:\n",
      "            MEANGAM\n",
      "count  1.163898e+07\n",
      "mean   3.702094e-12\n",
      "std    1.000000e+00\n",
      "min   -1.070685e+01\n",
      "25%   -6.964345e-01\n",
      "50%   -2.969104e-01\n",
      "75%    7.181219e-01\n",
      "max    3.795035e+00\n",
      "Scaled MEANGBH:\n",
      "            MEANGBH\n",
      "count  1.163901e+07\n",
      "mean  -8.856995e-13\n",
      "std    1.000000e+00\n",
      "min   -1.351667e+01\n",
      "25%   -6.591831e-01\n",
      "50%    9.146098e-02\n",
      "75%    6.992575e-01\n",
      "max    4.906124e+00\n",
      "Scaled MEANJZD:\n",
      "            MEANJZD\n",
      "count  1.163901e+07\n",
      "mean  -6.464743e-11\n",
      "std    1.000000e+00\n",
      "min   -3.212604e+02\n",
      "25%   -5.386404e-01\n",
      "50%   -1.707117e-01\n",
      "75%    3.894619e-01\n",
      "max    5.762484e+01\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for feature in right_skewed_features:\n",
    "    df_selected_features = extract_features([feature])\n",
    "    # comment the following line after one execution\n",
    "#     df_selected_features.to_csv('../features/'+feature+'.csv',index=False)\n",
    "    # pd.Series with index (label) = feature_name\n",
    "    x_min = right_skewed_scaling_params.loc['x_min',feature] \n",
    "    # pd.DataFrame, column=feature_name, row_index=0,1,2,etc\n",
    "    y_df = np.log(df_selected_features - x_min + 1)\n",
    "    y_mean = right_skewed_scaling_params.loc['y_mean',feature] # pd.Series\n",
    "    y_std = right_skewed_scaling_params.loc['y_std',feature] # pd.Series\n",
    "    x_scaled = (y_df - y_mean)/y_std\n",
    "\n",
    "    print('Scaled '+feature+':')\n",
    "    print(x_scaled.describe())\n",
    "    x_scaled.hist(bins=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Severe Outliers\n",
    "* From the figures above, I observe that most scaled features suffer from extremly small values (outliers on the left side), namely, `TOTBSQ`, `TOTPOT`, `TOTUSJZ`, `SAVNCPP`, `USFLUX`, `MEANSHR`, `MEANGAM`, `MEANGHB`, `MEANJZD`. \n",
    "    * The last one, `MEANJZD` suffers from extreme outliers which make most of its values cluster near zero while the minimum value is at -350 or so. \n",
    "    * Others have their miminum outlisers lie around -10, while the most of values cluster around zero from about -2 to +2. \n",
    "    \n",
    "* The three features, `TOTUSJH`, `ABSNJZH` and `EPSZ` are the only ones that do not suffer from extreme outliers. They are respectively the total unsigned current helicity, the absolute value of net vertical current helicity and the normalized vertical Lorentz force. \n",
    "\n",
    "I suspect that the extremely small outliers are due to lack of measurable magnetic fields. When $B\\sim 0$, the magnetic parameters are close zero, which correspond to the extremely small (negative) values in the scaled parameters. \n",
    "\n",
    "`EPSZ` does not suffer from the extremely small outliers because by definition $EPSZ\\propto {TOTFZ\\over TOTBSQ}$ and lack of measurable magnetic fields would cause both $TOTFZ$ and $TOTBSQ$ to become zero but their division may still stay finite. \n",
    "\n",
    "`TOTUSJH` and `ABSNJZH` both involve magnetic field and electric current. Lack of magnetic field measurement may not occur together with lack of current measurement, which might be the reason that these two parameters do not suffer from extremely small outliers. \n",
    "\n",
    "### Treatment of Extreme Outliers\n",
    "\n",
    "I believe the extreme outliers are due to lack of measurements. In other words, I do not think these outliers carry essential physical information. I plan to experiment with the following two operations. Look at this nice [summary of feature scalers in sklearn by Jeff Hale](https://link.medium.com/cO8ZUzGxk0). \n",
    "\n",
    "* Instead of using `y_mean` and `y_std` which are sensitive to outliers, I like to switch to `y_median` and `y_IQR` (interquartile range). This will avoid clustering most values very close to zero. But the extreme outliers would still have very negative values.\n",
    "\n",
    "* I can further convert those extreme values to `y_median`-n*`y_IQR`, here n could be 2, 3, 4, etc. The purpose is to make extreme values less important in the process of backproporgation but still keep them distinctive from most of values so that our neural network knows that they are clearly different.\n",
    "\n",
    "Well the two operations above are what I plan to do. I will execute them and check what the resulting histograms look like. \n",
    "\n",
    "We first separate the `right_skewed_features` into two groups:\n",
    "* One without extreme outliers, named `right_skewed_features_without_ol`, we will use the `y_mean` and `y_std` to standardize them.\n",
    "* One with extreme outliers, named `right_skewed_features_with_ol`, we will use `y_median` and `y_IQR` to scale them and get `x_scaled` = (`y`-`y_median`)/`y_IQR`, and take a look at the resulting histograms. After this operation, by definition, we will have\n",
    "    * `x_scaled_median` = 0\n",
    "    * `x_scaled_IQR` = 1\n",
    "* If the resulting histogram still looks suffered from extreme outliers, we will then convert any extreme outliers outside the range (`x_scaled_median`-n*`x_scaled_IQR`, `x_scaled_median`+n*`x_scaled_IQR`) = (-n,n) to the corresponding edges. Here n is a positive number to be chosen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [],
   "source": [
    "# right skewed features without extreme outliers\n",
    "right_skewed_features_without_ol = ['TOTUSJH','ABSNJZH','EPSZ']\n",
    "# right skewed features with extreme outliers\n",
    "right_skewed_features_with_ol = [x for x in right_skewed_features if x not in right_skewed_features_without_ol]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'SAVNCPP', 'USFLUX', 'MEANSHR', 'MEANGAM', 'MEANGBH', 'MEANJZD']\n"
     ]
    }
   ],
   "source": [
    "print(right_skewed_features_with_ol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7999D6zWj50YCZJ+kGRGxNx0+2p/qA8DswrhZwJ5U76mpV1J9Vsn4nG0cIiLWAGsAuru7o6enp3bImFUqFRqZ327ut7Xa2e+yVXc2vI6V84a4avvh/7vvOr+n4XW3gv8eWq8ZPTdyCGsDMHwlVR9wR6G+NF0ptQB4Lh1+2gQslHRsOnm+ENiUlr0gaUG6+mppzbrGsw0zM2uTMe2BSLqJ6t7DdEkDVK+muhK4RdJy4EngvDR8I3A20A+8BHwCICIOSLoc2JrGXRYRwyfmP0P1Sq+pwF3pxni3YWZm7TOmAImIJSMsOqNkbAAXjLCetcDakvr9wMkl9WfGuw0zM2sPvxPdzMyyOEDMzCyLA8TMzLI4QMzMLEsr3khoZuM0pwnv9TBrN++BmJlZFgeImZllcYCYmVkWB4iZmWVxgJiZWRYHiJmZZXGAmJlZFgeImZllcYCYmVkWB4iZmWVxgJiZWRYHiJmZZXGAmJlZFgeImZllcYCYmVmW7ACR9E5J2wq35yVdJOkLkp4q1M8uzLlEUr+kxySdWaj3plq/pFWF+gmSfiRpp6SbJR2d6q9Nj/vT8jm5z8PMzPJkB0hEPBYR8yNiPnAK8BJwe1p89fCyiNgIIOlEYDFwEtALfEPSFElTgK8DZwEnAkvSWIAvpXXNBQ4Cy1N9OXAwIt4OXJ3GmZlZGzXrENYZwOMR8R91xiwC1kfEyxHxC6AfODXd+iPiiYj4DbAeWCRJwOnArWn+OuCcwrrWpfu3Amek8WZm1ibN+krbxcBNhccXSloK3A+sjIiDwExgS2HMQKoB7K6pnwa8CXg2IoZKxs8cnhMRQ5KeS+OfLjYlaQWwAqCrq4tKpZL9BAcHBxua327ut7Wa3e/KeUOjD2pA19TybUzU3/mR/vfQDs3oueEASeclPgxckkrXAJcDkX5eBXwSKNtDCMr3gqLOeEZZ9vtCxBpgDUB3d3f09PSM9DRGValUaGR+u7nf1mp2v8ta/J3oK+cNcdX2kv/dt79Yd96uKz/Uoo7qO9L/HtqhGT034xDWWcBPImIfQETsi4hXIuK3wLeoHqKC6h7E7MK8WcCeOvWngWmSjqqpH7KutPyNwIEmPBczMxujZgTIEgqHryTNKCz7CLAj3d8ALE5XUJ0AzAV+DGwF5qYrro6mejhsQ0QEcA9wbprfB9xRWFdfun8u8P003szM2qShQ1iSXgd8EPhUofxPkuZTPaS0a3hZRDws6RbgZ8AQcEFEvJLWcyGwCZgCrI2Ih9O6LgbWS/oi8CBwbapfC9wgqZ/qnsfiRp6HmZmNX0MBEhEvUT15Xax9vM74K4ArSuobgY0l9Sf4/SGwYv3XwHkZLZuZWZP4nehmZpbFAWJmZlkcIGZmlsUBYmZmWRwgZmaWxQFiZmZZHCBmZpbFAWJmZlkcIGZmlsUBYmZmWRwgZmaWxQFiZmZZHCBmZpalWV9pa2avQnPqfFNip76t0CYO74GYmVkWB4iZmWVxgJiZWRafAzFrg3rnEswmK++BmJlZlob3QCTtAl4AXgGGIqJb0nHAzcAcYBfw0Yg4KEnAV4GzgZeAZRHxk7SePuDzabVfjIh1qX4KcB0wler3pn82ImKkbTT6fMysOUbb6/JVXJNfsw5h/XlEPF14vAq4OyKulLQqPb4YOAuYm26nAdcAp6UwWA10AwE8IGlDCoRrgBXAFqoB0gvcVWcbZtYGPixnrToHsgjoSffXARWqL+6LgOsjIoAtkqZJmpHGbo6IAwCSNgO9kirAGyLivlS/HjiHaoCMtA0zmwTqBdB1vce0sRPL1YwACeB7kgL4l4hYA3RFxF6AiNgr6fg0diawuzB3INXq1QdK6tTZxu9IWkF174Wuri4qlUr2kxwcHGxofru539Yab78r5w21rpkx6Jra+R7G49X+9zARNKPnZgTI+yNiT3oB3yzp0TpjVVKLjPqYpDBbA9Dd3R09PT1jnXqYSqVCI/Pbzf221nj7Xdbhwz0r5w1x1fbJc9HlynlDXPXDF0dcPtHOn0y2v19oTs8NX4UVEXvSz/3A7cCpwL50aIr0c38aPgDMLkyfBewZpT6rpE6dbZiZWRs0FCCSjpH0h8P3gYXADmAD0JeG9QF3pPsbgKWqWgA8lw5DbQIWSjpW0rFpPZvSshckLUhXcC2tWVfZNszMrA0a3aftAm6vvrZzFPDtiPi/krYCt0haDjwJnJfGb6R6CW8/1ct4PwEQEQckXQ5sTeMuGz6hDnyG31/Ge1e6AVw5wjbMzKwNGgqQiHgCeE9J/RngjJJ6ABeMsK61wNqS+v3AyWPdhpm9+vlTgicGvxPdzMyyOEDMzCyLA8TMzLJMngvDzczGwJ/B1T7eAzEzsywOEDMzy+IAMTOzLA4QMzPL4gAxM7MsvgrLzI4ovkqrebwHYmZmWRwgZmaWxQFiZmZZHCBmZpbFJ9HNmmS0k7NmrzbeAzEzsywOEDMzy+IAMTOzLA4QMzPLkh0gkmZLukfSI5IelvTZVP+CpKckbUu3swtzLpHUL+kxSWcW6r2p1i9pVaF+gqQfSdop6WZJR6f6a9Pj/rR8Tu7zMDOzPI3sgQwBKyPiXcAC4AJJJ6ZlV0fE/HTbCJCWLQZOAnqBb0iaImkK8HXgLOBEYElhPV9K65oLHASWp/py4GBEvB24Oo0zM7M2yg6QiNgbET9J918AHgFm1pmyCFgfES9HxC+AfuDUdOuPiCci4jfAemCRJAGnA7em+euAcwrrWpfu3wqckcabmVmbNOUcSDqE9F7gR6l0oaSHJK2VdGyqzQR2F6YNpNpI9TcBz0bEUE39kHWl5c+l8WZm1iYNv5FQ0uuB24CLIuJ5SdcAlwORfl4FfBIo20MIykMs6oxnlGXF3lYAKwC6urqoVCp1n0s9g4ODDc1vN/fbWmX9rpw3VD54AuiaOrH7q9XJfnP+Difb3y80p+eGAkTSa6iGx40R8R2AiNhXWP4t4Lvp4QAwuzB9FrAn3S+rPw1Mk3RU2ssojh9e14Cko4A3Agdq+4uINcAagO7u7ujp6cl+rpVKhUbmt5v7ba2yfpdN4Heir5w3xFXbJ88HT3Sy313n94x7zmT7+4Xm9Jz9Xyidc7gWeCQivlKoz4iIvenhR4Ad6f4G4NuSvgK8BZgL/Jjq3sRcSScAT1E90f6xiAhJ9wDnUj0v0gfcUVhXH3BfWv79iDhsD8TMbLzqfSSNvyvkUI1E/PuBjwPbJW1LtX+gehXVfKqHlHYBnwKIiIcl3QL8jOoVXBdExCsAki4ENgFTgLUR8XBa38XAeklfBB6kGliknzdI6qe657G4gedhZmYZsgMkIn5I+bmIjXXmXAFcUVLfWDYvIp6gepVWbf3XwHnj6dfMzJrL70Q3M7MsDhAzM8syeS7LMOuw4snVlfOGJvRVV2bt4D0QMzPL4gAxM7MsDhAzM8viADEzsywOEDMzy+IAMTOzLA4QMzPL4gAxM7MsDhAzM8viADEzsyz+KBMzszEa6btChj/a5kj7vhAHiFlS74uEzOxwPoRlZmZZHCBmZpbFAWJmZlkcIGZmlsUBYmZmWSb1VViSeoGvAlOA/x0RV3a4JZvgfKWVWfNM2gCRNAX4OvBBYADYKmlDRPyss52Z2ZGq3j9QXo3vEZm0AQKcCvRHxBMAktYDiwAHyBHMexhm7aOI6HQPWSSdC/RGxN+kxx8HTouICwtjVgAr0sN3Ao81sMnpwNMNzG8399ta7re13G/rjbXnP4qIN5ctmMx7ICqpHZKGEbEGWNOUjUn3R0R3M9bVDu63tdxva7nf1mtGz5P5KqwBYHbh8SxgT4d6MTM74kzmANkKzJV0gqSjgcXAhg73ZGZ2xJi0h7AiYkjShcAmqpfxro2Ih1u4yaYcCmsj99ta7re13G/rNdzzpD2JbmZmnTWZD2GZmVkHOUDMzCyLA2ScJH1OUkia3ule6pF0uaSHJG2T9D1Jb+l0T6OR9GVJj6a+b5c0rdM91SPpPEkPS/qtpAl7CaekXkmPSeqXtKrT/dQjaa2k/ZJ2dLqXsZA0W9I9kh5Jfwuf7XRP9Uj6A0k/lvTT1O//aGR9DpBxkDSb6kenPNnpXsbgyxHx7oiYD3wX+MdONzQGm4GTI+LdwM+BSzrcz2h2AH8J3NvpRkZS+Mifs4ATgSWSTuxsV3VdB/R2uolxGAJWRsS7gAXABRP89/sycHpEvAeYD/RKWpC7MgfI+FwN/D01b1iciCLi+cLDY5gcPX8vIobSwy1U39szYUXEIxHRyKcbtMPvPvInIn4DDH/kz4QUEfcCBzrdx1hFxN6I+Em6/wLwCDCzs12NLKoG08PXpFv2a4MDZIwkfRh4KiJ+2ulexkrSFZJ2A+czOfZAij4J3NXpJl4FZgK7C48HmMAvcJOZpDnAe4EfdbaT+iRNkbQN2A9sjojsfift+0BaQdK/A/+5ZNGlwD8AC9vbUX31+o2IOyLiUuBSSZcAFwKr29pgidF6TmMupXpo4MZ29lZmLP1OcKN+5I81TtLrgduAi2r2/ieciHgFmJ/OMd4u6eSIyDrn5AApiIgPlNUlzQNOAH4qCaqHVn4i6dSI+GUbWzzESP2W+DZwJxMgQEbrWVIf8BfAGTEB3qQ0jt/xROWP/GkxSa+hGh43RsR3Ot3PWEXEs5IqVM85ZQWID2GNQURsj4jjI2JORMyh+j/l+zoZHqORNLfw8MPAo53qZazSF4RdDHw4Il7qdD+vEv7InxZS9V+U1wKPRMRXOt3PaCS9efjqRklTgQ/QwGuDA+TV60pJOyQ9RPXQ24S+vDD5X8AfApvT5cff7HRD9Uj6iKQB4E+AOyVt6nRPtdJFCcMf+fMIcEuLP/KnIZJuAu4D3ilpQNLyTvc0ivcDHwdOT3+z2ySd3emm6pgB3JNeF7ZSPQfy3dyV+aNMzMwsi/dAzMwsiwPEzMyyOEDMzCyLA8TMzLI4QMzMLIsDxMzMsjhAzMwsy/8HyrPGzT5uEyMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_clip = 4.0 # the positive number for clipping\n",
    "for feature in right_skewed_features_with_ol:\n",
    "    # pd.DataFrame with column_name = feature & index = 0,1,2,3\n",
    "    x_df = pd.read_csv('../features/'+feature+'.csv')\n",
    "    # pd.Series with index (label) = feature_name\n",
    "    x_min = x_df.min() \n",
    "    # pd.DataFrame, column=feature_name, row_index=0,1,2,etc\n",
    "    y_df = np.log(x_df - x_min + 1)\n",
    "    y_quantiles = y_df.quantile([0.25,0.5,0.75]) # pd.DataFrame, row_index = 0.25,0.5,0.75\n",
    "    y_IQR = y_quantiles.loc[0.75]-y_quantiles.loc[0.25] # pd.Series\n",
    "    y_median = y_quantiles.loc[0.5] #pd.Series\n",
    "    x_scaled = (y_df - y_median)/y_IQR\n",
    "    x_scaled.clip(-n_clip,n_clip,inplace=True)\n",
    "    x_scaled.hist(bins=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the histograms for features in `right_skewed_features_with_ol` do look better. However, before experimenting with our neural network, it is hard to predict whether clipping will help the learning process or not. So we shall keep an open mind, and experiment with and without clipping."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling Left-Skewed Feature\n",
    "\n",
    "`TOTFZ` is mostly (but not always) negative, and its histogram is left skewed. For this feature, I will do the following scaling operations:\n",
    "* $y=\\ln(x_\\mathrm{max}-x +1)$\n",
    "* ${y-\\bar y \\over \\sigma_y}$,\n",
    "where $\\bar y$ and $\\sigma_y$ are the mean and standard deviation of $y$.\n",
    "\n",
    "I will define a function which takes in the feature name and returns `x_max`, `y_mean` and `y_std`. Before doing so, let us look into how well these scaling operations would do for the histogram of `TOTFZ`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_selected_features = extract_features(['TOTFZ'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled TOTFZ:\n",
      "              TOTFZ\n",
      "count  1.173987e+07\n",
      "mean  -2.930587e-10\n",
      "std    1.000000e+00\n",
      "min   -1.226266e+02\n",
      "25%   -7.479785e-01\n",
      "50%   -4.122708e-01\n",
      "75%    4.460956e-01\n",
      "max    4.890690e+00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11d6be8d0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_max = df_selected_features.max() \n",
    "y_df = np.log(-df_selected_features + x_max + 1) \n",
    "y_mean = y_df.mean() # pd.Series\n",
    "y_std = y_df.std() # pd.Series\n",
    "x_scaled = (y_df - y_mean)/y_std\n",
    "\n",
    "print('Scaled TOTFZ:')\n",
    "print(x_scaled.describe())\n",
    "x_scaled.hist(bins=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, it does not look good, because most values cluster around zero. Observing that the maximum value for the scaled x is about 5, while the minimum scaled x is about -120. So the skinny shape of the histogram is due to the very small outliers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [],
   "source": [
    "left_skewed_features_with_ol = ['TOTFZ']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # we extract all TOTFZ values and store them in a csv file\n",
    "# df_selected_features = extract_features(['TOTFZ'])\n",
    "# df_selected_features.to_csv('../features/TOTFZ.csv',index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wHTitqh4CSPIm4ApgGXBeVd3cM4ckaf6MFSBVNQ1Mt+e3MbiDauc+PwOO38X4s4CzRrRfDlw+on3sOSRJ88NPokuSuhggkqQuBogkqYsBIknqYoBIkroYIJKkLgaIJKmLASJJ6mKASJK6GCCSpC4GiCSpiwEiSepigEiSuhggkqQuBogkqYsBIknqYoBIkroYIJKkLgaIJKmLASJJ6mKASJK6GCCSpC4GiCSpiwEiSepigEiSuhggkqQuBogkqYsBIknqYoBIkroYIJKkLgaIJKmLASJJ6mKASJK6GCCSpC7LF3oBkqQ+qzdc9oi2LWe/Yt7m9wxEktRlxgBJcnCSq5NsSnJzkre29qckuTLJre3n/q09ST6QZHOSbyQ5bOhYJ7f+tyY5eaj9hUluamM+kCS9c0iS5sdszkC2A6dX1bOAI4HTkhwKbACuqqo1wFVtG+AYYE17rAc+DIMwAM4EjgAOB87cEQitz/qhceta+1hzSJLmz4wBUlV3VdX17fkDwCZgFXAccH7rdj7w6vb8OOCCGvgqsCLJ04CXA1dW1b1VdR9wJbCu7duvqv6uqgq4YKdjjTOHJGmejPUmepLVwAuAa4CVVXUXDEImyVNbt1XAHUPDtra23bVvHdFOxxx37bTe9QzOUFi5ciXT09PjlPtPtm3b1j12MVpK9VjL4rWU6lnoWk5/7vZZ951pnXNZy6wDJMm+wGeBt1XVj9rbFCO7jmirjvbdLmc2Y6pqI7ARYO3atTU1NTXDYUebnp6md+xitJTqsZbFaynVs9C1nDLibqtd2XLi1G73z2Uts7oLK8njGITHJ6vqc635ezsuG7Wfd7f2rcDBQ8MPAu6cof2gEe09c0iS5sls7sIKcC6wqareO7TrUmDHnVQnA5cMtZ/U7pQ6Evhhuwx1BXB0kv3bm+dHA1e0fQ8kObLNddJOxxpnDknSPJnNJawXA78P3JTkxtb2TuBs4KIkpwK3A8e3fZcDxwKbgZ8ArweoqnuT/DHw9dbvXVV1b3v+RuDjwBOAL7YH484hSZo/MwZIVX2F0e85ABw1on8Bp+3iWOcB541ovxZ4zoj2H4w7hyRpfvhJdElSFwNEktTFAJEkdTFAJEldDBBJUhcDRJLUxQCRJHUxQCRJXQwQSVIXA0SS1MUAkSR1MUAkSV0MEElSFwNEktTFAJEkdTFAJEldDBBJUhcDRJLUxQCRJHUxQCRJXQwQSVIXA0SS1MUAkSR1MUAkSV0MEElSFwNEktTFAJEkdTFAJEldDBBJUhcDRJLUxQCRJHUxQCRJXQwQSVKX5Qu9AEnS3Fm94bJHtG05+xWPyVyegUiSuhggkqQuExsgSdYluSXJ5iQbFno9krSnmcgASbIM+CBwDHAo8Nokhy7sqiRpzzKRAQIcDmyuqtuq6kHgQuC4BV6TJO1RJvUurFXAHUPbW4Ejdu6UZD2wvm1uS3JL53wHAvd0jl2MllI91rJ4LaV6JrqWvPthm+PW8i92tWNSAyQj2uoRDVUbgY2PerLk2qpa+2iPs1gspXqsZfFaSvVYy2iTeglrK3Dw0PZBwJ0LtBZJ2iNNaoB8HViT5JAkewEnAJcu8JokaY8ykZewqmp7kjcBVwDLgPOq6ubHcMpHfRlskVlK9VjL4rWU6rGWEVL1iLcOJEma0aRewpIkLTADRJLUxQCZwSR/ZUqS85LcneSbQ21PSXJlklvbz/0Xco2zleTgJFcn2ZTk5iRvbe2TWs/eSb6W5O9bPf+ttR+S5JpWz6fbTSITIcmyJDck+ULbnuRatiS5KcmNSa5tbZP6WluR5OIk325/f140V7UYILuxBL4y5ePAup3aNgBXVdUa4Kq2PQm2A6dX1bOAI4HT2p/FpNbzc+BlVfU84PnAuiRHAu8Gzmn13AecuoBrHNdbgU1D25NcC8C/qqrnD31mYlJfa+8H/rqqngk8j8Gf0dzUUlU+dvEAXgRcMbR9BnDGQq9rzBpWA98c2r4FeFp7/jTgloVeY2ddlwC/uxTqAZ4IXM/g2xTuAZa39oe9/hbzg8Fnsa4CXgZ8gcGHfSeylrbeLcCBO7VN3GsN2A/4Du2GqbmuxTOQ3Rv1lSmrFmgtc2VlVd0F0H4+dYHXM7Ykq4EXANcwwfW0Sz43AncDVwL/F7i/qra3LpP0ensf8HbgF237ACa3Fhh8s8WXklzXvhIJJvO19nTg+8DH2uXFjybZhzmqxQDZvVl9ZYrmT5J9gc8Cb6uqHy30eh6Nqnqoqp7P4F/vhwPPGtVtflc1viSvBO6uquuGm0d0XfS1DHlxVR3G4PL1aUleutAL6rQcOAz4cFW9APgxc3jpzQDZvaX4lSnfS/I0gPbz7gVez6wleRyD8PhkVX2uNU9sPTtU1f3ANIP3dlYk2fEB30l5vb0Y+L0kWxh8M/bLGJyRTGItAFTVne3n3cDnGQT8JL7WtgJbq+qatn0xg0CZk1oMkN1bil+Zcilwcnt+MoP3Eha9JAHOBTZV1XuHdk1qPb+aZEV7/gTgdxi8uXk18JrWbSLqqaozquqgqlrN4O/Il6vqRCawFoAk+yR50o7nwNHAN5nA11pVfRe4I8lvtKajgG8xR7X4SfQZJDmWwb+mdnxlylkLvKRZS/KXwBSDr2/+HnAm8FfARcCvAbcDx1fVvQu1xtlK8hLgb4Gb+OV19ncyeB9kEuv5TeB8Bq+rXwEuqqp3JXk6g3/FPwW4AXhdVf184VY6niRTwH+qqldOai1t3Z9vm8uBT1XVWUkOYDJfa88HPgrsBdwGvJ72muNR1mKASJK6eAlLktTFAJEkdTFAJEldDBBJUhcDRJLUxQCRJHUxQCRJXf4/rjF2G/hL5zIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_clip = 3.0\n",
    "for feature in left_skewed_features_with_ol:    \n",
    "    x_df = pd.read_csv('../features/'+feature+'.csv')\n",
    "    x_df.rename(columns={feature:'original x'}).hist(bins=40)\n",
    "    x_max = x_df.max() \n",
    "    (-x_df+x_max+1).rename(columns={feature:'-x+x_max+1'}).hist(bins=40)\n",
    "    y_df = np.log(-x_df + x_max + 1) \n",
    "    y_df.rename(columns={feature:'y=ln(-x+x_max+1)'}).hist(bins=60)\n",
    "    y_quantiles = y_df.quantile([0.25,0.5,0.75]) # pd.DataFrame, row_index = 0.25,0.5,0.75\n",
    "    y_IQR = y_quantiles.loc[0.75]-y_quantiles.loc[0.25] # pd.Series\n",
    "    y_median = y_quantiles.loc[0.5] #pd.Series\n",
    "#     y_clipped = y_df.clip(y_median[feature]-n_clip*y_IQR[feature], \n",
    "#               y_median[feature]+n_clip*y_IQR[feature])\n",
    "    \n",
    "    \n",
    "    x_scaled = (y_df - y_median)/y_IQR\n",
    "#     x_scaled.clip(-n_clip,n_clip,inplace=True)\n",
    "    x_scaled.rename(columns={feature:'(y-y_median/y_IQR)'}).hist(bins=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting, why is this scaled `TOTFZ` still skewed? Probably because ln() is not yet enough to correct the skewness. I decide to try [sklearn.preprocessing.PowerTransformer](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PowerTransformer.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.save('TOTFZ.npy',np.array(x_df[feature]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(11775600,)\n"
     ]
    }
   ],
   "source": [
    "x = np.load('TOTFZ.npy')\n",
    "print(x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(11739874,)\n"
     ]
    }
   ],
   "source": [
    "x = x[np.isfinite(x)]\n",
    "print(x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_pos = x[x>0]\n",
    "x_neg = x[x<0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([4.35066333e-07, 1.63149875e-06, 1.95779850e-05, 9.54970601e-05,\n",
       "        7.43202063e-04, 2.74296271e-02, 2.68370994e-01, 4.26897419e-01,\n",
       "        4.31544797e-01, 1.10202846e-01]),\n",
       " array([17.80611782, 18.59644046, 19.3867631 , 20.17708574, 20.96740838,\n",
       "        21.75773102, 22.54805367, 23.33837631, 24.12869895, 24.91902159,\n",
       "        25.70934423]),\n",
       " <a list of 1 Patch objects>)"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log10(x_pos+1),normed=True,histtype='step')\n",
    "plt.hist(np.log10(np.abs(x_neg)+1),normed=True,histtype='step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The transformation above is very simple and neglects $x=0$. If I include $x=0$, the histograms would become very bad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.35066333e-07, 1.63149875e-06, 1.95779850e-05, 9.54970601e-05,\n",
       "        7.43202063e-04, 2.74296271e-02, 2.68370994e-01, 4.26897419e-01,\n",
       "        4.31544797e-01, 1.10202846e-01]),\n",
       " array([17.80611782, 18.59644046, 19.3867631 , 20.17708574, 20.96740838,\n",
       "        21.75773102, 22.54805367, 23.33837631, 24.12869895, 24.91902159,\n",
       "        25.70934423]),\n",
       " <a list of 1 Patch objects>)"
      ]
     },
     "execution_count": 344,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log10(x[x>=0]+1),histtype='step',density=True)\n",
    "plt.hist(np.log10(-x[x<0]+1),histtype='step',density=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, it is the great number of zero values in `TOTFZ` that causes the difficulty for scaling this feature.  Does zero `TOTFZ` mean anything significant physically? Or does it mainly result from lack of observations? \n",
    "\n",
    "By definition, `TOTFZ` (total vertical Lorentz force) is $\\propto \\Sigma (B_h^2 -B_z^2)$. \n",
    "\n",
    "Well, we can put this problem aside for now, because by definition $EPSZ \\propto {TOTFZ\\over TOTBSQ}$ and both $EPSZ$ and $TOTBSQ$ are reasonally well scaled now. We can drop the feature `TOTFZ` for now, but I must keep this in mind.\n",
    "\n",
    "Below is my experiment of scaling `TOTFZ` using sklearn.preprocessing.PowerTransformer which by default uses [Yeo-Johnson transformation](https://en.wikipedia.org/wiki/Power_transform). The scaled values do not have a good-looking histogram either."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_df = pd.read_csv('../features/'+feature+'.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PowerTransformer\n",
    "pt = PowerTransformer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/numpy/core/_methods.py:121: RuntimeWarning: overflow encountered in multiply\n",
      "  x = um.multiply(x, x, out=x)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x12bde36a0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt.fit(x_df)\n",
    "pt_x = pt.transform(x_df)\n",
    "pt_x_df = pd.DataFrame(pt_x)\n",
    "pt_x_df.hist(bins=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling Non-Skewed Features\n",
    "There remain `R_VALUE` and `MEANGBT`. There histgrams look okay. Therefore, we only need to standardize them by\n",
    "\n",
    "$ {x-x_\\mathrm{mean}\\over \\sigma_x}$.\n",
    "\n",
    "In the following, we first save the flattened joined time series for both features into .csv files. Second, we scale them and look at the histograms after scaling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [],
   "source": [
    "non_skewed_features = ['MEANGBT','R_VALUE']\n",
    "# for feature in non_skewed_features:\n",
    "#     df_selected_features = extract_features([feature])\n",
    "#     df_selected_features.to_csv('../features/'+feature+'.csv',index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x133ee7b38>"
      ]
     },
     "execution_count": 358,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# `MEANGBT`, the mean gradient of the horizontal magnetic field.\n",
    "x_df = pd.read_csv('../features/MEANGBT.csv')['MEANGBT']\n",
    "x_mean = x_df.mean()\n",
    "x_std = x_df.std()\n",
    "x_scaled = (x_df - x_mean)/x_std\n",
    "x_scaled.hist(bins=20,histtype='step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x203babac8>"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# `MEANGBT`, the mean gradient of the horizontal magnetic field.\n",
    "x_df = pd.read_csv('../features/R_VALUE.csv')['R_VALUE']\n",
    "x_mean = x_df.mean()\n",
    "x_std = x_df.std()\n",
    "x_scaled = (x_df - x_mean)/x_std\n",
    "x_scaled.hist(bins=20,histtype='step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary on Feature Scaling\n",
    "\n",
    "The relevant features are in `relevant_features_0`. It includes the following four lists of features:\n",
    "* `right_skewed_features_with_ol`\n",
    "* `right_skewed_features_without_ol`\n",
    "* `left_skewed_features_with_ol`\n",
    "* `non_skewed_features`\n",
    "\n",
    "We decide to drop `TOTFZ` for now, which is the only feature in the list `left_skewed_features_with_ol`. These features shall be scaled differently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set0 = set(relevant_features_0)\n",
    "set1 = set(right_skewed_features_with_ol + right_skewed_features_without_ol + left_skewed_features_with_ol + non_skewed_features)\n",
    "set1 == set2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling Parameters Needed for Scaling Features\n",
    "\n",
    "We prepare these parameters in a .csv file, ready for use later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 370,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(right_skewed_features) == set(right_skewed_features_with_ol+right_skewed_features_without_ol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale_params_right_skewed = pd.DataFrame(index=['x_min','y_mean','y_std','y_median','y_IQR'])\n",
    "for feature in right_skewed_features:\n",
    "    x_df = pd.read_csv('../features/'+feature+'.csv')[feature]\n",
    "    x_min = x_df.min()\n",
    "    y_df = np.log(x_df - x_min +1)\n",
    "    y_mean = y_df.mean()\n",
    "    y_std = y_df.std()\n",
    "    y_quantiles = y_df.quantile([0.25,0.5,0.75])\n",
    "    y_median = y_quantiles.loc[0.5]\n",
    "    y_IQR = y_quantiles.loc[0.75] - y_quantiles.loc[0.25]\n",
    "    scale_params_right_skewed[feature] = [x_min, y_mean, y_std, y_median, y_IQR]\n",
    "\n",
    "scale_params_right_skewed.to_csv('scale_params_right_skewed.csv',index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = pd.read_csv('scale_params_right_skewed.csv')\n",
    "test.set_index('Unnamed: 0', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TOTUSJH</th>\n",
       "      <th>TOTBSQ</th>\n",
       "      <th>TOTPOT</th>\n",
       "      <th>TOTUSJZ</th>\n",
       "      <th>ABSNJZH</th>\n",
       "      <th>SAVNCPP</th>\n",
       "      <th>USFLUX</th>\n",
       "      <th>EPSZ</th>\n",
       "      <th>MEANSHR</th>\n",
       "      <th>MEANGAM</th>\n",
       "      <th>MEANGBH</th>\n",
       "      <th>MEANJZD</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>x_min</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.990590</td>\n",
       "      <td>1.821557</td>\n",
       "      <td>8.056775</td>\n",
       "      <td>4.735956</td>\n",
       "      <td>-52.278859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_mean</td>\n",
       "      <td>4.963492</td>\n",
       "      <td>20.880991</td>\n",
       "      <td>50.436895</td>\n",
       "      <td>28.536669</td>\n",
       "      <td>2.614397</td>\n",
       "      <td>27.131898</td>\n",
       "      <td>48.717942</td>\n",
       "      <td>0.384481</td>\n",
       "      <td>3.221742</td>\n",
       "      <td>3.251750</td>\n",
       "      <td>3.843436</td>\n",
       "      <td>3.980520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_std</td>\n",
       "      <td>1.697093</td>\n",
       "      <td>2.738754</td>\n",
       "      <td>5.203139</td>\n",
       "      <td>3.114336</td>\n",
       "      <td>1.619750</td>\n",
       "      <td>3.029859</td>\n",
       "      <td>4.841408</td>\n",
       "      <td>0.114633</td>\n",
       "      <td>0.280066</td>\n",
       "      <td>0.303707</td>\n",
       "      <td>0.284348</td>\n",
       "      <td>0.012390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_median</td>\n",
       "      <td>4.953131</td>\n",
       "      <td>20.957043</td>\n",
       "      <td>50.572453</td>\n",
       "      <td>28.739034</td>\n",
       "      <td>2.375839</td>\n",
       "      <td>27.375281</td>\n",
       "      <td>49.132270</td>\n",
       "      <td>0.347470</td>\n",
       "      <td>3.128495</td>\n",
       "      <td>3.161576</td>\n",
       "      <td>3.869443</td>\n",
       "      <td>3.978405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_IQR</td>\n",
       "      <td>2.642662</td>\n",
       "      <td>3.201025</td>\n",
       "      <td>3.731905</td>\n",
       "      <td>2.614015</td>\n",
       "      <td>2.450048</td>\n",
       "      <td>2.305769</td>\n",
       "      <td>2.726436</td>\n",
       "      <td>0.160022</td>\n",
       "      <td>0.377210</td>\n",
       "      <td>0.429611</td>\n",
       "      <td>0.386270</td>\n",
       "      <td>0.011499</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             TOTUSJH     TOTBSQ     TOTPOT    TOTUSJZ   ABSNJZH    SAVNCPP  \\\n",
       "Unnamed: 0                                                                   \n",
       "x_min       0.000000   0.000000   0.000000   0.000000  0.000000   0.000000   \n",
       "y_mean      4.963492  20.880991  50.436895  28.536669  2.614397  27.131898   \n",
       "y_std       1.697093   2.738754   5.203139   3.114336  1.619750   3.029859   \n",
       "y_median    4.953131  20.957043  50.572453  28.739034  2.375839  27.375281   \n",
       "y_IQR       2.642662   3.201025   3.731905   2.614015  2.450048   2.305769   \n",
       "\n",
       "               USFLUX      EPSZ   MEANSHR   MEANGAM   MEANGBH    MEANJZD  \n",
       "Unnamed: 0                                                                \n",
       "x_min        0.000000 -0.990590  1.821557  8.056775  4.735956 -52.278859  \n",
       "y_mean      48.717942  0.384481  3.221742  3.251750  3.843436   3.980520  \n",
       "y_std        4.841408  0.114633  0.280066  0.303707  0.284348   0.012390  \n",
       "y_median    49.132270  0.347470  3.128495  3.161576  3.869443   3.978405  \n",
       "y_IQR        2.726436  0.160022  0.377210  0.429611  0.386270   0.011499  "
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale_params_non_skewed = pd.DataFrame(index=['x_mean','x_std','x_median','x_IQR'])\n",
    "for feature in non_skewed_features:\n",
    "    x_df = pd.read_csv('../features/'+feature+'.csv')[feature]\n",
    "    x_mean = x_df.mean()\n",
    "    x_std = x_df.std()\n",
    "    x_quantiles = x_df.quantile([0.25,0.5,0.75])\n",
    "    x_median = x_quantiles.loc[0.5]\n",
    "    x_IQR = x_quantiles.loc[0.75]-x_quantiles.loc[0.25]\n",
    "    scale_params_non_skewed[feature] = [x_mean, x_std, x_median, x_IQR]\n",
    "\n",
    "scale_params_non_skewed.to_csv('scale_params_non_skewed.csv',index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = pd.read_csv('scale_params_non_skewed.csv')\n",
    "test.set_index('Unnamed: 0', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MEANGBT</th>\n",
       "      <th>R_VALUE</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>x_mean</td>\n",
       "      <td>117.743253</td>\n",
       "      <td>1.653711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>x_std</td>\n",
       "      <td>22.180823</td>\n",
       "      <td>1.893810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>x_median</td>\n",
       "      <td>118.847308</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>x_IQR</td>\n",
       "      <td>31.823989</td>\n",
       "      <td>3.611355</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               MEANGBT   R_VALUE\n",
       "Unnamed: 0                      \n",
       "x_mean      117.743253  1.653711\n",
       "x_std        22.180823  1.893810\n",
       "x_median    118.847308  0.000000\n",
       "x_IQR        31.823989  3.611355"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    78.707684\n",
       "1    76.225352\n",
       "2    80.909553\n",
       "3    82.132074\n",
       "4    77.375068\n",
       "Name: TOTUSJH, dtype: float64"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['TOTUSJH', 'TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'ABSNJZH', 'SAVNCPP', 'USFLUX', 'EPSZ', 'MEANSHR', 'MEANGAM', 'MEANGBH', 'MEANJZD']\n",
      "['TOTBSQ', 'TOTPOT', 'TOTUSJZ', 'SAVNCPP', 'USFLUX', 'MEANSHR', 'MEANGAM', 'MEANGBH', 'MEANJZD']\n",
      "['TOTUSJH', 'ABSNJZH', 'EPSZ']\n",
      "['TOTFZ']\n",
      "['MEANGBT', 'R_VALUE']\n"
     ]
    }
   ],
   "source": [
    "print(right_skewed_features)\n",
    "print(right_skewed_features_with_ol)\n",
    "print(right_skewed_features_without_ol)\n",
    "print(left_skewed_features_with_ol)\n",
    "print(non_skewed_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for skewed data, we log it, the way we log it depends on the direction the data is skewed\n",
    "def log_right_skewed(x,x_min):\n",
    "    y = np.log(x-x_min+1)\n",
    "    return y\n",
    "def log_left_skewed(x,x_max):\n",
    "    y = np.log(x_max -x +1)\n",
    "    return y\n",
    "\n",
    "def standardize(y,ybar,delta_y,robust):\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 368,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fill NaN values\n",
    "\n",
    "I believe there must be smart ways of filling nan values in time series. Let me apply the simplest way, filling nan with median. I choose median here because it is robust to outliers and outliers are very common in the features for this project. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35726"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_df.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11775600,)"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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