doc/binning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binning in physt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Necessary import evil\n",
    "%matplotlib inline\n",
    "from physt import histogram, binnings\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some data\n",
    "np.random.seed(42)\n",
    "\n",
    "heights1 = np.random.normal(169, 10, 100000)\n",
    "heights2 = np.random.normal(180, 6, 100000)\n",
    "numbers = np.random.rand(100000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ideal number of bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IoQ3yXHksGriI/IyesThOV5KCF0KIJGWEw23lHghiK+yTdpPYBKNBdlzbQXWg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\n5jKzxDfk55BIZaZCrQh4mBnysaa+ctDnEE6k8Ht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mwT3VVIf8mZ75SBJh6LoALjfMXjns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\nJAsU8MNI7PuQVHsbrpJSAo99Pef70xrwIiKSTQr4IdhUivAvfgZAaOu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5e4bee0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = [int(x) for x in np.logspace(0, 4, 50)]\n",
    "\n",
    "algos = binnings.bincount_methods\n",
    "Ys = { algo: [] for algo in algos}\n",
    "\n",
    "for x in X:\n",
    "    ex_dataset = np.random.exponential(1, x)\n",
    "    for algo in algos:\n",
    "        Ys[algo].append(binnings.ideal_bin_count(ex_dataset, algo))\n",
    "\n",
    "figure, axis = plt.subplots(figsize=(8, 8))\n",
    "for algo in algos:\n",
    "    if algo == \"default\":\n",
    "        axis.plot(X, Ys[algo], \":.\", label=algo, alpha=0.5, lw=2)\n",
    "    else:\n",
    "        axis.plot(X, Ys[algo], \"-\", label=algo, alpha=0.5, lw=2)\n",
    "axis.set_xscale(\"log\")\n",
    "axis.set_yscale(\"log\")\n",
    "axis.set_xlabel(\"Sample size\")\n",
    "axis.set_ylabel(\"Bin count\")\n",
    "axis.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binning schemes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponential binning\n",
    "\n",
    "Uses numpy.logscale to create bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TYu8Fbq6qI4Cb23uSHAmcDhzVylyWZI9W5nLgbOCI9po451nAY1V1OHAJcPGu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\nLEmSJPX4/wGAM8Mksq+hJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5db4249b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axis = plt.subplots(1, 2, figsize=(10, 4))\n",
    "hist1 = histogram(numbers, \"exponential\", 10, range=(0.0001, 1))\n",
    "hist1.plot(color=\"green\", ax=axis[0])\n",
    "hist1.plot(density=True, errors=True, ax=axis[1])\n",
    "axis[0].set_title(\"Absolute scale\")\n",
    "axis[1].set_title(\"Log scale\")\n",
    "axis[1].set_xscale(\"log\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Integer binning\n",
    "\n",
    "Useful for integer values (or something you want to round to integers), creates bins of width=1 around integers (i.e. 0.5-1.5, ...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iezPwbuDhJLu6tt8Erk2yHijgKeB9AFW1J8l24BH6MwBvcAafJOlEUlXjruGkkl7B5LjL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d2607c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sum of two dice (should be triangle, right?)\n",
    "dice = np.floor(np.random.rand(10000) * 6) + np.floor(np.random.rand(10000) * 6) + 2\n",
    "histogram(dice, \"integer\").plot(ticks=\"center\", density=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile-based binning\n",
    "\n",
    "Based on quantiles, this binning results in all bins containing roughly the same amount \n",
    "of observances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JP3+afTYAG/YTnwDOOpgEJUmSpIXknfQkSZKkjgWyJEk6IjktnQ6VBbIkSZLUsUCWJEmS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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d24db4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axis = plt.subplots(1, 2, figsize=(10, 4))\n",
    "# bins2 = binning.quantile_bins(heights1, 40)\n",
    "hist2 = histogram(heights1, \"quantile\", 40)\n",
    "hist2.plot(ax=axis[0]);\n",
    "hist2.plot(density=True, ax=axis[1]);\n",
    "axis[0].set_title(\"Frequencies\")\n",
    "axis[1].set_title(\"Density\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ok5d8j4jZwOyj/TySyiOi9Gg/T3O5zsJynYXlOgunLdQILVdnSx/iqwb65j3u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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d240ce48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axis = plt.subplots()\n",
    "\n",
    "histogram(heights1, \"quantile\", 10).plot(alpha=0.3, density=True, ax=axis, label=\"Quantile based\")\n",
    "histogram(heights1, 10).plot(alpha=0.3, density=True, ax=axis, color=\"green\", label=\"Equal spaced\")\n",
    "axis.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixed-width bins\n",
    "\n",
    "This binning is useful if you want \"human-friendly\" bin intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Histogram1D(bins=(31,), total=100000, dtype=int64)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d24c97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist_fixed = histogram(heights1, \"fixed_width\", 3)\n",
    "hist_fixed.plot()\n",
    "hist_fixed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \"Human\" bins\n",
    "\n",
    "The width and alignment of bins is guessed from the data with an approximate number of bins as (optional) parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Histogram1D(bins=(19,), total=100000, dtype=int64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d232f7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "human = histogram(heights1, \"human\", 15)\n",
    "human.plot()\n",
    "human"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Astropy binning\n",
    "\n",
    "Astropy includes its histogramming tools. If this package is available, we reuse its binning\n",
    "methods. These include:\n",
    "\n",
    "* Bayesian blocks\n",
    "* Knuth\n",
    "* Freedman\n",
    "* Scott\n",
    "\n",
    "See <http://docs.astropy.org/en/stable/visualization/histogram.html> for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d2491978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d221a978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d2324dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aeJJEVRUw7fk2VbW9qkaranRkZGTQZkiShsxMA+pEkuUA3fPJrv4YsKpvv5VdnSRJ0zLT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5d23244e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "middle_sized = np.random.normal(180, 6, 5000)\n",
    "\n",
    "for n in [\"blocks\", \"scott\", \"knuth\", \"freedman\"]:\n",
    "    algo = \"{0}\".format(n)\n",
    "    hist = histogram(middle_sized, algo, name=algo)\n",
    "    hist.plot(density=True)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}