062_Bonomi_Attack_LB_Full_Vectors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "79c3f202",
   "metadata": {},
   "source": [
    "## RUNNING THROUGH ALL VECTORS, NOT JUST THE FIRST TWO\n",
    "> In 061, we only checked against the first two vectors, since we knew we were only pulling those two vectors in the testing set of attack vectors.  This NB tests against all vectors, and thus we expect a decrease in precision (since we are testing all the vectors instead of just some).  Recall and accuracu will likely remain similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d264c4d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', None)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "plt.rcParams.update({'font.size': 18})\n",
    "plt.rc('legend', fontsize=12) \n",
    "\n",
    "import numpy as np\n",
    "import random\n",
    "from scipy.special import rel_entr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "74f8490c",
   "metadata": {},
   "outputs": [],
   "source": [
    "################## DATA FRAME ##################\n",
    "datafile = 'Data/Fitbit_Kaggle/dailyActivity_merged.csv'\n",
    "all_fields = ['Id', 'ActivityDate', 'TotalSteps', 'TotalDistance', 'TrackerDistance', \n",
    "          'VeryActiveDistance', 'ModeratelyActiveDistance', 'LightActiveDistance', 'SedentaryActiveDistance', \n",
    "          'VeryActiveMinutes', 'FairlyActiveMinutes', 'LightlyActiveMinutes', 'SedentaryMinutes', 'Calories']\n",
    "\n",
    "#pd.set_option('display.max_rows', 100)\n",
    "df = pd.read_csv(datafile, skipinitialspace=True, usecols=all_fields)\n",
    "fields = 'FairlyActiveMinutes'\n",
    "selected_data = df[['Id',fields]]\n",
    "n_rows, n_cols = df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e39c768c",
   "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>Id</th>\n",
       "      <th>FairlyActiveMinutes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1503960366</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1503960366</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1503960366</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1503960366</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1503960366</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "           Id  FairlyActiveMinutes\n",
       "0  1503960366                   13\n",
       "1  1503960366                   19\n",
       "2  1503960366                   11\n",
       "3  1503960366                   34\n",
       "4  1503960366                   10"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e670f502",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_IDs = df.Id.unique()\n",
    "num_users = len(all_IDs)\n",
    "\n",
    "user_dict = dict()\n",
    "for idx, user in enumerate(all_IDs):\n",
    "    temp_df = df.loc[df['Id'] == user]\n",
    "    user_dict[user] = temp_df[fields].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "47fef0c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_IDs = all_IDs[[0, 1]]  # [0, 5, 6, 10, 11, 15, 16, 20, 25, 30]\n",
    "training_IDs = [ID for ID in all_IDs if ID not in test_IDs]\n",
    "attack_IDs = list(test_IDs) + list(training_IDs[0:2])\n",
    "\n",
    "ths = [0,1,5,20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2ceb3473",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1503960366 1624580081]\n",
      "\n",
      "[13 19 11 34 10 20 16 31 12  8 27 21  5 14 23 11 28 12 34 35 15 24 22 24\n",
      "  6 46  8 11 31 23  0]\n",
      "\n",
      "[ 0  0  0  0  0  8 12  0  0 13  0  0  0  0  0  0  0  0  0  7  0  0  0  0\n",
      "  0  0  0  0  0  0  0]\n"
     ]
    }
   ],
   "source": [
    "print(test_IDs)\n",
    "print()\n",
    "print(user_dict[test_IDs[0]])\n",
    "print()\n",
    "print(user_dict[training_IDs[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d898a85f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51 16 58  4 42 13 33 58  0  0  0 15  0  1 41  0 53  0 71 24  7 94  0 12\n",
      "  6 17  0  6 19  0]\n",
      "30\n",
      "1644430081\n",
      "\n",
      "[ 0  0  0  0  0  8 12  0  0 13  0  0  0  0  0  0  0  0  0  7  0  0  0  0\n",
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      "31\n",
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      "31\n",
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      "\n",
      "[14  5  3  9 11 29  3  7 63 53 10  0 26  8 24 20 20 40 23 28  8 14 27 20\n",
      " 17  2  0 47 28 25 16]\n",
      "31\n",
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      "  0  0  0  0  0  0  0]\n",
      "31\n",
      "2320127002\n",
      "\n",
      "[13 32 48 24 72  7 16  7 43 26 27 35  0 11  0  9  0  0]\n",
      "18\n",
      "2347167796\n",
      "\n",
      "[21  8  0  0  1  8  6  0  5 10  0  5  1  0  5  0  7 23 20 18  7  6  0 23\n",
      "  5 11  0  0  0  0  0]\n",
      "31\n",
      "2873212765\n",
      "\n",
      "[ 0  8 25  0  0  2  7  0  3  9  0  2  7  0  2 13  0  0  4  0]\n",
      "20\n",
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      "\n",
      "[ 19  46  23  42  83  58  95  67  98   0  12  92  95   9  95  10   8  32\n",
      "  52  40 143  41  96  88  55  86 116 122 115   0]\n",
      "30\n",
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      "\n",
      "[15  0  0 18 21  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 11  0 46 42\n",
      "  0  0  0  5  0  8  0]\n",
      "31\n",
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      "\n",
      "[0 0 0 6]\n",
      "4\n",
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      "\n",
      "[ 0 15  9  0  0  0  9  0 18  0 19  0  5  8 21 47  8 18 38  0 11 26 13 34\n",
      " 11 28  0 14 12 18  0]\n",
      "31\n",
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      "\n",
      "[ 0 14 35  0  9  0  8 16 42 12 25  5  8 31 23 48  9 16 43 15  4 18 21 39\n",
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      "\n",
      "[ 0  0  0  0  0  0  6  0  0  0  0  0  0  0  1  1  0  0  0  0  4  2  0  6\n",
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      "31\n",
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      "\n",
      "[ 0  7  0 30 12 19 15  9  0 21 25  5  0 10 41 14 11 29 29  0  0 10  0  8\n",
      "  0 16 35 30 18 31  0]\n",
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      "\n",
      "[  0   0   0   8  24  66  30   8  29  41   0  66  95  15   8  16   9  19\n",
      "  36   0  40   0  15   5  16  46 125  12  37  41   0]\n",
      "31\n",
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      "\n",
      "[13  0 41 38  0  0  0 28  0 42 16  0  0 11 18 16 13 15  0  0  9 29  0 29\n",
      "  9  0  8 22 40  0  6]\n",
      "31\n",
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      "\n",
      "[16 11 30 54 56 37 32 23 16 74 30 24 65 38 32 16 51 36 45 72 20  8  9 21\n",
      " 16  0  0 11 37 15]\n",
      "30\n",
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      "\n",
      "[ 0  0  0  6 15  0  0  0 10 19  0  0  0  0  7  0  0  0  0  0  0  0  0  0\n",
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      "28\n",
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      "\n",
      "[ 0  0  0  0  0 12  0  0  0  0  0  0  0  3  0  0  0  0  0 95  0  0  0  0\n",
      "  0  0  0  0  0]\n",
      "29\n",
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      "\n",
      "[  0  18  24   0  18  24  31   0 113   0   0   0  18  13  30   0  13   0\n",
      "   9  34   0   0   0   0  35   5]\n",
      "26\n",
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      "\n",
      "[14 24  0  0  3 13 42 41  4 27 33 41  0 31  7 38  8 15 16  0 39 36 36 22\n",
      "  0  0 14 21 34  7  8]\n",
      "31\n",
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      "\n",
      "[ 8 22  6  0  0  0 31 17 33 34 50 25  0 24 22 12 16 42  0  0 14 31  0 23\n",
      " 13  0]\n",
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      "\n",
      "[ 6 26 32 21  0  0 51 69 13  6 59  0  0 39 33  6 48 36 17 15 26 36 12 14\n",
      " 35 42 27 50 23 40  4]\n",
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      "\n",
      "[ 8 12  5  8  6 21  6  7  5  6  3 14 33  9  5 10  9  8  1  0  0 22  8  9\n",
      " 15 20 14 12 10  7  4]\n",
      "31\n",
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      "\n",
      "[ 2 11 16  0 51  5 16  0 18 20  0 26  4 54 14  5 16 14  0]\n",
      "19\n",
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      "\n",
      "[15 14 21 23 21  0 10 19  8 16 12 10  0 16 18  4 10  7  0 10  4 20 10  3\n",
      "  5  0  0 13 13 10  6]\n",
      "31\n",
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      "\n",
      "[ 7 23  0  0  0  0 22 10 27 18 54 44 44  6 91  5 28 67 28  2  0  0  0  0\n",
      " 22  0 72  4 43 71  0]\n",
      "31\n",
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      "\n",
      "[ 0  0  0  0  0  0  0  0 10  0 20 45  8  0  0  0  0 14 20  0  0  0  0  0\n",
      "  0  0  0  0  0]\n",
      "29\n",
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      "\n",
      "[ 7 18 13  1 29 15  5 13 19 13  2  6  1  8  3  8  8  5  4 12  0  3  8 15\n",
      " 17 28  4 19 11 12  1]\n",
      "31\n",
      "8877689391\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for ID in training_IDs:\n",
    "    print(user_dict[ID])\n",
    "    print(len(user_dict[ID]))\n",
    "    print(ID)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d76f3627",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_elements = 31\n",
    "k_vec = [1,5,10,15,20,25,30]\n",
    "\n",
    "data_storage = np.zeros((len(attack_IDs), len(training_IDs), len(ths), max_elements, len(k_vec)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "10ba2dc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def isMatch(v1,v2,k,th):\n",
    "    '''\n",
    "    Are a match is there is a common k-subsequence that is matched with L1 dist <= th\n",
    "    '''\n",
    "    \n",
    "    # If len(v1)=31 and k=31, then this is range(0,1) ---- k <= len(v1)\n",
    "    for i in range(0,len(v1)-k+1):\n",
    "        #print(i)\n",
    "        a = np.array([v1[i:i+k]])\n",
    "        for j in range(0,len(v2)-k+1):\n",
    "            #b = np.array([v2[i:i+k]])  # Original code, different type of match, \n",
    "            b = np.array([v2[j:j+k]])  # Not run yet, this uses any sliding window\n",
    "            \n",
    "            # Should I zero pad b, truncate a, or just return false?\n",
    "            while (a.shape[1] > b.shape[1]):\n",
    "                b = np.append(b, 0)\n",
    "                b = np.reshape(b, (1, len(b)))\n",
    "            \n",
    "            if (np.linalg.norm((a - b), ord=1) <= th):\n",
    "                return True\n",
    "            \n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8720f5e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "matching_matrix = np.zeros((len(attack_IDs), len(training_IDs), len(ths), len(k_vec))) + 9\n",
    "for i, attack_ID in enumerate(attack_IDs):\n",
    "    #print(f\"{i} in attack_IDs\")\n",
    "    v1 = user_dict[attack_ID]\n",
    "    for k_idx, k in enumerate(k_vec):\n",
    "        #print(f\"{k_idx} in k_vec\")\n",
    "        for j, training_ID in enumerate(training_IDs):\n",
    "            #print(f\"{j} in training_IDs[:2]\")\n",
    "            #for k, training_value in enumerate(user_dict[training_ID]):\n",
    "            v2 = user_dict[training_ID]\n",
    "\n",
    "            for l, th in enumerate(ths):\n",
    "                if (isMatch(v1,v2,k,th)):\n",
    "                    #print(str(attack_ID) + \" vs \" + str(training_ID) + \" is a Match\")\n",
    "                    matching_matrix[i,j,l,k_idx] = 1\n",
    "                else:\n",
    "                    matching_matrix[i,j,l,k_idx] = 0\n",
    "            #print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a7bec321",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Th=0, k=1: Correct number of positives found (2)!\n",
      "Th=0, k=5: Correct number of positives found (2)!\n",
      "Th=0, k=10: Correct number of positives found (2)!\n",
      "Th=0, k=15: Correct number of positives found (2)!\n",
      "Th=0, k=20: Correct number of positives found (2)!\n",
      "Th=0, k=25: Correct number of positives found (2)!\n",
      "Th=0, k=30: Correct number of positives found (2)!\n",
      "Th=1, k=1: Correct number of positives found (2)!\n",
      "Th=1, k=5: Correct number of positives found (2)!\n",
      "Th=1, k=10: Correct number of positives found (2)!\n",
      "Th=1, k=15: Correct number of positives found (2)!\n",
      "Th=1, k=20: Correct number of positives found (2)!\n",
      "Th=1, k=25: Correct number of positives found (2)!\n",
      "Th=1, k=30: Correct number of positives found (2)!\n",
      "Th=5, k=1: Correct number of positives found (2)!\n",
      "Th=5, k=5: Correct number of positives found (2)!\n",
      "Th=5, k=10: Correct number of positives found (2)!\n",
      "Th=5, k=15: Correct number of positives found (2)!\n",
      "Th=5, k=20: Correct number of positives found (2)!\n",
      "Th=5, k=25: Correct number of positives found (2)!\n",
      "Th=5, k=30: Correct number of positives found (2)!\n",
      "Th=20, k=1: Correct number of positives found (2)!\n",
      "Th=20, k=5: Correct number of positives found (2)!\n",
      "Th=20, k=10: Correct number of positives found (2)!\n",
      "Th=20, k=15: Correct number of positives found (2)!\n",
      "Th=20, k=20: Correct number of positives found (2)!\n",
      "Th=20, k=25: Correct number of positives found (2)!\n",
      "Th=20, k=30: Correct number of positives found (2)!\n"
     ]
    }
   ],
   "source": [
    "n_attack_training = len(attack_IDs) - len(test_IDs)\n",
    "true_positives = np.zeros((len(ths), len(k_vec)))\n",
    "false_negatives = np.zeros((len(ths), len(k_vec)))\n",
    "\n",
    "for attack_idx, attack_ID in enumerate(attack_IDs):\n",
    "    if attack_ID in training_IDs:\n",
    "        label_idx = training_IDs.index(attack_ID)\n",
    "        for j in range(len(ths)):\n",
    "            for k_idx in range(len(k_vec)):\n",
    "                if matching_matrix[attack_idx, label_idx, j, k_idx] == 1:\n",
    "                    true_positives[j, k_idx] += 1\n",
    "                else:\n",
    "                    false_negatives[j, k_idx] += 1                    \n",
    "                    \n",
    "for j in range(len(ths)):\n",
    "    for k_idx in range(len(k_vec)):\n",
    "        #print(f\"{j}, {k_idx}\")\n",
    "        if true_positives[j, k_idx] == n_attack_training:\n",
    "            # Note that this is not necessarily mean all of them were true positives\n",
    "            print(f\"Th={ths[j]}, k={k_vec[k_idx]}: Correct number of positives found ({int(true_positives[j, k_idx])})!\")\n",
    "        else:\n",
    "            print(f\"Th={ths[j]}, k={k_vec[k_idx]}: Incorrect number of positives... found ({int(true_positives[j, k_idx])}) vs expected ({n_attack_training})\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a41d88f6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Th=0, k=1: Precision of 1.61\n",
      "Th=0, k=1: Recall of 100.00\n",
      "Th=0, k=1: Accuracy of 96.49\n",
      "\n",
      "Th=0, k=5: Precision of 9.09\n",
      "Th=0, k=5: Recall of 100.00\n",
      "Th=0, k=5: Accuracy of 99.42\n",
      "\n",
      "Th=0, k=10: Precision of 15.38\n",
      "Th=0, k=10: Recall of 100.00\n",
      "Th=0, k=10: Accuracy of 99.68\n",
      "\n",
      "Th=0, k=15: Precision of 66.67\n",
      "Th=0, k=15: Recall of 100.00\n",
      "Th=0, k=15: Accuracy of 99.97\n",
      "\n",
      "Th=0, k=20: Precision of 100.00\n",
      "Th=0, k=20: Recall of 100.00\n",
      "Th=0, k=20: Accuracy of 100.00\n",
      "\n",
      "Th=0, k=25: Precision of 100.00\n",
      "Th=0, k=25: Recall of 100.00\n",
      "Th=0, k=25: Accuracy of 100.00\n",
      "\n",
      "Th=0, k=30: Precision of 100.00\n",
      "Th=0, k=30: Recall of 100.00\n",
      "Th=0, k=30: Accuracy of 100.00\n",
      "\n",
      "Th=1, k=1: Precision of 1.61\n",
      "Th=1, k=1: Recall of 100.00\n",
      "Th=1, k=1: Accuracy of 96.49\n",
      "\n",
      "Th=1, k=5: Precision of 8.33\n",
      "Th=1, k=5: Recall of 100.00\n",
      "Th=1, k=5: Accuracy of 99.37\n",
      "\n",
      "Th=1, k=10: Precision of 12.50\n",
      "Th=1, k=10: Recall of 100.00\n",
      "Th=1, k=10: Accuracy of 99.60\n",
      "\n",
      "Th=1, k=15: Precision of 40.00\n",
      "Th=1, k=15: Recall of 100.00\n",
      "Th=1, k=15: Accuracy of 99.91\n",
      "\n",
      "Th=1, k=20: Precision of 100.00\n",
      "Th=1, k=20: Recall of 100.00\n",
      "Th=1, k=20: Accuracy of 100.00\n",
      "\n",
      "Th=1, k=25: Precision of 100.00\n",
      "Th=1, k=25: Recall of 100.00\n",
      "Th=1, k=25: Accuracy of 100.00\n",
      "\n",
      "Th=1, k=30: Precision of 100.00\n",
      "Th=1, k=30: Recall of 100.00\n",
      "Th=1, k=30: Accuracy of 100.00\n",
      "\n",
      "Th=5, k=1: Precision of 1.61\n",
      "Th=5, k=1: Recall of 100.00\n",
      "Th=5, k=1: Accuracy of 96.49\n",
      "\n",
      "Th=5, k=5: Precision of 4.55\n",
      "Th=5, k=5: Recall of 100.00\n",
      "Th=5, k=5: Accuracy of 98.79\n",
      "\n",
      "Th=5, k=10: Precision of 10.53\n",
      "Th=5, k=10: Recall of 100.00\n",
      "Th=5, k=10: Accuracy of 99.51\n",
      "\n",
      "Th=5, k=15: Precision of 33.33\n",
      "Th=5, k=15: Recall of 100.00\n",
      "Th=5, k=15: Accuracy of 99.88\n",
      "\n",
      "Th=5, k=20: Precision of 66.67\n",
      "Th=5, k=20: Recall of 100.00\n",
      "Th=5, k=20: Accuracy of 99.97\n",
      "\n",
      "Th=5, k=25: Precision of 100.00\n",
      "Th=5, k=25: Recall of 100.00\n",
      "Th=5, k=25: Accuracy of 100.00\n",
      "\n",
      "Th=5, k=30: Precision of 100.00\n",
      "Th=5, k=30: Recall of 100.00\n",
      "Th=5, k=30: Accuracy of 100.00\n",
      "\n",
      "Th=20, k=1: Precision of 1.61\n",
      "Th=20, k=1: Recall of 100.00\n",
      "Th=20, k=1: Accuracy of 96.49\n",
      "\n",
      "Th=20, k=5: Precision of 1.75\n",
      "Th=20, k=5: Recall of 100.00\n",
      "Th=20, k=5: Accuracy of 96.77\n",
      "\n",
      "Th=20, k=10: Precision of 3.64\n",
      "Th=20, k=10: Recall of 100.00\n",
      "Th=20, k=10: Accuracy of 98.47\n",
      "\n",
      "Th=20, k=15: Precision of 6.06\n",
      "Th=20, k=15: Recall of 100.00\n",
      "Th=20, k=15: Accuracy of 99.11\n",
      "\n",
      "Th=20, k=20: Precision of 15.38\n",
      "Th=20, k=20: Recall of 100.00\n",
      "Th=20, k=20: Accuracy of 99.68\n",
      "\n",
      "Th=20, k=25: Precision of 22.22\n",
      "Th=20, k=25: Recall of 100.00\n",
      "Th=20, k=25: Accuracy of 99.80\n",
      "\n",
      "Th=20, k=30: Precision of 40.00\n",
      "Th=20, k=30: Recall of 100.00\n",
      "Th=20, k=30: Accuracy of 99.91\n",
      "\n"
     ]
    }
   ],
   "source": [
    "precision = np.zeros((len(ths), len(k_vec)))\n",
    "recall = np.zeros((len(ths), len(k_vec)))\n",
    "accuracy = np.zeros((len(ths), len(k_vec)))\n",
    "\n",
    "for j in range(len(ths)):\n",
    "    for k_idx in range(len(k_vec)):\n",
    "        all_positives = np.count_nonzero(matching_matrix[:,:,j,k_idx] == 1) \n",
    "        false_positives = all_positives - true_positives[j, k_idx]\n",
    "        true_negatives = np.product(matching_matrix.shape) - all_positives - false_negatives[j, k_idx]\n",
    "\n",
    "        precision[j, k_idx] = true_positives[j, k_idx] / (true_positives[j, k_idx] + false_positives)\n",
    "        print(f\"Th={ths[j]}, k={k_vec[k_idx]}: Precision of {precision[j, k_idx]*100:.2f}\")\n",
    "        recall[j, k_idx] = true_positives[j, k_idx] / (true_positives[j, k_idx] + false_negatives[j, k_idx])\n",
    "        print(f\"Th={ths[j]}, k={k_vec[k_idx]}: Recall of {recall[j, k_idx]*100:.2f}\")\n",
    "        accuracy[j, k_idx] = (true_positives[j, k_idx] + true_negatives) / np.product(matching_matrix.shape)\n",
    "        print(f\"Th={ths[j]}, k={k_vec[k_idx]}: Accuracy of {accuracy[j, k_idx]*100:.2f}\")\n",
    "        print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2f08dfb",
   "metadata": {},
   "source": [
    "## Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9d0ab928",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constant x vec representing k (?)\n",
    "my_xs = []\n",
    "\n",
    "# Make one y vec for each threshold\n",
    "my_pres1 = []\n",
    "my_pres2 = []\n",
    "my_pres3 = []\n",
    "my_pres4 = []\n",
    "\n",
    "my_rec1 = []\n",
    "my_rec2 = []\n",
    "my_rec3 = []\n",
    "my_rec4 = []\n",
    "\n",
    "my_acc1 = []\n",
    "my_acc2 = []\n",
    "my_acc3 = []\n",
    "my_acc4 = []\n",
    "\n",
    "for k_idx in range(len(k_vec)):\n",
    "    my_xs.append(k_vec[k_idx])\n",
    "    \n",
    "    for j in range(len(ths)):\n",
    "        if j==0:\n",
    "            my_pres1.append(precision[j, k_idx])\n",
    "            my_rec1.append(recall[j, k_idx])\n",
    "            my_acc1.append(accuracy[j, k_idx])\n",
    "        elif j==1:\n",
    "            my_pres2.append(precision[j, k_idx])\n",
    "            my_rec2.append(recall[j, k_idx])\n",
    "            my_acc2.append(accuracy[j, k_idx])\n",
    "        elif j==2:\n",
    "            my_pres3.append(precision[j, k_idx])\n",
    "            my_rec3.append(recall[j, k_idx])\n",
    "            my_acc3.append(accuracy[j, k_idx])\n",
    "        elif j==3:\n",
    "            my_pres4.append(precision[j, k_idx])\n",
    "            my_rec4.append(recall[j, k_idx])\n",
    "            my_acc4.append(accuracy[j, k_idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a18ac279",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 0.7       # the width of the bars\n",
    "plt.figure(figsize=(12,8))\n",
    "rects1 = plt.bar(my_xs, my_pres1, width, color='r')\n",
    "rects2 = plt.bar(np.array(my_xs, int)+width, my_pres2, width, color='darkorange')\n",
    "rects3 = plt.bar(np.array(my_xs, float)+2*width, my_pres3, width, color='yellow')\n",
    "rects4 = plt.bar(np.array(my_xs, float)+3*width, my_pres4, width, color='gold')\n",
    "plt.ylabel('Precision')\n",
    "plt.xlabel('K')\n",
    "plt.title('Precision as a Function of K and Threshold')\n",
    "plt.xticks(my_xs)\n",
    "plt.legend((rects1[0], rects2[0], rects3[0], rects4[0]), ('Thresh=0', 'Thresh=1', 'Thresh=5', 'Thresh=20'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c8643caa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G4544hm3vHMO2e49hvPxEXatk87xe40k7nRja/MTR5ieGNj9xxvLdsFljOO4OY9j26XWvskZbjzokecJNZE/0oiQvGTY9M8lDo63YWruotTa3tTZ3xowZG6U4AABYk4kM0Vcn+fXqOSjJk621xRNYDwAArJeBheiquizJjUlmV9Wiqvqtqjqtqk7rr3JNkvuS3Jvk4iT/36BqAQCgu8ceX5qh+SdmaP6J2XnnI7LbbkdlaOjETJ/+6syZs2Dcj3f2hy/KeR/93AZt+6UvfSn77rtvXvCCF2Rj3A55YGOiW2snrGN5S/L2QR0fAGCL84UxjEVPkrtHTB9x01pX3+FF03Prt7+QJDn7zy7KtttunXe/+01ZuPChHH30mes83MqVKzN58sb5Ct5+++2XL3/5y3nrW9+6UY7niYUAAHT2zDPP5pRTPpzvfvf72W23nXLVVedl6623yvz5b82rXrV//u7v/ilveMN/yvz5B+R33vU/s3z509lxx+n5zKf+MLvssmMu+OTlufAvvpzJkydlzt6zcvln/1uS5PY77s/8I96aHz3wr3nX6SfkjN9dvy8WbuyH0gjRAAB0ds89D+Syyz6ciy/+gyxY8L5ceeU3c/LJRyVJli5dluuuuygrVqzMvHmn5qrLz8+MGdvni1f8dd5/9idzyac+mHPPuzT333FVpk2bmqVLl63e7513L8y3vnFhli37cWYPvTFvO+OcTJkyJYccckiWLVv2nDrOO++8HHrooRvtvFcRogEA6GzWrF0zNDQ7SXLAAXtn4cL/d3+I4447LEly110L84Mf3JfDju6N4H3m2Wezy847Jkn23+9lOektH8ixr5+XY18/f/W2rzvy4EybNjXTpk3NTjO2z8MPP5yZM2fmhhtu2Ehntn6EaAAAOps2bcrq15MmvSBPP/3M6ultttk6SdJasu++e+bGb17ynO2//pWP5vrv/J9c/fXr86FzP53bbvniqPtduXJlkuiJBgDg+WH27JdmyZIncuM/fD+v/JX9s2LFytx9zw+zz96z8sCih/PqeXNz8KuG8oW/ujbLl6/9iSx6ogEAeF6YOnVKrrji3Jxx+vl58qnlWblyZd719hPy8r1empN/84N58qnlaa3lzNNPyPTp243pWF/5ylfyjne8I0uWLMnrXve6DA0N5dprrx2nM3mu6t1pbvMxd+7ctjHu/Tcqj5Zdfx4HO3G004mhzU8cbX5iaPMbxR133PHcu0547PdAjHatq+qW1tqoBUzkEwsBAGCzJEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AACjeuzxpRmaf2KG5p+YnXc+IrvtdlSGhk7M9Omvzpw5C8b9eGd/+KKc99HPbdi2Z5+d3XbbLUNDQxkaGso111wzztX9LA9bAQDYbFQynrdNfuymtS7e4UXTc+u3v5AkOfvPLsq2226dd7/7TVm48KEcffSZ69z9ypUrM3nyxoubZ555Zt797ndvlGPpiQYAoLNnnnk2p5zy4ey774IcfvjpefrpnyRJ5s9/a8466xOZN+/UfOxjl+eWW+7IvMNPzQGvelOOeMM7snjxo0mSCz55eeb80oLsf+AJOf7Xz1q939vvuD/zj3hr9pxzTC745OUTcm7rQ080AACd3XPPA7nssg/n4ov/IAsWvC9XXvnNnHzyUUmSpUuX5brrLsqKFSszb96puery8zNjxvb54hV/nfef/clc8qkP5tzzLs39d1yVadOmZunSZav3e+fdC/Otb1yYZct+nNlDb8zbzjgnU6ZMySGHHJJly5Y9p47zzjsvhx56aJLk4x//eD772c9m7ty5Of/887P99tsP7PyFaAAAOps1a9cMDc1OkhxwwN5ZuHDx6mXHHXdYkuSuuxbmBz+4L4cd/fYkyTPPPptddt4xSbL/fi/LSW/5QI59/bwc+/r5q7d93ZEHZ9q0qZk2bWp2mrF9Hn744cycOTM33HDDWut529velg984AOpqnzgAx/I7/7u7+aSSy4Zz1P+GUI0AACdTZs2ZfXrSZNekKeffmb19DbbbJ0kaS3Zd989c+M3nxtmv/6Vj+b67/yfXP316/Ohcz+d22754qj7XblyZZKssyf6xS9+8ep5p5xySo4++ugxnuHaCdEAAAzE7NkvzZIlT+TGf/h+Xvkr+2fFipW5+54fZp+9Z+WBRQ/n1fPm5uBXDeULf3Vtli9/eq37WldP9OLFi7PLLrskSb7yla9kv/32G7fzGI0QDQDAQEydOiVXXHFuzjj9/Dz51PKsXLky73r7CXn5Xi/Nyb/5wTz51PK01nLm6Sdk+vTtxnSs3//938+tt96aqsoee+yRT33qU+N0FqOr1tpADzDe5s6d226++eaJOXjVhm/7+TEc98QxbHvnGLbdewxtY6KuVbJ5Xq/xpJ1ODG1+4mjzE0Ob3yjuuOOO7LPPPj87cyw5aNYYitlhDNuuvZN57bYez3v6rdlo17qqbmmtjVqAW9wBAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDADCqxx5fmqH5J2Zo/onZeecjsttuR2Vo6MRMn/7qzJmzYNyPd/aHL8p5H/3cBm37e7/3e9l7772z//7751d/9VezdOnS1cvOOeecvOxlL8vs2bNz7bXXjkutHrYCALC5uLOSbcew/ZIR0zNuWuvqO7xoem799heSJGf/2UXZdtut8+53vykLFz6Uo48+c52HW7lyZSZP3jhx87DDDss555yTyZMn5z3veU/OOeecfOQjH8ntt9+eyy+/PLfddlseeuihHHroobn77rszadKkMR1PTzQAAJ0988yzOeWUD2fffRfk8MNPz9NP/yRJMn/+W3PWWZ/IvHmn5mMfuzy33HJH5h1+ag541ZtyxBvekcWLH02SXPDJyzPnlxZk/wNPyPG/ftbq/d5+x/2Zf8Rbs+ecY3LBJy9f73oOP/zw1YH9oIMOyqJFi5IkV111VY4//vhMmzYts2bNyste9rL84z/+45jPX080AACd3XPPA7nssg/n4ov/IAsWvC9XXvnNnHzyUUmSpUuX5brrLsqKFSszb96puery8zNjxvb54hV/nfef/clc8qkP5tzzLs39d1yVadOmZunSZav3e+fdC/Otb1yYZct+nNlDb8zbzjgnU6ZMySGHHJJly5Y9p47zzjsvhx566M/Mu+SSS3LcccclSR588MEcdNBBq5fNnDkzDz744JjPX4gGAKCzWbN2zdDQ7CTJAQfsnYULF69edtxxhyVJ7rprYX7wg/ty2NFvT5I88+yz2WXnHZMk++/3spz0lg/k2NfPy7Gvn79629cdeXCmTZuaadOmZqcZ2+fhhx/OzJkzc8MNN6xXXX/yJ3+SyZMn56STTkqStPbcx7XXWB5b3ydEAwDQ2bRpU1a/njTpBXn66WdWT2+zzdZJktaSfffdMzd+85LnbP/1r3w013/n/+Tqr1+fD5376dx2yxdH3e/KlSuTZL16oi+99NJ87Wtfy9/+7d+uDsozZ87MAw88sHr9RYsWZdddd93g815FiAYAYCBmz35plix5Ijf+w/fzyl/ZPytWrMzd9/ww++w9Kw8sejivnjc3B79qKF/4q2uzfPnTa93Xunqiv/GNb+QjH/lIrrvuurzwhS9cPf8Nb3hDTjzxxPzO7/xOHnroodxzzz058MADx3xuQjQAAAMxdeqUXHHFuTnj9PPz5FPLs3Llyrzr7Sfk5Xu9NCf/5gfz5FPL01rLmaefkOnTtxvTsU4//fT8+7//ew47rDeU5KCDDsqFF16YfffdNwsWLMicOXMyefLkfOITnxjznTmSpEYbJ7Ipmzt3brv55psn5uBjGT/z+TEc98QxbHvnGLbdewxtY6KuVbJ5Xq/xpJ1ODG1+4mjzE0Ob3yjuuOOO7LPPPj87cyw5aNYYitlhDNuuvZN57baeO4aN199o17qqbmmtjVqAW9wBAEBHQjQAAHQkRAMAQEdCNADAJmxz+/7a5mhDrrEQDQCwidpqq63y2GOPCdID1FrLY489lq222qrTdm5xBwCwiZo5c2YWLVqUJUuW/L+Zjz46McU8MoZtV4xh2yl3jGHj9bPVVltl5syZnbYRogEANlFTpkzJrFkj7ks3Z86G79BtHceN4RwAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdDTREV9WRVXVXVd1bVe8dZfnPV9X/qqp/qqrbquotg6wHAADGw8BCdFVNSvKJJK9NMifJCVU1Z8Rqb09ye2vtFUnmJzm/qqYOqiYAABgPg+yJPjDJva21+1prP01yeZJjRqzTkmxXVZVk2ySPJ1k5wJoAAGDMBhmid0vywLDpRf15w308yT5JHkryz0ne2Vp7duSOqurUqrq5qm5esmTJoOoFAID1MsgQXaPMayOmj0hya5Jdkwwl+XhV/dxzNmrtotba3Nba3BkzZox3nQAA0MkgQ/SiJC8ZNj0zvR7n4d6S5Mut594k9yfZe4A1AQDAmA0yRN+UZK+qmtX/suDxSa4esc6PkrwmSarqxUlmJ7lvgDUBAMCYTR7UjltrK6vq9CTXJpmU5JLW2m1VdVp/+YVJPpTkM1X1z+kN/3hPa+3RQdUEAADjYWAhOklaa9ckuWbEvAuHvX4oyeGDrAEAAMabJxYCAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQ00BBdVUdW1V1VdW9VvXcN68yvqlur6raqum6Q9QAAwHiYPKgdV9WkJJ9IcliSRUluqqqrW2u3D1tnepJPJjmytfajqtppUPUAAMB4GWRP9IFJ7m2t3dda+2mSy5McM2KdE5N8ubX2oyRprT0ywHoAAGBcDDJE75bkgWHTi/rzhnt5ku2r6ttVdUtV/fpoO6qqU6vq5qq6ecmSJQMqFwAA1s8gQ3SNMq+NmJ6c5IAkr0tyRJIPVNXLn7NRaxe11ua21ubOmDFj/CsFAIAOBjYmOr2e55cMm56Z5KFR1nm0tfZvSf6tqq5P8ookdw+wLgAAGJNB9kTflGSvqppVVVOTHJ/k6hHrXJXkkKqaXFUvTPIrSe4YYE0AADBmA+uJbq2trKrTk1ybZFKSS1prt1XVaf3lF7bW7qiqbyT5fpJnk/xFa+0Hg6oJAADGwyCHc6S1dk2Sa0bMu3DE9P9I8j8GWQcAAIwnTywEAICOhGgAAOhIiAYAgI6EaAAA6EiIBgCAjoRoAADoSIgGAICOhGgAAOhIiAYAgI6EaAAA6EiIBgCAjoRoAADoSIgGAICOhGgAAOho8toWVtWyJG20RUlaa+3nBlIVAABswtYaoltr222sQgAAYHOxrp7oF61teWvt8fEtBwAANn1rDdFJbklvOEeNsqwl2XPcKwIAgE3cuoZzzNpYhQAAwOZiXT3Rq1XV9kn2SrLVqnmttesHURQAAGzK1itEV9VvJ3lnkplJbk1yUJIbk/zngVUGAACbqPW9T/Q7k/xykh+21l6d5BeTLBlYVQAAsAlb3xD9k9baT5Kkqqa11u5MMntwZQEAwKZrfcdEL6qq6Um+muRvquqJJA8NqigAANiUrVeIbq39av/l2VX1rSQ/n+QbA6sKAAA2Yes1nKOqDqqq7ZKktXZdkm+lNy4aAACed9Z3TPSfJ1k+bPrf+vMAAOB5Z31DdLXW2qqJ1tqz6XCPaQAA2JKsb4i+r6rOqKop/Z93JrlvkIUBAMCman1D9GlJXpXkwSSLkvxKklMHVRQAAGzK1vfuHI8kOX7AtQAAwGZhfe/O8fKq+tuq+kF/ev+q+oPBlgYAAJum9R3OcXGS9yVZkSStte9HzzQAAM9T6xuiX9ha+8cR81aOdzEAALA5WN8Q/WhV/UKSliRV9cYkiwdWFQAAbMLW917Pb09yUZK9q+rBJPcnOWlgVQEAwCZsfe/OcV+SQ6tqm/R6r59OclySHw6wNgAA2CStdThHVf1cVb2vqj5eVYcl+XGSNye5N8mCjVEgAABsatbVE/25JE8kuTHJKUl+P8nUJMe21m4dbGkAALBpWleI3rO19h+SpKr+IsmjSXZvrS0beGUAALCJWtfdOVasetFaeybJ/QI0AADPd+vqiX5FVT3Vf11Jtu5PV5LWWvu5gVYHAACboLWG6NbapI1VCAAAbC7W92ErAABAnxANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAADQkRANAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQ00RFfVkVV1V1XdW1XvXct6v1xVz1TVGwdZDwAAjIeBheiqmpTkE0lem2ROkhOqas4a1vtIkmsHVQsAAIynQfZEH5jk3tbafa21nya5PMkxo6z3jiRXJnlkgLUAAMC4GWSI3i3JA8OmF/XnrVZVuyX51SQXDrAOAAAYV4MM0TXKvDZi+qNJ3tNae2atO6o6tapurqqblyxZMl71AQDABpk8wH0vSvKSYdMzkzw0Yp25SS6vqiTZMclRVbWytfbV4Su11i5KclGSzJ07d2QQBwCAjWqQIfqmJHtV1awkDyY5PsmJw1dorc1a9bqqPpPkayMDNAAAbGoGFqJbayur6vT07roxKcklrbXbquq0/nLjoAEA2CwNsic6rbVrklwzYt6o4bm19huDrAUAAMaLJxYCAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQ00BBdVUdW1V1VdW9VvXeU5SdV1ff7P9+tqlcMsh4AABgPAwvRVTUpySeSvDbJnCQnVNWcEavdn2Rea23/JB9KctGg6gEAgPEyyJ7oA5Pc21q7r7X20ySXJzlm+Aqtte+21p7oT/59kpkDrAcAAMbFIEP0bkkeGDa9qD9vTX4ryf8eYD0AADAuJg9w3zXKvDbqilWvTi9EH7yG5acmOTVJdt999/GqDwAANsgge6IXJXnJsOmZSR4auVJV7Z/kL5Ic01p7bLQdtdYuaq3Nba3NnTFjxkCKBQCA9TXIEH1Tkr2qalZVTU1yfJKrh69QVbsn+XKSN7XW7h5gLQAAMG4GNpyjtbayqk5Pcm2SSUkuaa3dVlWn9ZdfmOSDSXZI8smqSpKVrbW5g6oJAADGwyDHRKe1dk2Sa0bMu3DY699O8tuDrAEAAMabJxYCAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQkRAMAQEdCNAAAdCREAwBAR0I0AAB0JEQDAEBHQjQAAHQ00BBdVUdW1V1VdW9VvXeU5VVVF/SXf7+qfmmQ9QAAwHgYWIiuqklJPpHktUnmJDmhquaMWO21Sfbq/5ya5M8HVQ8AAIyXQfZEH5jk3tbafa21nya5PMkxI9Y5JslnW8/fJ5leVbsMsCYAABizQYbo3ZI8MGx6UX9e13UAAGCTUq21wey46r8mOaK19tv96TclObC19o5h63w9yTmtte/0p/82ye+31m4Zsa9T0xvukSSzk9w1kKLHZsckj050EZsR12tiuO4Tx7WfGK77xHHtJ4brPr5e2lqbMdqCyQM86KIkLxk2PTPJQxuwTlprFyW5aLwLHE9VdXNrbe5E17G5cL0mhus+cVz7ieG6TxzXfmK47hvPIIdz3JRkr6qaVVVTkxyf5OoR61yd5Nf7d+k4KMmTrbXFA6wJAADGbGA90a21lVV1epJrk0xKcklr7baqOq2//MIk1yQ5Ksm9SX6c5C2DqgcAAMbLIIdzpLV2TXpBefi8C4e9bknePsgaNqJNerjJJsj1mhiu+8Rx7SeG6z5xXPuJ4bpvJAP7YiEAAGypPPYbAAA6EqLHqKouqapHquoHE13L5qCqFlbVP1fVrVV180TXsyUbrW1W1Yuq6m+q6p7+n9tPZI1bqjVc+7Or6sF+27+1qo6ayBq3RFX1kqr6VlXdUVW3VdU7+/O1+wFay3XX5gesqraqqn+sqn/qX/s/6s/X5jcCwznGqKr+U5Ll6T15cb+JrmdTV1ULk8xtrbmH5YCN1jar6r8neby1dm5VvTfJ9q2190xknVuiNVz7s5Msb62dN5G1bcn6T7zdpbX2varaLsktSY5N8hvR7gdmLdd9QbT5gaqqSrJNa215VU1J8p0k70zya9HmB05P9Bi11q5P8vhE1wEjraFtHpPk0v7rS9P7j45x5t+FidFaW9xa+17/9bIkd6T3FFztfoDWct0ZsNazvD85pf/Tos1vFEI0G1tL8tdVdUv/SZRsXC9edS/2/p87TXA9zzenV9X3+8M9fLw6QFW1R5JfTPIP0e43mhHXPdHmB66qJlXVrUkeSfI3rTVtfiMRotnY/mNr7ZeSvDbJ2/sfe8PzwZ8n+YUkQ0kWJzl/QqvZglXVtkmuTPKu1tpTE13P88Uo112b3whaa8+01obSe+rzgVVlaOlGIkSzUbXWHur/+UiSryQ5cGIret55uD9+cdU4xkcmuJ7njdbaw/3/7J5NcnG0/YHojwu9MsnnW2tf7s/W7gdstOuuzW9crbWlSb6d5Mho8xuFEM1GU1Xb9L90kqraJsnhSdzVZOO6Osmb+6/fnOSqCazleWXVf2h9vxptf9z1v2T16SR3tNb+dNgi7X6A1nTdtfnBq6oZVTW9/3rrJIcmuTPa/Ebh7hxjVFWXJZmfZMckDyf5w9bapye0qE1UVe2ZXu9z0nta5hdaa38ygSVt0UZrm0m+muSvkuye5EdJ/mtrzRfgxtkarv389D7WbkkWJnnrqjGLjI+qOjjJDUn+Ocmz/dlnpTc+V7sfkLVc9xOizQ9UVe2f3hcHJ6XXMfpXrbU/rqodos0PnBANAAAdGc4BAAAdCdEAANCREA0AAB0J0QAA0JEQDQAAHQnRAFuwqlo+7PVRVXVPVe0+kTUBbAkmT3QBAAxeVb0myZ8lOby19qOJrgdgcydEA2zhquqQ9B67fFRr7V8muh6ALYGHrQBswapqRZJlSea31r4/0fUAbCmMiQbYsq1I8t0kvzXRhQBsSYRogC3bs0kWJPnlqjproosB2FIYEw2whWut/biqjk5yQ1U93Fr79ETXBLC5E6IBngdaa49X1ZFJrq+qR1trV010TQCbM18sBACAjoyJBgCAjoRoAADoSIgGAICOhGgAAOhIiAYAgI6EaAAA6EiIBgCAjoRoAADo6P8CSUCUQNJEGXcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 0.8       # the width of the bars\n",
    "plt.figure(figsize=(12,8))\n",
    "rects1 = plt.bar(my_xs, my_rec1, width, color='r')\n",
    "rects2 = plt.bar(np.array(my_xs, int)+width, my_rec2, width, color='orange')\n",
    "rects3 = plt.bar(np.array(my_xs, float)+2*width, my_rec3, width, color='yellow')\n",
    "rects4 = plt.bar(np.array(my_xs, float)+3*width, my_rec4, width, color='gold')\n",
    "plt.ylabel('Recall')\n",
    "#plt.ylim((0.995, 1.005))\n",
    "plt.xlabel('K')\n",
    "plt.title('Recall as a Function of K and Threshold')\n",
    "plt.xticks(my_xs)\n",
    "plt.legend((rects1[0], rects2[0], rects3[0], rects4[0]), ('Thresh=0', 'Thresh=1', 'Thresh=5', 'Thresh=20'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "feff0b1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 0.8       # the width of the bars\n",
    "plt.figure(figsize=(12,8))\n",
    "rects1 = plt.bar(my_xs, my_acc1, width, color='r')\n",
    "rects2 = plt.bar(np.array(my_xs, int)+width, my_acc2, width, color='orange')\n",
    "rects3 = plt.bar(np.array(my_xs, float)+2*width, my_acc3, width, color='yellow')\n",
    "rects4 = plt.bar(np.array(my_xs, float)+3*width, my_acc4, width, color='gold')\n",
    "plt.ylim((0.96, 1.001))\n",
    "plt.ylabel('Accuracy')\n",
    "plt.xlabel('K')\n",
    "plt.title('Accuracy as a Function of K and Threshold')\n",
    "plt.xticks(my_xs)\n",
    "plt.legend((rects1[0], rects2[0], rects3[0], rects4[0]), ('Thresh=0', 'Thresh=1', 'Thresh=5', 'Thresh=20'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2565cc2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}