Scoring Example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook serves to act as an example of outlier scoring using the developed methodology contained within this repository, as well as some basic ways to visualize the data for analysis. The outlier scoring module is called 'kinship.py' as it is a k-Nearest Neighbors method to identify the objects in the least dense regions of feature space. This notebook uses an example 'Cluster Outlier Object' (coo) for which features have already been calculated.\n",
    "\n",
    "Last updated by Daniel Giles on 2/28/2020."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some standard imports for math and data handling\n",
    "import sys\n",
    "import numpy as np\n",
    "np.set_printoptions(threshold=sys.maxsize)\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_columns',100)\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle\n",
    "\n",
    "from sklearn import preprocessing\n",
    "\n",
    "# Import the custom code developed for this work\n",
    "sys.path.append('python')\n",
    "from clusterOutliers import clusterOutliers as coo\n",
    "import quarterTools as qt\n",
    "import kinship\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This data is derived from a subset of long cadence lightcurves\n",
    "from Quarter 8 of Data Release 25 of the Kepler prime mission.\n",
    "Quarter 8 of the Kepler data contains 3 month long lightcurves\n",
    "sampled every 30 minutes.\n",
    "Quarter 8 also contains Boyajian's star, a known anomaly.\n",
    "Features are calculated via keplerml.py which provide measurements\n",
    "of variability.\n",
    "\"\"\"\n",
    "with open('data/output/Q8_sample.coo','rb') as file:\n",
    "    Q8 = pickle.load(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "                                      longtermtrend  meanmedrat     skews  \\\n",
       "kplr000757076-2011073133259_llc.fits  -7.336779e-07    1.000003  0.052550   \n",
       "kplr000757099-2011073133259_llc.fits   1.141257e-05    0.998371 -0.242674   \n",
       "kplr000757137-2011073133259_llc.fits  -2.126846e-07    0.999979 -0.102988   \n",
       "kplr000757280-2011073133259_llc.fits   1.619512e-07    0.999989 -0.131370   \n",
       "kplr000757450-2011073133259_llc.fits  -7.148782e-06    0.999703 -0.297628   \n",
       "\n",
       "                                             varss  coeffvar      stds  \\\n",
       "kplr000757076-2011073133259_llc.fits  3.715534e-08  0.000193  0.000193   \n",
       "kplr000757099-2011073133259_llc.fits  1.980448e-04  0.014096  0.014073   \n",
       "kplr000757137-2011073133259_llc.fits  4.099948e-07  0.000640  0.000640   \n",
       "kplr000757280-2011073133259_llc.fits  5.975731e-08  0.000244  0.000244   \n",
       "kplr000757450-2011073133259_llc.fits  1.026218e-05  0.003204  0.003203   \n",
       "\n",
       "                                     numoutliers numnegoutliers  \\\n",
       "kplr000757076-2011073133259_llc.fits           2              0   \n",
       "kplr000757099-2011073133259_llc.fits           0              0   \n",
       "kplr000757137-2011073133259_llc.fits           0              0   \n",
       "kplr000757280-2011073133259_llc.fits           0              0   \n",
       "kplr000757450-2011073133259_llc.fits          17             16   \n",
       "\n",
       "                                     numposoutliers numout1s      kurt  \\\n",
       "kplr000757076-2011073133259_llc.fits              2      972  0.242376   \n",
       "kplr000757099-2011073133259_llc.fits              0     1196 -0.978336   \n",
       "kplr000757137-2011073133259_llc.fits              0      957  0.221703   \n",
       "kplr000757280-2011073133259_llc.fits              0     1126 -0.641047   \n",
       "kplr000757450-2011073133259_llc.fits              1      943  9.002654   \n",
       "\n",
       "                                           mad  maxslope  minslope  \\\n",
       "kplr000757076-2011073133259_llc.fits  0.000128  0.023703 -0.023006   \n",
       "kplr000757099-2011073133259_llc.fits  0.011042  0.522800 -0.513769   \n",
       "kplr000757137-2011073133259_llc.fits  0.000407  0.016571 -0.017038   \n",
       "kplr000757280-2011073133259_llc.fits  0.000183  0.012257 -0.013225   \n",
       "kplr000757450-2011073133259_llc.fits  0.002023  0.115150 -0.099047   \n",
       "\n",
       "                                      meanpslope  meannslope   g_asymm  \\\n",
       "kplr000757076-2011073133259_llc.fits    0.007895   -0.007714 -1.023481   \n",
       "kplr000757099-2011073133259_llc.fits    0.234838   -0.226238 -1.038011   \n",
       "kplr000757137-2011073133259_llc.fits    0.005815   -0.005764 -1.008851   \n",
       "kplr000757280-2011073133259_llc.fits    0.004338   -0.004448 -0.975237   \n",
       "kplr000757450-2011073133259_llc.fits    0.034572   -0.033941 -1.018571   \n",
       "\n",
       "                                      rough_g_asymm  diff_asymm  skewslope  \\\n",
       "kplr000757076-2011073133259_llc.fits       0.979605    0.000181   0.032752   \n",
       "kplr000757099-2011073133259_llc.fits       0.962705    0.008600   0.000094   \n",
       "kplr000757137-2011073133259_llc.fits       0.999356    0.000051  -0.042503   \n",
       "kplr000757280-2011073133259_llc.fits       1.027397   -0.000110  -0.007222   \n",
       "kplr000757450-2011073133259_llc.fits       0.991661    0.000630   0.169811   \n",
       "\n",
       "                                      varabsslope  varslope  meanabsslope  \\\n",
       "kplr000757076-2011073133259_llc.fits     0.000037  0.000098      0.007807   \n",
       "kplr000757099-2011073133259_llc.fits     0.021980  0.075090      0.230457   \n",
       "kplr000757137-2011073133259_llc.fits     0.000019  0.000053      0.005793   \n",
       "kplr000757280-2011073133259_llc.fits     0.000011  0.000031      0.004397   \n",
       "kplr000757450-2011073133259_llc.fits     0.004362  0.005535      0.034255   \n",
       "\n",
       "                                      absmeansecder num_pspikes num_nspikes  \\\n",
       "kplr000757076-2011073133259_llc.fits       1.296529          16          15   \n",
       "kplr000757099-2011073133259_llc.fits      12.192034           1           3   \n",
       "kplr000757137-2011073133259_llc.fits       0.344510          15          16   \n",
       "kplr000757280-2011073133259_llc.fits       0.714940          14          16   \n",
       "kplr000757450-2011073133259_llc.fits       5.612058          13          13   \n",
       "\n",
       "                                     num_psdspikes num_nsdspikes  stdratio  \\\n",
       "kplr000757076-2011073133259_llc.fits             0             1  1.012352   \n",
       "kplr000757099-2011073133259_llc.fits             3             4  0.984210   \n",
       "kplr000757137-2011073133259_llc.fits             3             4  0.984147   \n",
       "kplr000757280-2011073133259_llc.fits             0             1  0.981786   \n",
       "kplr000757450-2011073133259_llc.fits             6             9  1.046505   \n",
       "\n",
       "                                       pstrend num_zcross num_pm len_nmax  \\\n",
       "kplr000757076-2011073133259_llc.fits  0.171981       1071   1000      151   \n",
       "kplr000757099-2011073133259_llc.fits  0.400322        417    279      176   \n",
       "kplr000757137-2011073133259_llc.fits  0.404187        230    293      145   \n",
       "kplr000757280-2011073133259_llc.fits  0.195491        437    964      117   \n",
       "kplr000757450-2011073133259_llc.fits  0.173591        248   1006      122   \n",
       "\n",
       "                                     len_nmin  mautocorrcoef  ptpslopes  \\\n",
       "kplr000757076-2011073133259_llc.fits      148       0.389605   0.000291   \n",
       "kplr000757099-2011073133259_llc.fits      177       0.963671   0.002868   \n",
       "kplr000757137-2011073133259_llc.fits      142       0.449750   0.001068   \n",
       "kplr000757280-2011073133259_llc.fits      106      -0.001955   0.000489   \n",
       "kplr000757450-2011073133259_llc.fits      133       0.273197   0.002891   \n",
       "\n",
       "                                      periodicity  periodicityr  naiveperiod  \\\n",
       "kplr000757076-2011073133259_llc.fits     0.671680     53.237100     0.445727   \n",
       "kplr000757099-2011073133259_llc.fits     0.645756     17.251794     0.380534   \n",
       "kplr000757137-2011073133259_llc.fits     0.628720     49.910494     0.457204   \n",
       "kplr000757280-2011073133259_llc.fits     0.658702     48.197151     0.571263   \n",
       "kplr000757450-2011073133259_llc.fits     0.775956     54.915584     0.549177   \n",
       "\n",
       "                                       maxvars  maxvarsr   oeratio       amp  \\\n",
       "kplr000757076-2011073133259_llc.fits  0.000137  0.014869  1.000010  0.000900   \n",
       "kplr000757099-2011073133259_llc.fits  0.005337  0.778116  1.000071  0.051816   \n",
       "kplr000757137-2011073133259_llc.fits  0.000545  0.061769  0.999897  0.003075   \n",
       "kplr000757280-2011073133259_llc.fits  0.000220  0.020501  0.999981  0.001008   \n",
       "kplr000757450-2011073133259_llc.fits  0.004413  0.319009  1.000537  0.011980   \n",
       "\n",
       "                                       normamp       mbp     mid20     mid35  \\\n",
       "kplr000757076-2011073133259_llc.fits  0.000900  0.362524  0.148962  0.269766   \n",
       "kplr000757099-2011073133259_llc.fits  0.051901  0.253059  0.169354  0.347546   \n",
       "kplr000757137-2011073133259_llc.fits  0.003075  0.386027  0.151713  0.264631   \n",
       "kplr000757280-2011073133259_llc.fits  0.001008  0.290406  0.169929  0.304503   \n",
       "kplr000757450-2011073133259_llc.fits  0.011983  0.319704  0.155602  0.285138   \n",
       "\n",
       "                                         mid50     mid65     mid80  \\\n",
       "kplr000757076-2011073133259_llc.fits  0.402215  0.555213  0.765741   \n",
       "kplr000757099-2011073133259_llc.fits  0.509381  0.656905  0.838609   \n",
       "kplr000757137-2011073133259_llc.fits  0.386437  0.552207  0.772000   \n",
       "kplr000757280-2011073133259_llc.fits  0.458243  0.622605  0.813770   \n",
       "kplr000757450-2011073133259_llc.fits  0.423865  0.590191  0.825396   \n",
       "\n",
       "                                      percentamp  magratio  sautocorrcoef  \\\n",
       "kplr000757076-2011073133259_llc.fits    0.000868  0.964818      -0.458060   \n",
       "kplr000757099-2011073133259_llc.fits    0.034631  0.510012       0.836633   \n",
       "kplr000757137-2011073133259_llc.fits    0.002384  0.648345       0.798693   \n",
       "kplr000757280-2011073133259_llc.fits    0.000749  0.743016      -0.384460   \n",
       "kplr000757450-2011073133259_llc.fits    0.037443  3.125493      -0.226896   \n",
       "\n",
       "                                      autocorrcoef  flatmean  tflatmean  \\\n",
       "kplr000757076-2011073133259_llc.fits      0.444859  0.004618   0.004576   \n",
       "kplr000757099-2011073133259_llc.fits      0.917945  0.500015   0.565626   \n",
       "kplr000757137-2011073133259_llc.fits      0.971835  0.013298   0.013264   \n",
       "kplr000757280-2011073133259_llc.fits      0.891416  0.002672   0.002727   \n",
       "kplr000757450-2011073133259_llc.fits      0.885174  0.019575   0.029384   \n",
       "\n",
       "                                      roundmean  troundmean  roundrat  \\\n",
       "kplr000757076-2011073133259_llc.fits   0.007057   -0.051637 -0.136673   \n",
       "kplr000757099-2011073133259_llc.fits  -1.753103    3.462622 -0.506293   \n",
       "kplr000757137-2011073133259_llc.fits  -0.168593    0.175329 -0.961580   \n",
       "kplr000757280-2011073133259_llc.fits  -0.032428    0.022367 -1.449829   \n",
       "kplr000757450-2011073133259_llc.fits  -0.004926   -0.053882  0.091415   \n",
       "\n",
       "                                       flatrat  \n",
       "kplr000757076-2011073133259_llc.fits  1.009108  \n",
       "kplr000757099-2011073133259_llc.fits  0.884003  \n",
       "kplr000757137-2011073133259_llc.fits  1.002531  \n",
       "kplr000757280-2011073133259_llc.fits  0.980077  \n",
       "kplr000757450-2011073133259_llc.fits  0.666173  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q8_sample.data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q8_data_scaled = qt.data_scaler(Q8_sample.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q8_scores = kinship.kinship_scores(Q8_data_scaled,kmin=1,samp_size=1000,n_iter=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "kinship_scores can calculate scores for multiple k-values at once, as well as\n",
    "an average of those scores. The method returns a list of numpy arrays.\n",
    "\n",
    "For example purposes, we only calculated the score to the first nearest neighbor\n",
    "in each sample, so we really only have one set of scores.\n",
    "\"\"\"\n",
    "Q8_scores = Q8_scores[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's a personal preference to store scores in a dataframe to keep scores organized by identifier, and this enables multiple scores to be generated and saved in the same place.\n",
    "\n",
    "The cluster outlier object doesn't automatically have a scores dataframe, so one needs to be added. The save method will retain any given attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q8_sample.scores = pd.DataFrame(index=Q8_sample.data.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# placing scores into the pandas dataframe of other scores\n",
    "# this ties scores to the appropriate files.\n",
    "Q8_sample.scores['s1'] = Q8_scores "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores_sorted = Q8_sample.scores['s1'].sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q8_sample.save()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have used Boyajian's star, also informally known as Tabby's star, as a guage of whether our methodology can find anomalies previously identified. Below we show that Boyajian's star does indeed appear to have a notable outlier score, shown by the vertical dashed line in the histogram, and the horizontal dashed line in the plot of outlier score versus rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "tabby_sampler = qt.make_sampler()\n",
    "tabby_score = tabby_sampler(scores_sorted)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAFwCAYAAAChGSA/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAe4ElEQVR4nO3df5TV9X3n8ee7UkOjp2AQaQIIVsENm7InlENSutqoxYqW6G5+rNm2IalnOW2Tpt3TPY1Jeo7bpHbNNqc2po1doq4m28RY065QpXYquJidKCJJaEKqghVltEBQaDGZZKnv/eN+J7kZZgYG7v1+7/d7n49z7pl7P9/P/d73fBle85nP/dzvNzITSVL9/FDVBUiSTowBLkk1ZYBLUk0Z4JJUUwa4JNWUAS5JNTWl6gLKcOaZZ+b8+fOrLkPqukOHDgEwbdq0iitRpzz22GPfzMyZY23riwCfP38+W7durboMqevWr18PwKpVqyquRJ0SEbvH2+YUiiTVVGkBHhG3RcS+iPjaGNv+S0RkRJxZPI6IuCkidkbE9ohY0tZ3dUQ8WdxWl1W/JPWaMkfgtwOXjW6MiLnACuCZtuaVwILitga4uej7KuA64A3AMuC6iDijq1VLNTJlyhSmTOmLmVFR4hx4Zm6OiPljbLoR+G3gnra2K4FPZ+tELQ9HxPSIeDXwJmAgM18AiIgBWr8UPtfF0qXaWLlyZdUlqESVzoFHxJuBocz86qhNs4Fn2x7vKdrGa5ekvlPZ31oR8UrgQ8ClY20eoy0naB9r/2toTb9w9tlnn2CVUr1s27YNgCVLlhyjp5qgyhH4ucA5wFcj4mlgDrAtIn6M1sh6blvfOcBzE7QfJTPXZubSzFw6c+aYSyilxhkaGmJoaKjqMlSSygI8M/8uM8/KzPmZOZ9WOC/JzH8E1gHvLFajvBE4lJnPA/cDl0bEGcWbl5cWbZLUd8pcRvg54EvA+RGxJyKumaD7fcBTwE7gU8CvARRvXn4EeLS4fXjkDU1J6jdlrkJ5xzG2z2+7n8B7xul3G3BbR4uTpBpywajUIFOnTq26BJXIAJcaZMWKFVWXoBJ5LhRJqilH4Oqq+dfe+737T99wRYWV9IctW7YAsGzZsoorURkMcKlB9u7dW3UJKpFTKJJUUwa4JNWUAS5JNeUcuNQgp512WtUlqEQGuNQgF198cdUlqEROoUhSTRngUoMMDg4yODhYdRkqiVMoUoMcOHCg6hJUIkfgklRTjsBVGj9WL3WWI3BJqilH4KqEo/HumDZtWtUlqEQGuNQgF154YdUlqEROoUhSTRngUoNs3ryZzZs3V12GSuIUitQghw4dqroElcgRuCTVlAEuSTVlgEtSTTkHrsqNrAl3PfjJmzFjRtUlqEQGuNQgy5cvr7oElcgpFEmqKQNcapCNGzeycePGqstQSZxCkRrkpZdeqroElcgRuCTVlAEuSTVlgEtSTTkHLjXIrFmzqi5BJTLApQZZtmxZ1SWoRE6hSFJNlRbgEXFbROyLiK+1tf1BRPx9RGyPiL+MiOlt2z4QETsj4vGI+Lm29suKtp0RcW1Z9Ut1MDAwwMDAQNVlqCRljsBvBy4b1TYAvC4zFwNPAB8AiIhFwNXAvy6e88mIOCUiTgH+BFgJLALeUfSVBAwPDzM8PFx1GSpJaQGemZuBF0a1/U1mHikePgzMKe5fCdyZmd/JzH8AdgLLitvOzHwqM78L3Fn0laS+00tz4L8MbCjuzwaebdu2p2gbr12S+k5PBHhEfAg4AvzZSNMY3XKC9rH2uSYitkbE1v3793emUEnqIZUvI4yI1cDPA5dk5kgY7wHmtnWbAzxX3B+v/Qdk5lpgLcDSpUvHDHmpaWbP9g/SflJpgEfEZcD7gZ/JzG+1bVoHfDYi/hB4DbAA2EJrBL4gIs4Bhmi90fkfy61axzJygQaVb8mSJVWXoBKVFuAR8TngTcCZEbEHuI7WqpNXAAMRAfBwZv5KZn49Iu4CdtCaWnlPZv5LsZ/3AvcDpwC3ZebXy/oeJKmXlBbgmfmOMZpvnaD/9cD1Y7TfB9zXwdKkxtiwobUOYOXKlRVXojJUPgcuqXOOHDly7E5qjJ5YhSJJmjwDXJJqygCXpJpyDlxqkHnz5lVdgkpkgEsNsnjx4qpLUImcQpGkmjLApQZZv34969evr7oMlcQAl6SaMsAlqaYMcEmqKQNckmrKZYRSg5x77rlVl6ASGeBSgyxa5DW++4lTKFKDHDlyxDMS9hEDXGqQDRs2fO+c4Go+p1DUM9ovxfb0DVdUWIlUD47AJammDHBJqikDXJJqyjlwqUHOP//8qktQiQxwqUEWLlxYdQkqkVMoUoMMDw8zPDxcdRkqiQEuNcjAwAADAwNVl6GSGOCSVFMGuCTVlAEuSTVlgEtSTbmMUGoQTyfbXwxwdUz7yahUDS/o0F+cQpEa5PDhwxw+fLjqMlQSA1xqkE2bNrFp06aqy1BJDHBJqikDXJJqygCXpJoqLcAj4raI2BcRX2tre1VEDETEk8XXM4r2iIibImJnRGyPiCVtz1ld9H8yIlaXVb8k9ZoyR+C3A5eNarsWeCAzFwAPFI8BVgILitsa4GZoBT5wHfAGYBlw3UjoS4LFixezePHiqstQSUoL8MzcDLwwqvlK4I7i/h3AVW3tn86Wh4HpEfFq4OeAgcx8ITNfBAY4+peC1LfmzZvHvHnzqi5DJal6DnxWZj4PUHw9q2ifDTzb1m9P0TZeuyTg4MGDHDx4sOoyVJJe/SRmjNGWE7QfvYOINbSmXzj77LM7V5lK0f6pzqdvuKLCSurloYceAmDVqlUVV6IyVD0C31tMjVB83Ve07wHmtvWbAzw3QftRMnNtZi7NzKUzZ87seOGSVLWqA3wdMLKSZDVwT1v7O4vVKG8EDhVTLPcDl0bEGcWbl5cWbZLUd0qbQomIzwFvAs6MiD20VpPcANwVEdcAzwBvK7rfB1wO7AS+BbwbIDNfiIiPAI8W/T6cmaPfGJWkvlBagGfmO8bZdMkYfRN4zzj7uQ24rYOlSVIt9eqbmJJOwJIlS47dSY1hgEsNMnu2q2r7SdVvYkrqoAMHDnDgwIGqy1BJDHCpQQYHBxkcHKy6DJXEAJekmjLAJammDHBJqikDXJJqymWEUoMsW7as6hJUIgNcapBZs2ZVXYJKZICr53lq2eO3d+9ewCDvF86BSw2yZcsWtmzZUnUZKokBLkk1ZYBLUk0Z4JJUUwa4JNWUq1CkBlm+fHnVJahEBrjUIDNmzKi6BJXIKRSpQYaGhhgaGqq6DJXEEbjUINu2bQO8Mk+/cAQuSTVlgKtW5l977w98tF7qZwa4JNWUAS5JNeWbmFKDXHDBBVWXoBIZ4FKDTJ8+veoSVCKnUKQG2b17N7t37666DJXEEbjUINu3bwdg3rx5FVeiMjgCl6SaMsAlqaYMcEmqKQNckmrKNzGlBrnooouqLkElMsClBjn99NOrLkElcgpFapBdu3axa9euqstQSXoiwCPiP0fE1yPiaxHxuYiYGhHnRMQjEfFkRHw+Ik4t+r6ieLyz2D6/2uql3rFjxw527NhRdRkqSeUBHhGzgfcBSzPzdcApwNXAR4EbM3MB8CJwTfGUa4AXM/M84MainyT1ncoDvDAF+JGImAK8EngeuBi4u9h+B3BVcf/K4jHF9ksiIkqsVZJ6QuUBnplDwMeAZ2gF9yHgMeBgZh4puu0BRq4RNRt4tnjukaK/V3KV1HeOO8Aj4sJihDy6fUpEXHiiBUTEGbRG1ecArwFOA1aO0TVHnjLBtvb9romIrRGxdf/+/SdaniT1rMksI9wEvBrYN6p9WrHtlBOs4WeBf8jM/QAR8RfAcmB6REwpRtlzgOeK/nuAucCe4hfKNOCF0TvNzLXAWoClS5ceFfBSE61YsaLqElSiyQR4MMZIl9b0xUsnUcMzwBsj4pXAt4FLgK20fim8FbgTWA3cU/RfVzz+UrF9Y2Ya0BXx+pS9ZerUqVWXoBIdM8AjYl1xN4H/FRHfadt8CvA6YPBEC8jMRyLibmAbcAT4Mq2R873AnRHxe0XbrcVTbgU+ExE7aY28rz7R15aa5oknngBg4cKFFVeiMhzPCPxA8TVoLef7dtu27wJfBD51MkVk5nXAdaOanwKWjdF3GHjbybye6q995P/0DVdUWElvefzxxwEDvF8cM8Az890AEfE08LHMPJnpEklShxz3HHhm/m43C5EkTc5xB3hEvAq4ntabjGcxagliZv5oZ0uTJE1kMqtQbgVeT+sNxucYe0WKJKkkkwnwS4AVmflIt4qRdHJWrhzrM3BqqskE+D7gcLcKkXTypkzxFP/9ZDLnQvkQ8OGI8IzxUo/ydLL9ZTK/rn8HmA/si4jdwP9r35iZiztYl6QTMHIxh0WLFlVcicowmQC/+9hdJEllcR24JNVU5ecDlySdmMl8kOefmWDttx/kkaRyTWYO/L2jHv8wrQ/2vIXWJzQlVWzVqlVVl6ASTWYO/I6x2iNiG60P+XyiU0VJko6tE3PgmwB/7Us9YPv27Wzfvr3qMlSSTgT41cA3O7AfSSdp9+7d7N69u+oyVJLJvIn5d/zgm5gBzAJeBfxqh+uSJB3DyXyQ52VgP/BgZv5950qSJB0PP8gjSTU16VOXRcTFwCJa0ylfz8wHO12UpBPj2Qj7y2TmwGcDfwn8JK0LOgC8JiK2Av8uM58b98lSF3mB4+/zfOD9ZTKrUG4C/gU4LzPnZuZcYEHRdlM3ipMkjW8yf2+tAN6Umf8w0pCZT0XE+4AHOl6ZpEnbtm0bAEuWLKm4EpWhE+vAX+7APiR1wNDQEENDQ1WXoZJMJsAfAG6KiLkjDRFxNvBxHIFLUukmE+DvA14JPBURuyPiaWBX0fa+LtQmSZrAZNaBPwssiYgVwL+i9UnMHZn5t90qTpI0vmOOwCNiZUQ8HRHTADJzIDM/kZk3AY8W2y7teqWSjmnq1KlMnTq16jJUkuMZgb8X+IPMPDR6Q2YeioiPAr8B/E2ni5M0OStWrKi6BJXoeObAFwMTTZNsBP5NZ8qRJB2v4wnwmUy8VDCBGZ0pR9LJ2LJlC1u2bKm6DJXkeKZQ9tAahT85zvbFgAtPpR6wd+/eqktQiY5nBH4v8JGI+JHRGyLilcCHiz6SpBIdzwj8euCtwJMR8Qlg5Nzfr6X1BmcAv9+d8iRJ4zlmgGfmvohYDtxMK6hjZBNwP/BrmenfbZJUsuP6IE9m7gYuj4gzgPNohfiTmfliJ4qIiOnALcDraP1i+GXgceDzwHzgaeDtmfliRAStj+9fDnwLeFdmbutEHVLdnXbaaVWXoBJN6uzvRWA/2oU6Pg78dWa+NSJOpfXx/A8CD2TmDRFxLXAt8H5gJa3T2C4A3kDrL4M3dKEmqXYuvvjiqktQiTpxNsKTEhE/ClwI3AqQmd/NzIPAlcAdRbc7gKuK+1cCn86Wh4HpEfHqksuWpMpVHuDAj9O6OPL/jIgvR8QtEXEaMCsznwcovp5V9J8NPNv2/D1Fm9T3BgcHGRwcrLoMlaQXAnwKsAS4OTNfD7xEa7pkPDFGWx7VKWJNRGyNiK379+/vTKVSjztw4AAHDhyougyVpBcCfA+wJzMfKR7fTSvQ945MjRRf97X1n9v2/Dl8/xqd35OZazNzaWYunTlzZteKl6SqVB7gmfmPwLMRcX7RdAmwA1gHrC7aVgP3FPfXAe+MljcCh0amWiSpn0xqFUoX/TrwZ8UKlKeAd9P65XJXRFwDPAO8reh7H60lhDtpLSN8d/nlSlL1eiLAM/MrwNIxNl0yRt8E3tP1ojSu+df27pkT2mt7+oYrKqykGtOmTau6BJWoJwJcUmdceOGFVZegElU+By5JOjEGuNQgmzdvZvPmzVWXoZI4hSI1yKFDR135UA3mCFySasoAl6SaMsAlqaacA5caZMYMry/eTwxwqUGWL19edQkqkVMoklRTBrjUIBs3bmTjxo1Vl6GSOIUiNchLL71UdQkqkSNwSaopA1ySasoAl6Sacg5capBZs2ZVXYJKZIBLDbJs2bKqS1CJnEKRpJoywKUGGRgYYGBgoOoyVBKnUKQGGR4erroElcgRuCTVlCNwNVa/X6FezecIXJJqyhG41CCzZ8+uugSVyACXGmTJkiVVl6ASOYUiSTVlgEsNsmHDBjZs2FB1GSqJUyhSgxw5cqTqElQiR+CSVFMGuCTVlAEuSTXlHLjUIPPmzau6BJXIAJcaZPHixVWXoBI5hSJJNWWASw2yfv161q9fX3UZKknPBHhEnBIRX46IvyoenxMRj0TEkxHx+Yg4tWh/RfF4Z7F9fpV1S1JVeibAgd8AvtH2+KPAjZm5AHgRuKZovwZ4MTPPA24s+klS3+mJAI+IOcAVwC3F4wAuBu4uutwBXFXcv7J4TLH9kqK/NK751977A+cHl5qgJwIc+CPgt4GXi8czgIOZOfK54D3AyHkyZwPPAhTbDxX9JamvVL6MMCJ+HtiXmY9FxJtGmsfomsexrX2/a4A1AGeffXYHKpV637nnnlt1CSpR5QEO/DTw5oi4HJgK/CitEfn0iJhSjLLnAM8V/fcAc4E9ETEFmAa8MHqnmbkWWAuwdOnSowJeauIl1xYtWlR1CSpR5VMomfmBzJyTmfOBq4GNmfkLwCbgrUW31cA9xf11xWOK7Rsz04CWaJ2N0DMS9o9eGIGP5/3AnRHxe8CXgVuL9luBz0TETloj76srqq+vNOUNwKZ8H+MZORf4qlWrKq5EZeipAM/MB4EHi/tPAcvG6DMMvK3UwiSpB1U+hSJJOjEGuCTVlAEuSTXVU3Pgkk7O+eefX3UJKpEBLjXIwoULqy5BJXIKRWqQ4eFhhoeHqy5DJXEELtGcT2UODAwArgPvF47AJammDHBJqikDXJJqyjlwaZSmzIer+QxwaQIjYV6XIPd0sv3FAJcaxAs69BfnwKUGOXz4MIcPH666DJXEAJcaZNOmTWzatKnqMlQSA1ySasoAl6SaMsAlqaYMcEmqKZcRSg2yePHiqktQiQxwqUHmzZtXdQkqkVMoUoMcPHiQgwcPVl2GSmKASw3y0EMP8dBDD1VdhkpigEtSTRngklRTBrgk1ZQBLkk15TJCqUGWLFlSdQkqkQEuNcjs2bOrLkElcgpFapADBw5w4MCBqstQSQxwqUEGBwcZHBysugyVxACXpJpyDlw6Dl6pXr3IEbgk1ZQBLkk1VfkUSkTMBT4N/BjwMrA2Mz8eEa8CPg/MB54G3p6ZL0ZEAB8HLge+BbwrM7dVUXvTtU8bqB6WLVtWdQkqUS+MwI8Av5WZrwXeCLwnIhYB1wIPZOYC4IHiMcBKYEFxWwPcXH7JUm+aNWsWs2bNqroMlaTyAM/M50dG0Jn5z8A3gNnAlcAdRbc7gKuK+1cCn86Wh4HpEfHqksuWetLevXvZu3dv1WWoJJUHeLuImA+8HngEmJWZz0Mr5IGzim6zgWfbnranaJP63pYtW9iyZUvVZagkPRPgEXE68AXgNzPznybqOkZbjrG/NRGxNSK27t+/v1NlSlLP6IkAj4gfphXef5aZf1E07x2ZGim+7iva9wBz254+B3hu9D4zc21mLs3MpTNnzuxe8ZJUkV5YhRLArcA3MvMP2zatA1YDNxRf72lrf29E3Am8ATg0MtUilcEP9ahXVB7gwE8DvwT8XUR8pWj7IK3gvisirgGeAd5WbLuP1hLCnbSWEb673HIlqTdUHuCZ+UXGntcGuGSM/gm8p6tFSTW1fPnyqktQiSoPcEmdM2PGjKpLUIl64k1MSZ0xNDTE0NBQ1WWoJI7ApQbZtq11VgmvzNMfHIFLUk0Z4JJUU06h6CiehVCqBwNcOgl+qEdVMsClBrnggguqLkElMsClBpk+fXrVJahEvokpNcju3bvZvXt31WWoJI7ApQbZvn07APPmzau4EpXBEbgk1ZQBLkk15RSK1CEuKVTZHIFLUk05Ape6YGQ0XvZI/KKLLir19VQtA1xqkNNPP73qElQip1CkBtm1axe7du2qugyVxBG41CA7duwA4Nxzz624EpXBAJe6yJUp6ianUCSpphyBSyVxNK5OcwQuSTXlCFxqkBUrVlRdgkpkgEsNMnXq1KpLUIkMcKkC3ZoPf+KJJwBYuHBhx/ap3mWAC/BCxr1gvH+DyQT8448/Dhjg/cI3MSWpphyBSxXzrx+dKANc6nHHmi9v3/6Jny6lJPUIA1yqEUframeASw2ycuXKqktQiQzwPuZornnO+537v3ffj+s3nwEuNch3v/kMAKeeefakliV6npZ6MsClBjly8HmgFeDj8S+v5qhtgEfEZcDHgVOAWzLzhopLqgX/80rNUcsAj4hTgD8BVgB7gEcjYl1m7qi2Mqn+OvGJUJWjlgEOLAN2ZuZTABFxJ3AlYICPwVG3OmGsn6PxQn2kr6HfXXUN8NnAs22P9wBvqKiWnmVwq9uO9TM23pujx3peJ4K/H96YrWuAxxht+QMdItYAa4qHhyPi8bbN04BD4zxuv38m8M2TrvYHjX7tTvSfqM9Y246nzWPiMenoMYmPHqO6Y/c94WMywWvX4edk3rhbMrN2N+CngPvbHn8A+MAknr92vMej7m/tQu1rO91/oj5jbTueNo+Jx8Rj0vvHpK5nI3wUWBAR50TEqcDVwLpJPH/9BI9Hb+u0ye7/ePpP1GesbcfT5jHxmHhMTqyttGMSxW+G2omIy4E/orWM8LbMvL4Lr7E1M5d2er915jE5msfkaB6To3XjmNR1DpzMvA+4r8svs7bL+68jj8nRPCZH85gcrePHpLYjcEnqd3WdA5ekvmeAS1JNGeCSVFMG+EmIiNMi4rGI+Pmqa+kFEfHaiPjTiLg7In616np6QURcFRGfioh7IuLSquvpBRHx4xFxa0TcXXUtVSry447i5+MXTmQffRngEXFbROyLiK+Nar8sIh6PiJ0Rce1x7Or9wF3dqbJcnTgmmfmNzPwV4O1A7ZeQdeiY/O/M/E/Au4D/0MVyS9GhY/JUZl7T3UqrMcnj8++Bu4ufjzefyOv1ZYADtwOXtTe0neFwJbAIeEdELIqIn4iIvxp1OysifpbWybP2ll18l9zOSR6T4jlvBr4IPFBu+V1xOx04JoXfKZ5Xd7fTuWPSRLdznMcHmMP3z+n0LyfyYrVdB34yMnNzRMwf1TzmGQ4z878BR02RRMRFwGm0/kG+HRH3ZebLXS28izpxTIr9rAPWRcS9wGe7V3H3dejnJIAbgA2Zua27FXdfp35Ommoyx4fWSfjmAF/hBAfTfRng45jUGQ4z80MAEfEu4Jt1Du8JTOqYRMSbaP1Z+Aq6/yGrqkz2TJi/DvwsMC0izsvMP+1mcRWZ7M/JDOB64PUR8YEi6JtsvONzE/DHEXEFJ/iRewP8+455hsOxZObtnS+lZ0zqmGTmg8CD3SqmR0z2mNxE6z9qk032mBwAfqV75fScMY9PZr4EvPtkdtyvc+Bj2QPMbXs8B3iuolp6hcfkaB6To3lMJta142OAf9/JnuGwiTwmR/OYHM1jMrGuHZ++DPCI+BzwJeD8iNgTEddk5hHgvcD9wDeAuzLz61XWWSaPydE8JkfzmEys7OPjyawkqab6cgQuSU1ggEtSTRngklRTBrgk1ZQBLkk1ZYBLUk0Z4JJUUwa4+kpEzIyIT0bE0xHxnYjYGxEPRMSKqmuTJsuTWanffAF4JXANsBM4C/gZYEY3XiwiTs3M73Zj35IjcPWNiJgOXABcm5kPZObuzHw0Mz+WmXcWfU6NiN+PiN3FCP2piHhf2z4ujIhHImK4GL3fWJzfYmT7gxFxc0R8LCL2A/+3aJ8WEWuLq7X8c0T8n4hY2va8aRHxmWL7cPG6v1nawVEtOQJXPzlc3N4cEV/MzOEx+txBK+R/A/gyMI/iTHIRMRvYAHyG1iXSzgVuAV4GfqttH78IrC32E8VFHe4FDtG6wMELwGpgY0Scn5nPA78H/ESxfR8wH5jZoe9bDeW5UNRXIuItwKdoTaN8mdYI+c8z85GIWAA8AazMzL8e47nX07qu5cKRC3gUF/T4H8AZmfmtiHgQeFVmLm573sW0zj43MzO/3db+FeCzmfnfI2IdcCAzT+r80OovTqGor2TmF4DXAKtojaaXAw9HxAeB19MaTW8a5+mvBb406upLXwROBc5ra3ts1PN+ktYvjP0RcXjkBryO1ige4Gbg7RHx1WL65WdO+JtU33AKRX2nmDoZKG4fjohbgP8K/NIxnhqMf6WZ9vaXRm37IVoXv75gjOf9U1HThoiYR+vCt5cA90bEnzsi10QcgUuwg9Zg5u9p/Z+4aIJ+PxUR7f9v/i3wXWDXBPvfBswCXs7MnaNu+0Y6ZeY3M/MzmfkuWqtkVkfEK074u1LjGeDqGxExIyI2RsQvRsTi4gopbwN+G3ggM78K3AXcEhFvKbZfEBEjI/NP0pp++WREvLa4GO0NwB9n5rcmeOm/pTXXfk9ErCz2+1MR8bsRcUFR24cj4qqIWBARr6V1ceinMvM73TkaagKnUNRPDgMP01phch7wCmAI+CytVSAA7wQ+QutCxGfSup7hjQCZORQRK4E/AL4CHCye+8GJXjQzMyIuL17jU7TWnu+lFeqfLrp9h9aV2s8Bhos6V53sN6xmcxWKJNWUUyiSVFMGuCTVlAEuSTVlgEtSTRngklRTBrgk1ZQBLkk1ZYBLUk0Z4JJUU/8fikymgSUip0IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.logspace(-4,0,100)\n",
    "fig,ax = plt.subplots(1,1,figsize=(5,5),constrained_layout=True)\n",
    "ax.hist(scores_sorted,bins=bins)\n",
    "ax.axvline(tabby_score,linestyle='--',c='black',alpha=.4)\n",
    "ax.set_xlabel('Scores',fontsize=14)\n",
    "ax.set_ylabel('Count',fontsize=14)\n",
    "#plt.yscale('log')\n",
    "plt.xscale('log')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(5,5),constrained_layout=True)\n",
    "plt.scatter(range(len(scores_sorted)),scores_sorted)\n",
    "ax.axhline(tabby_score,linestyle='--',c='black',alpha=.4)\n",
    "ax.set_xlabel('Outlier Rank',fontsize=14)\n",
    "ax.set_ylabel('Score',fontsize=14)\n",
    "plt.ylim(1E-4,1E0)\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 'elbow' of the following plot can be thought of as the cutoff between 'outlying' points and 'normal' points. This elbow appears to occur somewhere around the 2,000th most outlying points in this log-scale plot, and closer to the 1,000th point in a linear scale plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(5,5),constrained_layout=True)\n",
    "plt.scatter(range(len(scores_sorted)),scores_sorted)\n",
    "ax.axhline(scores_sorted[2000],linestyle='--',c='black',alpha=.4)\n",
    "ax.set_xlabel('Outlier Rank',fontsize=14)\n",
    "ax.set_ylabel('Score',fontsize=14)\n",
    "plt.ylim(1E-4,1E0) # zoomed in to better see the elbow.\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0.1)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(5,5),constrained_layout=True)\n",
    "plt.scatter(range(len(scores_sorted)),scores_sorted)\n",
    "ax.axhline(scores_sorted[1000],linestyle='--',c='black',alpha=.4)\n",
    "ax.set_xlabel('Outlier Rank',fontsize=14)\n",
    "ax.set_ylabel('Score',fontsize=14)\n",
    "plt.ylim(0,.1) # zoomed in to better see the elbow.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}