visualizing_outlier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Identifying outliers to prioritize high-activity measurements for risk assessment\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A screening campaign was performed to identify chemical products that are of potential health concern. Our main goal: <br>\n",
    "visualize the dataset in the space of decision-making metrics <br>\n",
    "to identify any risk groups that are outliers due to technical or human error. <br>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load libraries\n",
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pyod\n",
    "from scipy import stats\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.font_manager\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group_id</th>\n",
       "      <th>risk</th>\n",
       "      <th>prior_activity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>7598.000000</td>\n",
       "      <td>7872.000000</td>\n",
       "      <td>7871.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3136.902606</td>\n",
       "      <td>1.906901</td>\n",
       "      <td>0.086016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2237.903178</td>\n",
       "      <td>20.630979</td>\n",
       "      <td>0.125375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1063.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.009500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2842.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.028700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4971.750000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.107950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7605.000000</td>\n",
       "      <td>1241.945661</td>\n",
       "      <td>0.738300</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          group_id         risk  prior_activity\n",
       "count  7598.000000  7872.000000     7871.000000\n",
       "mean   3136.902606     1.906901        0.086016\n",
       "std    2237.903178    20.630979        0.125375\n",
       "min       1.000000     0.000000        0.000000\n",
       "25%    1063.000000     0.000000        0.009500\n",
       "50%    2842.000000     0.000000        0.028700\n",
       "75%    4971.750000     0.000000        0.107950\n",
       "max    7605.000000  1241.945661        0.738300"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read dataset\n",
    "dataset = pd.read_csv(\"screening_dataset.csv\")\n",
    "# look at dataset\n",
    "dataset.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "group_id          274\n",
       "risk                0\n",
       "prior_activity      1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check missing values, drop if they exist\n",
    "dataset.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "group_id          0\n",
       "risk              0\n",
       "prior_activity    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drop na\n",
    "dataset_drop_na = dataset.dropna().reset_index(drop=True)\n",
    "dataset_drop_na.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset was transformed and structured previously. More cleaning needs to be done before further mining."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "'group_id' is numeric instead of character. <br>\n",
    "'risk' needs re-scaling. significant figures need to be reduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group_id</th>\n",
       "      <th>risk</th>\n",
       "      <th>prior_activity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5299.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0775</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   group_id  risk  prior_activity\n",
       "0       1.0   0.0          0.0053\n",
       "1       2.0   0.0          0.0461\n",
       "2       3.0   0.0          0.0000\n",
       "3       4.0   0.0          0.0095\n",
       "4    5299.0   0.0          0.0775"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# re-scaling decision-metric, risk, to 0-1 range\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "dataset_drop_na[:]['risk'] = scaler.fit_transform(dataset_drop_na[['risk']])\n",
    "dataset_drop_na.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group_id</th>\n",
       "      <th>risk</th>\n",
       "      <th>prior_activity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5299.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   group_id  risk  prior_activity\n",
       "0       1.0   0.0            0.01\n",
       "1       2.0   0.0            0.05\n",
       "2       3.0   0.0            0.00\n",
       "3       4.0   0.0            0.01\n",
       "4    5299.0   0.0            0.08"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# iterating the columns \n",
    "dataset_drop_na_round = dataset_drop_na.round({'risk': 2, 'prior_activity': 2})\n",
    "dataset_drop_na_round.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fixing data type for group_id\n",
    "dataset_drop_na_round[\"group_id\"] =  dataset_drop_na_round[\"group_id\"].astype(int).astype(str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# adding group_size\n",
    "dataset_drop_na_round['group_size'] = dataset_drop_na_round.groupby('group_id')['group_id'].transform('count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize after filtering smaller group sizes less than 4 and with risk greater than than zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# filter\n",
    "dataset_size = dataset_drop_na_round[(dataset_drop_na_round.group_size > 3) ]\n",
    "dataset_size_pos = dataset_size[(dataset_size.risk > 0 ) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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"
    }
   ],
   "source": [
    "# Fixing random state for reproducibility\n",
    "np.random.seed(19680801)\n",
    "\n",
    "\n",
    "x = dataset_size_pos['group_size']\n",
    "y = dataset_size_pos['risk']\n",
    "z = dataset_size_pos['prior_activity']\n",
    "N = len(y)\n",
    "\n",
    "colors = y\n",
    "area = x \n",
    "\n",
    "plt.scatter(z, y, s=x, c=colors, alpha=0.5)\n",
    "\n",
    "plt.xlabel('prior activity')\n",
    "plt.ylabel('risk')\n",
    "plt.title('groups with outliers')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}