Teclov_LinearSVM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear SVM - Email Spam Classifier\n",
    "\n",
    "\n",
    "In this section, we'll build a linear SVM classifier to classify emails into spam and ham. The dataset, taken from the UCI ML repository, contains about 4600 emails labelled as **spam** or **ham**. \n",
    "\n",
    "The dataset can be downloaded here: https://archive.ics.uci.edu/ml/datasets/spambase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Understanding\n",
    "\n",
    "Let's first load the data and understand the attributes meanings, shape of the dataset etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.model_selection import validation_curve\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0     1     2    3     4     5     6     7     8     9  ...    48     49  \\\n",
      "0  0.00  0.64  0.64  0.0  0.32  0.00  0.00  0.00  0.00  0.00 ...  0.00  0.000   \n",
      "1  0.21  0.28  0.50  0.0  0.14  0.28  0.21  0.07  0.00  0.94 ...  0.00  0.132   \n",
      "2  0.06  0.00  0.71  0.0  1.23  0.19  0.19  0.12  0.64  0.25 ...  0.01  0.143   \n",
      "3  0.00  0.00  0.00  0.0  0.63  0.00  0.31  0.63  0.31  0.63 ...  0.00  0.137   \n",
      "4  0.00  0.00  0.00  0.0  0.63  0.00  0.31  0.63  0.31  0.63 ...  0.00  0.135   \n",
      "\n",
      "    50     51     52     53     54   55    56  57  \n",
      "0  0.0  0.778  0.000  0.000  3.756   61   278   1  \n",
      "1  0.0  0.372  0.180  0.048  5.114  101  1028   1  \n",
      "2  0.0  0.276  0.184  0.010  9.821  485  2259   1  \n",
      "3  0.0  0.137  0.000  0.000  3.537   40   191   1  \n",
      "4  0.0  0.135  0.000  0.000  3.537   40   191   1  \n",
      "\n",
      "[5 rows x 58 columns]\n"
     ]
    }
   ],
   "source": [
    "# load the data\n",
    "email_rec = pd.read_csv(\"Spam.txt\",  sep = ',', header= None )\n",
    "print(email_rec.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As of now, the columns are named as integers. Let's manually name the columns appropriately (column names are available at the UCI website here: https://archive.ics.uci.edu/ml/machine-learning-databases/spambase/spambase.names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   word_freq_make  word_freq_address  word_freq_all  word_freq_3d  \\\n",
      "0            0.00               0.64           0.64           0.0   \n",
      "1            0.21               0.28           0.50           0.0   \n",
      "2            0.06               0.00           0.71           0.0   \n",
      "3            0.00               0.00           0.00           0.0   \n",
      "4            0.00               0.00           0.00           0.0   \n",
      "\n",
      "   word_freq_our  word_freq_over  word_freq_remove  word_freq_internet  \\\n",
      "0           0.32            0.00              0.00                0.00   \n",
      "1           0.14            0.28              0.21                0.07   \n",
      "2           1.23            0.19              0.19                0.12   \n",
      "3           0.63            0.00              0.31                0.63   \n",
      "4           0.63            0.00              0.31                0.63   \n",
      "\n",
      "   word_freq_order  word_freq_mail  ...   char_freq_;  char_freq_(  \\\n",
      "0             0.00            0.00  ...          0.00        0.000   \n",
      "1             0.00            0.94  ...          0.00        0.132   \n",
      "2             0.64            0.25  ...          0.01        0.143   \n",
      "3             0.31            0.63  ...          0.00        0.137   \n",
      "4             0.31            0.63  ...          0.00        0.135   \n",
      "\n",
      "   char_freq_[  char_freq_!  char_freq_$  char_freq_hash  \\\n",
      "0          0.0        0.778        0.000           0.000   \n",
      "1          0.0        0.372        0.180           0.048   \n",
      "2          0.0        0.276        0.184           0.010   \n",
      "3          0.0        0.137        0.000           0.000   \n",
      "4          0.0        0.135        0.000           0.000   \n",
      "\n",
      "   capital_run_length_average  capital_run_length_longest  \\\n",
      "0                       3.756                          61   \n",
      "1                       5.114                         101   \n",
      "2                       9.821                         485   \n",
      "3                       3.537                          40   \n",
      "4                       3.537                          40   \n",
      "\n",
      "   capital_run_length_total  spam  \n",
      "0                       278     1  \n",
      "1                      1028     1  \n",
      "2                      2259     1  \n",
      "3                       191     1  \n",
      "4                       191     1  \n",
      "\n",
      "[5 rows x 58 columns]\n"
     ]
    }
   ],
   "source": [
    "# renaming the columns\n",
    "email_rec.columns  = [\"word_freq_make\", \"word_freq_address\", \"word_freq_all\", \"word_freq_3d\", \n",
    "                      \"word_freq_our\", \"word_freq_over\", \"word_freq_remove\", \"word_freq_internet\", \n",
    "                      \"word_freq_order\", \"word_freq_mail\", \"word_freq_receive\", \"word_freq_will\", \n",
    "                      \"word_freq_people\", \"word_freq_report\", \"word_freq_addresses\", \"word_freq_free\", \n",
    "                      \"word_freq_business\", \"word_freq_email\", \"word_freq_you\", \"word_freq_credit\", \n",
    "                      \"word_freq_your\", \"word_freq_font\", \"word_freq_000\", \"word_freq_money\", \"word_freq_hp\", \n",
    "                      \"word_freq_hpl\", \"word_freq_george\", \"word_freq_650\", \"word_freq_lab\", \"word_freq_labs\", \n",
    "                      \"word_freq_telnet\", \"word_freq_857\", \"word_freq_data\", \"word_freq_415\", \"word_freq_85\", \n",
    "                      \"word_freq_technology\", \"word_freq_1999\", \"word_freq_parts\", \"word_freq_pm\", \"word_freq_direct\",\n",
    "                      \"word_freq_cs\", \"word_freq_meeting\", \"word_freq_original\", \"word_freq_project\", \"word_freq_re\", \n",
    "                      \"word_freq_edu\", \"word_freq_table\", \"word_freq_conference\", \"char_freq_;\", \"char_freq_(\", \n",
    "                      \"char_freq_[\", \"char_freq_!\", \"char_freq_$\", \"char_freq_hash\", \"capital_run_length_average\", \n",
    "                      \"capital_run_length_longest\", \"capital_run_length_total\", \"spam\"]\n",
    "print(email_rec.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4601, 58)\n"
     ]
    }
   ],
   "source": [
    "# look at dimensions of the df\n",
    "print(email_rec.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 4601 entries, 0 to 4600\n",
      "Data columns (total 58 columns):\n",
      "word_freq_make                4601 non-null float64\n",
      "word_freq_address             4601 non-null float64\n",
      "word_freq_all                 4601 non-null float64\n",
      "word_freq_3d                  4601 non-null float64\n",
      "word_freq_our                 4601 non-null float64\n",
      "word_freq_over                4601 non-null float64\n",
      "word_freq_remove              4601 non-null float64\n",
      "word_freq_internet            4601 non-null float64\n",
      "word_freq_order               4601 non-null float64\n",
      "word_freq_mail                4601 non-null float64\n",
      "word_freq_receive             4601 non-null float64\n",
      "word_freq_will                4601 non-null float64\n",
      "word_freq_people              4601 non-null float64\n",
      "word_freq_report              4601 non-null float64\n",
      "word_freq_addresses           4601 non-null float64\n",
      "word_freq_free                4601 non-null float64\n",
      "word_freq_business            4601 non-null float64\n",
      "word_freq_email               4601 non-null float64\n",
      "word_freq_you                 4601 non-null float64\n",
      "word_freq_credit              4601 non-null float64\n",
      "word_freq_your                4601 non-null float64\n",
      "word_freq_font                4601 non-null float64\n",
      "word_freq_000                 4601 non-null float64\n",
      "word_freq_money               4601 non-null float64\n",
      "word_freq_hp                  4601 non-null float64\n",
      "word_freq_hpl                 4601 non-null float64\n",
      "word_freq_george              4601 non-null float64\n",
      "word_freq_650                 4601 non-null float64\n",
      "word_freq_lab                 4601 non-null float64\n",
      "word_freq_labs                4601 non-null float64\n",
      "word_freq_telnet              4601 non-null float64\n",
      "word_freq_857                 4601 non-null float64\n",
      "word_freq_data                4601 non-null float64\n",
      "word_freq_415                 4601 non-null float64\n",
      "word_freq_85                  4601 non-null float64\n",
      "word_freq_technology          4601 non-null float64\n",
      "word_freq_1999                4601 non-null float64\n",
      "word_freq_parts               4601 non-null float64\n",
      "word_freq_pm                  4601 non-null float64\n",
      "word_freq_direct              4601 non-null float64\n",
      "word_freq_cs                  4601 non-null float64\n",
      "word_freq_meeting             4601 non-null float64\n",
      "word_freq_original            4601 non-null float64\n",
      "word_freq_project             4601 non-null float64\n",
      "word_freq_re                  4601 non-null float64\n",
      "word_freq_edu                 4601 non-null float64\n",
      "word_freq_table               4601 non-null float64\n",
      "word_freq_conference          4601 non-null float64\n",
      "char_freq_;                   4601 non-null float64\n",
      "char_freq_(                   4601 non-null float64\n",
      "char_freq_[                   4601 non-null float64\n",
      "char_freq_!                   4601 non-null float64\n",
      "char_freq_$                   4601 non-null float64\n",
      "char_freq_hash                4601 non-null float64\n",
      "capital_run_length_average    4601 non-null float64\n",
      "capital_run_length_longest    4601 non-null int64\n",
      "capital_run_length_total      4601 non-null int64\n",
      "spam                          4601 non-null int64\n",
      "dtypes: float64(55), int64(3)\n",
      "memory usage: 2.0 MB\n"
     ]
    }
   ],
   "source": [
    "# ensure that data type are correct\n",
    "email_rec.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "word_freq_make                0\n",
       "word_freq_address             0\n",
       "word_freq_all                 0\n",
       "word_freq_3d                  0\n",
       "word_freq_our                 0\n",
       "word_freq_over                0\n",
       "word_freq_remove              0\n",
       "word_freq_internet            0\n",
       "word_freq_order               0\n",
       "word_freq_mail                0\n",
       "word_freq_receive             0\n",
       "word_freq_will                0\n",
       "word_freq_people              0\n",
       "word_freq_report              0\n",
       "word_freq_addresses           0\n",
       "word_freq_free                0\n",
       "word_freq_business            0\n",
       "word_freq_email               0\n",
       "word_freq_you                 0\n",
       "word_freq_credit              0\n",
       "word_freq_your                0\n",
       "word_freq_font                0\n",
       "word_freq_000                 0\n",
       "word_freq_money               0\n",
       "word_freq_hp                  0\n",
       "word_freq_hpl                 0\n",
       "word_freq_george              0\n",
       "word_freq_650                 0\n",
       "word_freq_lab                 0\n",
       "word_freq_labs                0\n",
       "word_freq_telnet              0\n",
       "word_freq_857                 0\n",
       "word_freq_data                0\n",
       "word_freq_415                 0\n",
       "word_freq_85                  0\n",
       "word_freq_technology          0\n",
       "word_freq_1999                0\n",
       "word_freq_parts               0\n",
       "word_freq_pm                  0\n",
       "word_freq_direct              0\n",
       "word_freq_cs                  0\n",
       "word_freq_meeting             0\n",
       "word_freq_original            0\n",
       "word_freq_project             0\n",
       "word_freq_re                  0\n",
       "word_freq_edu                 0\n",
       "word_freq_table               0\n",
       "word_freq_conference          0\n",
       "char_freq_;                   0\n",
       "char_freq_(                   0\n",
       "char_freq_[                   0\n",
       "char_freq_!                   0\n",
       "char_freq_$                   0\n",
       "char_freq_hash                0\n",
       "capital_run_length_average    0\n",
       "capital_run_length_longest    0\n",
       "capital_run_length_total      0\n",
       "spam                          0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# there are no missing values in the dataset \n",
    "email_rec.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also look at the fraction of spam and ham emails in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    4601.000000\n",
       "mean        0.394045\n",
       "std         0.488698\n",
       "min         0.000000\n",
       "25%         0.000000\n",
       "50%         0.000000\n",
       "75%         1.000000\n",
       "max         1.000000\n",
       "Name: spam, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# look at fraction of spam emails \n",
    "# 39.4% spams\n",
    "email_rec['spam'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Preparation\n",
    "\n",
    "Let's now conduct some prelimininary data preparation steps, i.e. rescaling the variables, splitting into train and test etc. To understand why rescaling is required, let's print the summary stats of all columns - you'll notice that the columns at the end (capital_run_length_longest, capital_run_length_total etc.) have much higher values (means = 52, 283 etc.) than most other columns which represent fraction of word occurrences (no. of times word appears in email/total no. of words in email)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>word_freq_make</th>\n",
       "      <th>word_freq_address</th>\n",
       "      <th>word_freq_all</th>\n",
       "      <th>word_freq_3d</th>\n",
       "      <th>word_freq_our</th>\n",
       "      <th>word_freq_over</th>\n",
       "      <th>word_freq_remove</th>\n",
       "      <th>word_freq_internet</th>\n",
       "      <th>word_freq_order</th>\n",
       "      <th>word_freq_mail</th>\n",
       "      <th>...</th>\n",
       "      <th>char_freq_;</th>\n",
       "      <th>char_freq_(</th>\n",
       "      <th>char_freq_[</th>\n",
       "      <th>char_freq_!</th>\n",
       "      <th>char_freq_$</th>\n",
       "      <th>char_freq_hash</th>\n",
       "      <th>capital_run_length_average</th>\n",
       "      <th>capital_run_length_longest</th>\n",
       "      <th>capital_run_length_total</th>\n",
       "      <th>spam</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "      <td>4601.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.104553</td>\n",
       "      <td>0.213015</td>\n",
       "      <td>0.280656</td>\n",
       "      <td>0.065425</td>\n",
       "      <td>0.312223</td>\n",
       "      <td>0.095901</td>\n",
       "      <td>0.114208</td>\n",
       "      <td>0.105295</td>\n",
       "      <td>0.090067</td>\n",
       "      <td>0.239413</td>\n",
       "      <td>...</td>\n",
       "      <td>0.038575</td>\n",
       "      <td>0.139030</td>\n",
       "      <td>0.016976</td>\n",
       "      <td>0.269071</td>\n",
       "      <td>0.075811</td>\n",
       "      <td>0.044238</td>\n",
       "      <td>5.191515</td>\n",
       "      <td>52.172789</td>\n",
       "      <td>283.289285</td>\n",
       "      <td>0.394045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.305358</td>\n",
       "      <td>1.290575</td>\n",
       "      <td>0.504143</td>\n",
       "      <td>1.395151</td>\n",
       "      <td>0.672513</td>\n",
       "      <td>0.273824</td>\n",
       "      <td>0.391441</td>\n",
       "      <td>0.401071</td>\n",
       "      <td>0.278616</td>\n",
       "      <td>0.644755</td>\n",
       "      <td>...</td>\n",
       "      <td>0.243471</td>\n",
       "      <td>0.270355</td>\n",
       "      <td>0.109394</td>\n",
       "      <td>0.815672</td>\n",
       "      <td>0.245882</td>\n",
       "      <td>0.429342</td>\n",
       "      <td>31.729449</td>\n",
       "      <td>194.891310</td>\n",
       "      <td>606.347851</td>\n",
       "      <td>0.488698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</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>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</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>1.588000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.065000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.276000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.380000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.160000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.188000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.315000</td>\n",
       "      <td>0.052000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.706000</td>\n",
       "      <td>43.000000</td>\n",
       "      <td>266.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4.540000</td>\n",
       "      <td>14.280000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>42.810000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>5.880000</td>\n",
       "      <td>7.270000</td>\n",
       "      <td>11.110000</td>\n",
       "      <td>5.260000</td>\n",
       "      <td>18.180000</td>\n",
       "      <td>...</td>\n",
       "      <td>4.385000</td>\n",
       "      <td>9.752000</td>\n",
       "      <td>4.081000</td>\n",
       "      <td>32.478000</td>\n",
       "      <td>6.003000</td>\n",
       "      <td>19.829000</td>\n",
       "      <td>1102.500000</td>\n",
       "      <td>9989.000000</td>\n",
       "      <td>15841.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 58 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       word_freq_make  word_freq_address  word_freq_all  word_freq_3d  \\\n",
       "count     4601.000000        4601.000000    4601.000000   4601.000000   \n",
       "mean         0.104553           0.213015       0.280656      0.065425   \n",
       "std          0.305358           1.290575       0.504143      1.395151   \n",
       "min          0.000000           0.000000       0.000000      0.000000   \n",
       "25%          0.000000           0.000000       0.000000      0.000000   \n",
       "50%          0.000000           0.000000       0.000000      0.000000   \n",
       "75%          0.000000           0.000000       0.420000      0.000000   \n",
       "max          4.540000          14.280000       5.100000     42.810000   \n",
       "\n",
       "       word_freq_our  word_freq_over  word_freq_remove  word_freq_internet  \\\n",
       "count    4601.000000     4601.000000       4601.000000         4601.000000   \n",
       "mean        0.312223        0.095901          0.114208            0.105295   \n",
       "std         0.672513        0.273824          0.391441            0.401071   \n",
       "min         0.000000        0.000000          0.000000            0.000000   \n",
       "25%         0.000000        0.000000          0.000000            0.000000   \n",
       "50%         0.000000        0.000000          0.000000            0.000000   \n",
       "75%         0.380000        0.000000          0.000000            0.000000   \n",
       "max        10.000000        5.880000          7.270000           11.110000   \n",
       "\n",
       "       word_freq_order  word_freq_mail     ...       char_freq_;  char_freq_(  \\\n",
       "count      4601.000000     4601.000000     ...       4601.000000  4601.000000   \n",
       "mean          0.090067        0.239413     ...          0.038575     0.139030   \n",
       "std           0.278616        0.644755     ...          0.243471     0.270355   \n",
       "min           0.000000        0.000000     ...          0.000000     0.000000   \n",
       "25%           0.000000        0.000000     ...          0.000000     0.000000   \n",
       "50%           0.000000        0.000000     ...          0.000000     0.065000   \n",
       "75%           0.000000        0.160000     ...          0.000000     0.188000   \n",
       "max           5.260000       18.180000     ...          4.385000     9.752000   \n",
       "\n",
       "       char_freq_[  char_freq_!  char_freq_$  char_freq_hash  \\\n",
       "count  4601.000000  4601.000000  4601.000000     4601.000000   \n",
       "mean      0.016976     0.269071     0.075811        0.044238   \n",
       "std       0.109394     0.815672     0.245882        0.429342   \n",
       "min       0.000000     0.000000     0.000000        0.000000   \n",
       "25%       0.000000     0.000000     0.000000        0.000000   \n",
       "50%       0.000000     0.000000     0.000000        0.000000   \n",
       "75%       0.000000     0.315000     0.052000        0.000000   \n",
       "max       4.081000    32.478000     6.003000       19.829000   \n",
       "\n",
       "       capital_run_length_average  capital_run_length_longest  \\\n",
       "count                 4601.000000                 4601.000000   \n",
       "mean                     5.191515                   52.172789   \n",
       "std                     31.729449                  194.891310   \n",
       "min                      1.000000                    1.000000   \n",
       "25%                      1.588000                    6.000000   \n",
       "50%                      2.276000                   15.000000   \n",
       "75%                      3.706000                   43.000000   \n",
       "max                   1102.500000                 9989.000000   \n",
       "\n",
       "       capital_run_length_total         spam  \n",
       "count               4601.000000  4601.000000  \n",
       "mean                 283.289285     0.394045  \n",
       "std                  606.347851     0.488698  \n",
       "min                    1.000000     0.000000  \n",
       "25%                   35.000000     0.000000  \n",
       "50%                   95.000000     0.000000  \n",
       "75%                  266.000000     1.000000  \n",
       "max                15841.000000     1.000000  \n",
       "\n",
       "[8 rows x 58 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "email_rec.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting into X and y\n",
    "X = email_rec.drop(\"spam\", axis = 1)\n",
    "y = email_rec.spam.values.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scaling the features\n",
    "# note that the scale function standardises each column, i.e.\n",
    "# x = x-mean(x)/std(x)\n",
    "\n",
    "from sklearn.preprocessing import scale\n",
    "X = scale(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into train and test\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.397826086957\n",
      "0.385228095583\n"
     ]
    }
   ],
   "source": [
    "# confirm that splitting also has similar distribution of spam and ham \n",
    "# emails\n",
    "print(y_train.mean())\n",
    "print(y_test.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Building\n",
    "\n",
    "Let's build a linear SVM mode now. The ```SVC()``` class does that in sklearn. We highly recommend reading the documentation at least once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class SVC in module sklearn.svm.classes:\n",
      "\n",
      "class SVC(sklearn.svm.base.BaseSVC)\n",
      " |  C-Support Vector Classification.\n",
      " |  \n",
      " |  The implementation is based on libsvm. The fit time complexity\n",
      " |  is more than quadratic with the number of samples which makes it hard\n",
      " |  to scale to dataset with more than a couple of 10000 samples.\n",
      " |  \n",
      " |  The multiclass support is handled according to a one-vs-one scheme.\n",
      " |  \n",
      " |  For details on the precise mathematical formulation of the provided\n",
      " |  kernel functions and how `gamma`, `coef0` and `degree` affect each\n",
      " |  other, see the corresponding section in the narrative documentation:\n",
      " |  :ref:`svm_kernels`.\n",
      " |  \n",
      " |  Read more in the :ref:`User Guide <svm_classification>`.\n",
      " |  \n",
      " |  Parameters\n",
      " |  ----------\n",
      " |  C : float, optional (default=1.0)\n",
      " |      Penalty parameter C of the error term.\n",
      " |  \n",
      " |  kernel : string, optional (default='rbf')\n",
      " |       Specifies the kernel type to be used in the algorithm.\n",
      " |       It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or\n",
      " |       a callable.\n",
      " |       If none is given, 'rbf' will be used. If a callable is given it is\n",
      " |       used to pre-compute the kernel matrix from data matrices; that matrix\n",
      " |       should be an array of shape ``(n_samples, n_samples)``.\n",
      " |  \n",
      " |  degree : int, optional (default=3)\n",
      " |      Degree of the polynomial kernel function ('poly').\n",
      " |      Ignored by all other kernels.\n",
      " |  \n",
      " |  gamma : float, optional (default='auto')\n",
      " |      Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.\n",
      " |      If gamma is 'auto' then 1/n_features will be used instead.\n",
      " |  \n",
      " |  coef0 : float, optional (default=0.0)\n",
      " |      Independent term in kernel function.\n",
      " |      It is only significant in 'poly' and 'sigmoid'.\n",
      " |  \n",
      " |  probability : boolean, optional (default=False)\n",
      " |      Whether to enable probability estimates. This must be enabled prior\n",
      " |      to calling `fit`, and will slow down that method.\n",
      " |  \n",
      " |  shrinking : boolean, optional (default=True)\n",
      " |      Whether to use the shrinking heuristic.\n",
      " |  \n",
      " |  tol : float, optional (default=1e-3)\n",
      " |      Tolerance for stopping criterion.\n",
      " |  \n",
      " |  cache_size : float, optional\n",
      " |      Specify the size of the kernel cache (in MB).\n",
      " |  \n",
      " |  class_weight : {dict, 'balanced'}, optional\n",
      " |      Set the parameter C of class i to class_weight[i]*C for\n",
      " |      SVC. If not given, all classes are supposed to have\n",
      " |      weight one.\n",
      " |      The \"balanced\" mode uses the values of y to automatically adjust\n",
      " |      weights inversely proportional to class frequencies in the input data\n",
      " |      as ``n_samples / (n_classes * np.bincount(y))``\n",
      " |  \n",
      " |  verbose : bool, default: False\n",
      " |      Enable verbose output. Note that this setting takes advantage of a\n",
      " |      per-process runtime setting in libsvm that, if enabled, may not work\n",
      " |      properly in a multithreaded context.\n",
      " |  \n",
      " |  max_iter : int, optional (default=-1)\n",
      " |      Hard limit on iterations within solver, or -1 for no limit.\n",
      " |  \n",
      " |  decision_function_shape : 'ovo', 'ovr', default='ovr'\n",
      " |      Whether to return a one-vs-rest ('ovr') decision function of shape\n",
      " |      (n_samples, n_classes) as all other classifiers, or the original\n",
      " |      one-vs-one ('ovo') decision function of libsvm which has shape\n",
      " |      (n_samples, n_classes * (n_classes - 1) / 2).\n",
      " |  \n",
      " |      .. versionchanged:: 0.19\n",
      " |          decision_function_shape is 'ovr' by default.\n",
      " |  \n",
      " |      .. versionadded:: 0.17\n",
      " |         *decision_function_shape='ovr'* is recommended.\n",
      " |  \n",
      " |      .. versionchanged:: 0.17\n",
      " |         Deprecated *decision_function_shape='ovo' and None*.\n",
      " |  \n",
      " |  random_state : int, RandomState instance or None, optional (default=None)\n",
      " |      The seed of the pseudo random number generator to use when shuffling\n",
      " |      the data.  If int, random_state is the seed used by the random number\n",
      " |      generator; If RandomState instance, random_state is the random number\n",
      " |      generator; If None, the random number generator is the RandomState\n",
      " |      instance used by `np.random`.\n",
      " |  \n",
      " |  Attributes\n",
      " |  ----------\n",
      " |  support_ : array-like, shape = [n_SV]\n",
      " |      Indices of support vectors.\n",
      " |  \n",
      " |  support_vectors_ : array-like, shape = [n_SV, n_features]\n",
      " |      Support vectors.\n",
      " |  \n",
      " |  n_support_ : array-like, dtype=int32, shape = [n_class]\n",
      " |      Number of support vectors for each class.\n",
      " |  \n",
      " |  dual_coef_ : array, shape = [n_class-1, n_SV]\n",
      " |      Coefficients of the support vector in the decision function.\n",
      " |      For multiclass, coefficient for all 1-vs-1 classifiers.\n",
      " |      The layout of the coefficients in the multiclass case is somewhat\n",
      " |      non-trivial. See the section about multi-class classification in the\n",
      " |      SVM section of the User Guide for details.\n",
      " |  \n",
      " |  coef_ : array, shape = [n_class-1, n_features]\n",
      " |      Weights assigned to the features (coefficients in the primal\n",
      " |      problem). This is only available in the case of a linear kernel.\n",
      " |  \n",
      " |      `coef_` is a readonly property derived from `dual_coef_` and\n",
      " |      `support_vectors_`.\n",
      " |  \n",
      " |  intercept_ : array, shape = [n_class * (n_class-1) / 2]\n",
      " |      Constants in decision function.\n",
      " |  \n",
      " |  Examples\n",
      " |  --------\n",
      " |  >>> import numpy as np\n",
      " |  >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])\n",
      " |  >>> y = np.array([1, 1, 2, 2])\n",
      " |  >>> from sklearn.svm import SVC\n",
      " |  >>> clf = SVC()\n",
      " |  >>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE\n",
      " |  SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
      " |      decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',\n",
      " |      max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
      " |      tol=0.001, verbose=False)\n",
      " |  >>> print(clf.predict([[-0.8, -1]]))\n",
      " |  [1]\n",
      " |  \n",
      " |  See also\n",
      " |  --------\n",
      " |  SVR\n",
      " |      Support Vector Machine for Regression implemented using libsvm.\n",
      " |  \n",
      " |  LinearSVC\n",
      " |      Scalable Linear Support Vector Machine for classification\n",
      " |      implemented using liblinear. Check the See also section of\n",
      " |      LinearSVC for more comparison element.\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      SVC\n",
      " |      sklearn.svm.base.BaseSVC\n",
      " |      abc.NewBase\n",
      " |      sklearn.svm.base.BaseLibSVM\n",
      " |      abc.NewBase\n",
      " |      sklearn.base.BaseEstimator\n",
      " |      sklearn.base.ClassifierMixin\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __init__(self, C=1.0, kernel='rbf', degree=3, gamma='auto', coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape='ovr', random_state=None)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data and other attributes defined here:\n",
      " |  \n",
      " |  __abstractmethods__ = frozenset()\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.svm.base.BaseSVC:\n",
      " |  \n",
      " |  decision_function(self, X)\n",
      " |      Distance of the samples X to the separating hyperplane.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape (n_samples, n_features)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      X : array-like, shape (n_samples, n_classes * (n_classes-1) / 2)\n",
      " |          Returns the decision function of the sample for each class\n",
      " |          in the model.\n",
      " |          If decision_function_shape='ovr', the shape is (n_samples,\n",
      " |          n_classes)\n",
      " |  \n",
      " |  predict(self, X)\n",
      " |      Perform classification on samples in X.\n",
      " |      \n",
      " |      For an one-class model, +1 or -1 is returned.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |          For kernel=\"precomputed\", the expected shape of X is\n",
      " |          [n_samples_test, n_samples_train]\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      y_pred : array, shape (n_samples,)\n",
      " |          Class labels for samples in X.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from sklearn.svm.base.BaseSVC:\n",
      " |  \n",
      " |  predict_log_proba\n",
      " |      Compute log probabilities of possible outcomes for samples in X.\n",
      " |      \n",
      " |      The model need to have probability information computed at training\n",
      " |      time: fit with attribute `probability` set to True.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape (n_samples, n_features)\n",
      " |          For kernel=\"precomputed\", the expected shape of X is\n",
      " |          [n_samples_test, n_samples_train]\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      T : array-like, shape (n_samples, n_classes)\n",
      " |          Returns the log-probabilities of the sample for each class in\n",
      " |          the model. The columns correspond to the classes in sorted\n",
      " |          order, as they appear in the attribute `classes_`.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      The probability model is created using cross validation, so\n",
      " |      the results can be slightly different than those obtained by\n",
      " |      predict. Also, it will produce meaningless results on very small\n",
      " |      datasets.\n",
      " |  \n",
      " |  predict_proba\n",
      " |      Compute probabilities of possible outcomes for samples in X.\n",
      " |      \n",
      " |      The model need to have probability information computed at training\n",
      " |      time: fit with attribute `probability` set to True.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape (n_samples, n_features)\n",
      " |          For kernel=\"precomputed\", the expected shape of X is\n",
      " |          [n_samples_test, n_samples_train]\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      T : array-like, shape (n_samples, n_classes)\n",
      " |          Returns the probability of the sample for each class in\n",
      " |          the model. The columns correspond to the classes in sorted\n",
      " |          order, as they appear in the attribute `classes_`.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      The probability model is created using cross validation, so\n",
      " |      the results can be slightly different than those obtained by\n",
      " |      predict. Also, it will produce meaningless results on very small\n",
      " |      datasets.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.svm.base.BaseLibSVM:\n",
      " |  \n",
      " |  fit(self, X, y, sample_weight=None)\n",
      " |      Fit the SVM model according to the given training data.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |          Training vectors, where n_samples is the number of samples\n",
      " |          and n_features is the number of features.\n",
      " |          For kernel=\"precomputed\", the expected shape of X is\n",
      " |          (n_samples, n_samples).\n",
      " |      \n",
      " |      y : array-like, shape (n_samples,)\n",
      " |          Target values (class labels in classification, real numbers in\n",
      " |          regression)\n",
      " |      \n",
      " |      sample_weight : array-like, shape (n_samples,)\n",
      " |          Per-sample weights. Rescale C per sample. Higher weights\n",
      " |          force the classifier to put more emphasis on these points.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self : object\n",
      " |          Returns self.\n",
      " |      \n",
      " |      Notes\n",
      " |      ------\n",
      " |      If X and y are not C-ordered and contiguous arrays of np.float64 and\n",
      " |      X is not a scipy.sparse.csr_matrix, X and/or y may be copied.\n",
      " |      \n",
      " |      If X is a dense array, then the other methods will not support sparse\n",
      " |      matrices as input.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from sklearn.svm.base.BaseLibSVM:\n",
      " |  \n",
      " |  coef_\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __getstate__(self)\n",
      " |  \n",
      " |  __repr__(self)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __setstate__(self, state)\n",
      " |  \n",
      " |  get_params(self, deep=True)\n",
      " |      Get parameters for this estimator.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      deep : boolean, optional\n",
      " |          If True, will return the parameters for this estimator and\n",
      " |          contained subobjects that are estimators.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      params : mapping of string to any\n",
      " |          Parameter names mapped to their values.\n",
      " |  \n",
      " |  set_params(self, **params)\n",
      " |      Set the parameters of this estimator.\n",
      " |      \n",
      " |      The method works on simple estimators as well as on nested objects\n",
      " |      (such as pipelines). The latter have parameters of the form\n",
      " |      ``<component>__<parameter>`` so that it's possible to update each\n",
      " |      component of a nested object.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.ClassifierMixin:\n",
      " |  \n",
      " |  score(self, X, y, sample_weight=None)\n",
      " |      Returns the mean accuracy on the given test data and labels.\n",
      " |      \n",
      " |      In multi-label classification, this is the subset accuracy\n",
      " |      which is a harsh metric since you require for each sample that\n",
      " |      each label set be correctly predicted.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape = (n_samples, n_features)\n",
      " |          Test samples.\n",
      " |      \n",
      " |      y : array-like, shape = (n_samples) or (n_samples, n_outputs)\n",
      " |          True labels for X.\n",
      " |      \n",
      " |      sample_weight : array-like, shape = [n_samples], optional\n",
      " |          Sample weights.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      score : float\n",
      " |          Mean accuracy of self.predict(X) wrt. y.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(SVC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model building\n",
    "\n",
    "# instantiate an object of class SVC()\n",
    "# note that we are using cost C=1\n",
    "model = SVC(C = 1)\n",
    "\n",
    "# fit\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "# predict\n",
    "y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[811,  38],\n",
       "       [ 61, 471]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Evaluate the model using confusion matrix \n",
    "from sklearn import metrics\n",
    "metrics.confusion_matrix(y_true=y_test, y_pred=y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy 0.928312816799\n",
      "precision 0.925343811395\n",
      "recall 0.885338345865\n"
     ]
    }
   ],
   "source": [
    "# print other metrics\n",
    "\n",
    "# accuracy\n",
    "print(\"accuracy\", metrics.accuracy_score(y_test, y_pred))\n",
    "\n",
    "# precision\n",
    "print(\"precision\", metrics.precision_score(y_test, y_pred))\n",
    "\n",
    "# recall/sensitivity\n",
    "print(\"recall\", metrics.recall_score(y_test, y_pred))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "specificity 0.9552414605418139\n"
     ]
    }
   ],
   "source": [
    "# specificity (% of hams correctly classified)\n",
    "print(\"specificity\", 811/(811+38))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SVM we have built so far gives decently good results - an accuracy of 92%, sensitivity/recall (TNR) of 88%. \n",
    "\n",
    "### Interpretation of Results\n",
    "\n",
    "In the confusion matrix, the elements at (0, 0) and (1,1) correspond to the more frequently occurring class, i.e. ham emails. Thus, it implies that:\n",
    "- 92% of all emails are classified correctly\n",
    "- 88.5% of spams are identified correctly (sensitivity/recall)\n",
    "- Specificity, or % of hams classified correctly, is 95%\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyperparameter Tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function confusion_matrix in module sklearn.metrics.classification:\n",
      "\n",
      "confusion_matrix(y_true, y_pred, labels=None, sample_weight=None)\n",
      "    Compute confusion matrix to evaluate the accuracy of a classification\n",
      "    \n",
      "    By definition a confusion matrix :math:`C` is such that :math:`C_{i, j}`\n",
      "    is equal to the number of observations known to be in group :math:`i` but\n",
      "    predicted to be in group :math:`j`.\n",
      "    \n",
      "    Thus in binary classification, the count of true negatives is\n",
      "    :math:`C_{0,0}`, false negatives is :math:`C_{1,0}`, true positives is\n",
      "    :math:`C_{1,1}` and false positives is :math:`C_{0,1}`.\n",
      "    \n",
      "    Read more in the :ref:`User Guide <confusion_matrix>`.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    y_true : array, shape = [n_samples]\n",
      "        Ground truth (correct) target values.\n",
      "    \n",
      "    y_pred : array, shape = [n_samples]\n",
      "        Estimated targets as returned by a classifier.\n",
      "    \n",
      "    labels : array, shape = [n_classes], optional\n",
      "        List of labels to index the matrix. This may be used to reorder\n",
      "        or select a subset of labels.\n",
      "        If none is given, those that appear at least once\n",
      "        in ``y_true`` or ``y_pred`` are used in sorted order.\n",
      "    \n",
      "    sample_weight : array-like of shape = [n_samples], optional\n",
      "        Sample weights.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    C : array, shape = [n_classes, n_classes]\n",
      "        Confusion matrix\n",
      "    \n",
      "    References\n",
      "    ----------\n",
      "    .. [1] `Wikipedia entry for the Confusion matrix\n",
      "           <https://en.wikipedia.org/wiki/Confusion_matrix>`_\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> from sklearn.metrics import confusion_matrix\n",
      "    >>> y_true = [2, 0, 2, 2, 0, 1]\n",
      "    >>> y_pred = [0, 0, 2, 2, 0, 2]\n",
      "    >>> confusion_matrix(y_true, y_pred)\n",
      "    array([[2, 0, 0],\n",
      "           [0, 0, 1],\n",
      "           [1, 0, 2]])\n",
      "    \n",
      "    >>> y_true = [\"cat\", \"ant\", \"cat\", \"cat\", \"ant\", \"bird\"]\n",
      "    >>> y_pred = [\"ant\", \"ant\", \"cat\", \"cat\", \"ant\", \"cat\"]\n",
      "    >>> confusion_matrix(y_true, y_pred, labels=[\"ant\", \"bird\", \"cat\"])\n",
      "    array([[2, 0, 0],\n",
      "           [0, 0, 1],\n",
      "           [1, 0, 2]])\n",
      "    \n",
      "    In the binary case, we can extract true positives, etc as follows:\n",
      "    \n",
      "    >>> tn, fp, fn, tp = confusion_matrix([0, 1, 0, 1], [1, 1, 1, 0]).ravel()\n",
      "    >>> (tn, fp, fn, tp)\n",
      "    (0, 2, 1, 1)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(metrics.confusion_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-Fold Cross Validation\n",
    "\n",
    "Let's first run a simple k-fold cross validation to get a sense of the **average metrics** as computed over multiple *folds*. the easiest way to do cross-validation is to use the ```cross_val_score()``` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a KFold object with 5 splits \n",
    "folds = KFold(n_splits = 5, shuffle = True, random_state = 4)\n",
    "\n",
    "# instantiating a model with cost=1\n",
    "model = SVC(C = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# computing the cross-validation scores \n",
    "# note that the argument cv takes the 'folds' object, and\n",
    "# we have specified 'accuracy' as the metric\n",
    "\n",
    "cv_results = cross_val_score(model, X_train, y_train, cv = folds, scoring = 'accuracy') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.91770186  0.93944099  0.91925466  0.93012422  0.94254658]\n",
      "mean accuracy = 0.9298136645962731\n"
     ]
    }
   ],
   "source": [
    "# print 5 accuracies obtained from the 5 folds\n",
    "print(cv_results)\n",
    "print(\"mean accuracy = {}\".format(cv_results.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid Search to Find Optimal Hyperparameter C\n",
    "\n",
    "K-fold CV helps us compute average metrics over multiple folds, and that is the best indication of the 'test accuracy/other metric scores' we can have. \n",
    "\n",
    "But we want to use CV to compute the optimal values of hyperparameters (in this case, the cost C is a hyperparameter). This is done using the ```GridSearchCV()``` method, which computes metrics (such as accuracy, recall etc.) \n",
    "\n",
    "In this case, we have only one hyperparameter, though you can have multiple, such as C and gamma in non-linear SVMs. In that case, you need to search through a *grid* of multiple values of C and gamma to find the optimal combination, and hence the name GridSearchCV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# specify range of parameters (C) as a list\n",
    "params = {\"C\": [0.1, 1, 10, 100, 1000]}\n",
    "\n",
    "model = SVC()\n",
    "\n",
    "# set up grid search scheme\n",
    "# note that we are still using the 5 fold CV scheme we set up earlier\n",
    "model_cv = GridSearchCV(estimator = model, param_grid = params, \n",
    "                        scoring= 'accuracy', \n",
    "                        cv = folds, \n",
    "                        verbose = 1,\n",
    "                       return_train_score=True)      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 5 candidates, totalling 25 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  25 out of  25 | elapsed:    9.6s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=KFold(n_splits=5, random_state=4, shuffle=True),\n",
       "       error_score='raise',\n",
       "       estimator=SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False),\n",
       "       fit_params=None, iid=True, n_jobs=1,\n",
       "       param_grid={'C': [0.1, 1, 10, 100, 1000]}, pre_dispatch='2*n_jobs',\n",
       "       refit=True, return_train_score=True, scoring='accuracy', verbose=1)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit the model - it will fit 5 folds across all values of C\n",
    "model_cv.fit(X_train, y_train)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>mean_fit_time</th>\n",
       "      <th>mean_score_time</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>mean_train_score</th>\n",
       "      <th>param_C</th>\n",
       "      <th>params</th>\n",
       "      <th>rank_test_score</th>\n",
       "      <th>split0_test_score</th>\n",
       "      <th>split0_train_score</th>\n",
       "      <th>split1_test_score</th>\n",
       "      <th>...</th>\n",
       "      <th>split2_test_score</th>\n",
       "      <th>split2_train_score</th>\n",
       "      <th>split3_test_score</th>\n",
       "      <th>split3_train_score</th>\n",
       "      <th>split4_test_score</th>\n",
       "      <th>split4_train_score</th>\n",
       "      <th>std_fit_time</th>\n",
       "      <th>std_score_time</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>std_train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.272942</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.905280</td>\n",
       "      <td>0.910714</td>\n",
       "      <td>0.1</td>\n",
       "      <td>{'C': 0.1}</td>\n",
       "      <td>5</td>\n",
       "      <td>0.895963</td>\n",
       "      <td>0.912267</td>\n",
       "      <td>0.900621</td>\n",
       "      <td>...</td>\n",
       "      <td>0.906832</td>\n",
       "      <td>0.912267</td>\n",
       "      <td>0.902174</td>\n",
       "      <td>0.911491</td>\n",
       "      <td>0.920807</td>\n",
       "      <td>0.906056</td>\n",
       "      <td>0.015064</td>\n",
       "      <td>0.000734</td>\n",
       "      <td>0.008505</td>\n",
       "      <td>0.002355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.179737</td>\n",
       "      <td>0.033372</td>\n",
       "      <td>0.929814</td>\n",
       "      <td>0.947593</td>\n",
       "      <td>1</td>\n",
       "      <td>{'C': 1}</td>\n",
       "      <td>2</td>\n",
       "      <td>0.917702</td>\n",
       "      <td>0.951863</td>\n",
       "      <td>0.939441</td>\n",
       "      <td>...</td>\n",
       "      <td>0.919255</td>\n",
       "      <td>0.950699</td>\n",
       "      <td>0.930124</td>\n",
       "      <td>0.946040</td>\n",
       "      <td>0.942547</td>\n",
       "      <td>0.943711</td>\n",
       "      <td>0.004683</td>\n",
       "      <td>0.001155</td>\n",
       "      <td>0.010130</td>\n",
       "      <td>0.003135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.162986</td>\n",
       "      <td>0.027241</td>\n",
       "      <td>0.931056</td>\n",
       "      <td>0.971584</td>\n",
       "      <td>10</td>\n",
       "      <td>{'C': 10}</td>\n",
       "      <td>1</td>\n",
       "      <td>0.909938</td>\n",
       "      <td>0.973991</td>\n",
       "      <td>0.944099</td>\n",
       "      <td>...</td>\n",
       "      <td>0.933230</td>\n",
       "      <td>0.973602</td>\n",
       "      <td>0.928571</td>\n",
       "      <td>0.968944</td>\n",
       "      <td>0.939441</td>\n",
       "      <td>0.970885</td>\n",
       "      <td>0.010262</td>\n",
       "      <td>0.001996</td>\n",
       "      <td>0.011809</td>\n",
       "      <td>0.001924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.213353</td>\n",
       "      <td>0.026252</td>\n",
       "      <td>0.928571</td>\n",
       "      <td>0.989130</td>\n",
       "      <td>100</td>\n",
       "      <td>{'C': 100}</td>\n",
       "      <td>3</td>\n",
       "      <td>0.914596</td>\n",
       "      <td>0.989519</td>\n",
       "      <td>0.925466</td>\n",
       "      <td>...</td>\n",
       "      <td>0.936335</td>\n",
       "      <td>0.989907</td>\n",
       "      <td>0.930124</td>\n",
       "      <td>0.988354</td>\n",
       "      <td>0.936335</td>\n",
       "      <td>0.988354</td>\n",
       "      <td>0.021210</td>\n",
       "      <td>0.001567</td>\n",
       "      <td>0.008098</td>\n",
       "      <td>0.000650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.268392</td>\n",
       "      <td>0.022661</td>\n",
       "      <td>0.920497</td>\n",
       "      <td>0.994332</td>\n",
       "      <td>1000</td>\n",
       "      <td>{'C': 1000}</td>\n",
       "      <td>4</td>\n",
       "      <td>0.908385</td>\n",
       "      <td>0.996118</td>\n",
       "      <td>0.931677</td>\n",
       "      <td>...</td>\n",
       "      <td>0.923913</td>\n",
       "      <td>0.994177</td>\n",
       "      <td>0.919255</td>\n",
       "      <td>0.993789</td>\n",
       "      <td>0.919255</td>\n",
       "      <td>0.993789</td>\n",
       "      <td>0.031640</td>\n",
       "      <td>0.002353</td>\n",
       "      <td>0.007569</td>\n",
       "      <td>0.000905</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean_fit_time  mean_score_time  mean_test_score  mean_train_score param_C  \\\n",
       "0       0.272942         0.054458         0.905280          0.910714     0.1   \n",
       "1       0.179737         0.033372         0.929814          0.947593       1   \n",
       "2       0.162986         0.027241         0.931056          0.971584      10   \n",
       "3       0.213353         0.026252         0.928571          0.989130     100   \n",
       "4       0.268392         0.022661         0.920497          0.994332    1000   \n",
       "\n",
       "        params  rank_test_score  split0_test_score  split0_train_score  \\\n",
       "0   {'C': 0.1}                5           0.895963            0.912267   \n",
       "1     {'C': 1}                2           0.917702            0.951863   \n",
       "2    {'C': 10}                1           0.909938            0.973991   \n",
       "3   {'C': 100}                3           0.914596            0.989519   \n",
       "4  {'C': 1000}                4           0.908385            0.996118   \n",
       "\n",
       "   split1_test_score       ...         split2_test_score  split2_train_score  \\\n",
       "0           0.900621       ...                  0.906832            0.912267   \n",
       "1           0.939441       ...                  0.919255            0.950699   \n",
       "2           0.944099       ...                  0.933230            0.973602   \n",
       "3           0.925466       ...                  0.936335            0.989907   \n",
       "4           0.931677       ...                  0.923913            0.994177   \n",
       "\n",
       "   split3_test_score  split3_train_score  split4_test_score  \\\n",
       "0           0.902174            0.911491           0.920807   \n",
       "1           0.930124            0.946040           0.942547   \n",
       "2           0.928571            0.968944           0.939441   \n",
       "3           0.930124            0.988354           0.936335   \n",
       "4           0.919255            0.993789           0.919255   \n",
       "\n",
       "   split4_train_score  std_fit_time  std_score_time  std_test_score  \\\n",
       "0            0.906056      0.015064        0.000734        0.008505   \n",
       "1            0.943711      0.004683        0.001155        0.010130   \n",
       "2            0.970885      0.010262        0.001996        0.011809   \n",
       "3            0.988354      0.021210        0.001567        0.008098   \n",
       "4            0.993789      0.031640        0.002353        0.007569   \n",
       "\n",
       "   std_train_score  \n",
       "0         0.002355  \n",
       "1         0.003135  \n",
       "2         0.001924  \n",
       "3         0.000650  \n",
       "4         0.000905  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# results of grid search CV\n",
    "cv_results = pd.DataFrame(model_cv.cv_results_)\n",
    "cv_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a better sense of how training and test accuracy varies with C, let's plot the tranining and test accuracies against C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d117898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot of C versus train and test scores\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(cv_results['param_C'], cv_results['mean_test_score'])\n",
    "plt.plot(cv_results['param_C'], cv_results['mean_train_score'])\n",
    "plt.xlabel('C')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(['test accuracy', 'train accuracy'], loc='upper left')\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though the training accuracy monotonically increases with C, the test accuracy gradually reduces. Thus, we can conclude that higher values of C tend to **overfit** the model. This is because a high C value aims to classify all training examples correctly (since C is the *cost of misclassification* - if you impose a high cost on the model, it will avoid misclassifying any points by overfitting the data). \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's finally look at the optimal C values found by GridSearchCV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " The highest test accuracy is 0.931055900621118 at C = 10\n"
     ]
    }
   ],
   "source": [
    "best_score = model_cv.best_score_\n",
    "best_C = model_cv.best_params_['C']\n",
    "\n",
    "print(\" The highest test accuracy is {0} at C = {1}\".format(best_score, best_C))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now look at the metrics corresponding to C=10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model with the best value of C\n",
    "model = SVC(C=best_C)\n",
    "\n",
    "# fit\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "# predict\n",
    "y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy 0.930485155684\n",
      "precision 0.924124513619\n",
      "recall 0.892857142857\n"
     ]
    }
   ],
   "source": [
    "# metrics\n",
    "# print other metrics\n",
    "\n",
    "# accuracy\n",
    "print(\"accuracy\", metrics.accuracy_score(y_test, y_pred))\n",
    "\n",
    "# precision\n",
    "print(\"precision\", metrics.precision_score(y_test, y_pred))\n",
    "\n",
    "# recall/sensitivity\n",
    "print(\"recall\", metrics.recall_score(y_test, y_pred))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimising for Other Evaluation Metrics\n",
    "\n",
    "In this case, we had optimised (tuned) the model based on overall accuracy, though that may not always be the best metric to optimise. For example, if you are concerned more about catching all spams (positives), you may want to maximise TPR or sensitivity/recall. If, on the other hand, you want to avoid classifying hams as spams (so that any important mails don't get into the spam box), you would maximise the TNR or specificity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Tuning hyper-parameters for accuracy\n",
      " The highest accuracy score is 0.931055900621118 at C = {'C': 10}\n",
      "\n",
      "\n",
      "# Tuning hyper-parameters for precision\n",
      " The highest precision score is 0.936509856470386 at C = {'C': 0.1}\n",
      "\n",
      "\n",
      "# Tuning hyper-parameters for recall\n",
      " The highest recall score is 0.8994650196111064 at C = {'C': 10}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# specify params\n",
    "params = {\"C\": [0.1, 1, 10, 100, 1000]}\n",
    "\n",
    "# specify scores/metrics in an iterable\n",
    "scores = ['accuracy', 'precision', 'recall']\n",
    "\n",
    "for score in scores:\n",
    "    print(\"# Tuning hyper-parameters for {}\".format(score))\n",
    "    \n",
    "    # set up GridSearch for score metric\n",
    "    clf = GridSearchCV(SVC(), \n",
    "                       params, \n",
    "                       cv=folds,\n",
    "                       scoring=score,\n",
    "                       return_train_score=True)\n",
    "    # fit\n",
    "    clf.fit(X_train, y_train)\n",
    "\n",
    "    print(\" The highest {0} score is {1} at C = {2}\".format(score, clf.best_score_, clf.best_params_))\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, you can see that the optimal value of the hyperparameter varies significantly with the choice of evaluation metric."
   ]
  }
 ],
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