Project-MachineLearning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>A Data Driven Approach to Predicting Chemical Reaction Kinetics: Machine Learning</h2>\n",
    "<br>\n",
    "Maneet Goyal<sup>1</sup>, Keren Zhang<sup>2</sup>\n",
    "<br>\n",
    "<i><sup>1</sup>School of Civil and Environmental Engineering, <sup>2</sup>School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA</i>\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"1000\"\n",
       "            height=\"500\"\n",
       "            src=\"Report/kineticsML_Report.pdf\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x1b8a9bcb550>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Displaying the report\n",
    "from IPython.display import IFrame\n",
    "IFrame(\"Report/kineticsML_Report.pdf\", width=1000, height=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Libs/Packages\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "import itertools\n",
    "from collections import Counter\n",
    "from imblearn.over_sampling import RandomOverSampler\n",
    "from imblearn.over_sampling import SMOTE\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- No. of Data points (rows) imported: 1979 -----\n"
     ]
    }
   ],
   "source": [
    "# Reading data for reaction order classification experiments\n",
    "# This notebook doesn't perform regression studies for acttivation energy prediction; refer to our report for more details on it.\n",
    "reac_df = pd.read_excel(\"MLDataDump/TrainingDataNewSpecies.xlsx\", header=0, index_col=0)\n",
    "print('----- No. of Data points (rows) imported: {} -----'.format(len(reac_df.index)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- No. of Data points (rows) available for experiments: 1962 -----\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\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>Reaction Link</th>\n",
       "      <th>Records</th>\n",
       "      <th>Reactants</th>\n",
       "      <th>Products</th>\n",
       "      <th>Reactants_List</th>\n",
       "      <th>Products_List</th>\n",
       "      <th>Reactants_SIDs_List</th>\n",
       "      <th>Products_SIDs_List</th>\n",
       "      <th>Products_Available</th>\n",
       "      <th>Status_50</th>\n",
       "      <th>Status_75</th>\n",
       "      <th>Status_100</th>\n",
       "      <th>ReactionOrder</th>\n",
       "      <th>ActivationEnergy</th>\n",
       "      <th>ReactantCID</th>\n",
       "      <th>ProductCID</th>\n",
       "      <th>FeatureVector</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>776</th>\n",
       "      <td>http://kinetics.nist.gov/kinetics/ReactionSear...</td>\n",
       "      <td>2</td>\n",
       "      <td>Â·CH2 + Â·CH2</td>\n",
       "      <td>C2H2 + HÂ· + HÂ·</td>\n",
       "      <td>['·CH2', '·CH2']</td>\n",
       "      <td>['C2H2', 'H·', 'H·']</td>\n",
       "      <td>[10972, 10972]</td>\n",
       "      <td>[3537, 8457, 8457]</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>2.0</td>\n",
       "      <td>46000.0</td>\n",
       "      <td>[123164, 123164]</td>\n",
       "      <td>[6326, 5362549, 5362549]</td>\n",
       "      <td>[ 0.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>777</th>\n",
       "      <td>http://kinetics.nist.gov/kinetics/ReactionSear...</td>\n",
       "      <td>3</td>\n",
       "      <td>Â·CH2 + Â·CH2</td>\n",
       "      <td>C2H2 + H2</td>\n",
       "      <td>['·CH2', '·CH2']</td>\n",
       "      <td>['C2H2', 'H2']</td>\n",
       "      <td>[10972, 10972]</td>\n",
       "      <td>[3537, 7937]</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>2.0</td>\n",
       "      <td>50000.0</td>\n",
       "      <td>[123164, 123164]</td>\n",
       "      <td>[6326, 783]</td>\n",
       "      <td>[-1.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>780</th>\n",
       "      <td>http://kinetics.nist.gov/kinetics/ReactionSear...</td>\n",
       "      <td>2</td>\n",
       "      <td>Â·CH2</td>\n",
       "      <td>Â·CH + HÂ·</td>\n",
       "      <td>['·CH2']</td>\n",
       "      <td>['·CH', 'H·']</td>\n",
       "      <td>[10972]</td>\n",
       "      <td>[10960, 8457]</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>2.0</td>\n",
       "      <td>361500.0</td>\n",
       "      <td>[123164]</td>\n",
       "      <td>[-1, 5362549]</td>\n",
       "      <td>[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>781</th>\n",
       "      <td>http://kinetics.nist.gov/kinetics/ReactionSear...</td>\n",
       "      <td>2</td>\n",
       "      <td>Â·CH2</td>\n",
       "      <td>H2 + C</td>\n",
       "      <td>['·CH2']</td>\n",
       "      <td>['H2', 'C']</td>\n",
       "      <td>[10972]</td>\n",
       "      <td>[7937, 3419]</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>2.0</td>\n",
       "      <td>257500.0</td>\n",
       "      <td>[123164]</td>\n",
       "      <td>[783, 5462310]</td>\n",
       "      <td>[-1.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1594</th>\n",
       "      <td>http://kinetics.nist.gov/kinetics/ReactionSear...</td>\n",
       "      <td>1</td>\n",
       "      <td>Â·Cl + Â·CH2</td>\n",
       "      <td>Â·CH + HCl</td>\n",
       "      <td>['·Cl', '·CH2']</td>\n",
       "      <td>['·CH', 'HCl']</td>\n",
       "      <td>[11174, 10972]</td>\n",
       "      <td>[10960, 8171]</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>2.0</td>\n",
       "      <td>106000.0</td>\n",
       "      <td>[5360523, 123164]</td>\n",
       "      <td>[-1, 313]</td>\n",
       "      <td>[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          Reaction Link  Records  \\\n",
       "RID                                                                \n",
       "776   http://kinetics.nist.gov/kinetics/ReactionSear...        2   \n",
       "777   http://kinetics.nist.gov/kinetics/ReactionSear...        3   \n",
       "780   http://kinetics.nist.gov/kinetics/ReactionSear...        2   \n",
       "781   http://kinetics.nist.gov/kinetics/ReactionSear...        2   \n",
       "1594  http://kinetics.nist.gov/kinetics/ReactionSear...        1   \n",
       "\n",
       "          Reactants          Products    Reactants_List         Products_List  \\\n",
       "RID                                                                             \n",
       "776   Â·CH2 + Â·CH2  C2H2 + HÂ· + HÂ·  ['·CH2', '·CH2']  ['C2H2', 'H·', 'H·']   \n",
       "777   Â·CH2 + Â·CH2         C2H2 + H2  ['·CH2', '·CH2']        ['C2H2', 'H2']   \n",
       "780           Â·CH2        Â·CH + HÂ·          ['·CH2']         ['·CH', 'H·']   \n",
       "781           Â·CH2            H2 + C          ['·CH2']           ['H2', 'C']   \n",
       "1594   Â·Cl + Â·CH2        Â·CH + HCl   ['·Cl', '·CH2']        ['·CH', 'HCl']   \n",
       "\n",
       "     Reactants_SIDs_List  Products_SIDs_List  Products_Available  Status_50  \\\n",
       "RID                                                                           \n",
       "776       [10972, 10972]  [3537, 8457, 8457]                True       True   \n",
       "777       [10972, 10972]        [3537, 7937]                True       True   \n",
       "780              [10972]       [10960, 8457]                True       True   \n",
       "781              [10972]        [7937, 3419]                True       True   \n",
       "1594      [11174, 10972]       [10960, 8171]                True       True   \n",
       "\n",
       "      Status_75  Status_100  ReactionOrder  ActivationEnergy  \\\n",
       "RID                                                            \n",
       "776        True        True            2.0           46000.0   \n",
       "777        True        True            2.0           50000.0   \n",
       "780        True        True            2.0          361500.0   \n",
       "781        True        True            2.0          257500.0   \n",
       "1594       True        True            2.0          106000.0   \n",
       "\n",
       "            ReactantCID                ProductCID  \\\n",
       "RID                                                 \n",
       "776    [123164, 123164]  [6326, 5362549, 5362549]   \n",
       "777    [123164, 123164]               [6326, 783]   \n",
       "780            [123164]             [-1, 5362549]   \n",
       "781            [123164]            [783, 5462310]   \n",
       "1594  [5360523, 123164]                 [-1, 313]   \n",
       "\n",
       "                                          FeatureVector  \n",
       "RID                                                      \n",
       "776   [ 0.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...  \n",
       "777   [-1.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...  \n",
       "780   [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...  \n",
       "781   [-1.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...  \n",
       "1594  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Filtering subset of the dataframe which has reaction order reported\n",
    "subset_reac_df = reac_df.query('ReactionOrder >= 0')\n",
    "print('----- No. of Data points (rows) available for experiments: {} -----'.format(len(subset_reac_df.index)))\n",
    "subset_reac_df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>FeatureVector</th>\n",
       "      <th>ReactionOrder</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>776</th>\n",
       "      <td>[ 0.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>777</th>\n",
       "      <td>[-1.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>780</th>\n",
       "      <td>[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>781</th>\n",
       "      <td>[-1.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1594</th>\n",
       "      <td>[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          FeatureVector  ReactionOrder\n",
       "RID                                                                   \n",
       "776   [ 0.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...            2.0\n",
       "777   [-1.  0.  0. -1.  0.  0.  0.  0.  0.  0.  0.  ...            2.0\n",
       "780   [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...            2.0\n",
       "781   [-1.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...            2.0\n",
       "1594  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  ...            2.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Filtering just the columns we need\n",
    "subset_for_exp = subset_reac_df[['FeatureVector', 'ReactionOrder']]\n",
    "subset_for_exp.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Exploring Class Balance/Distribution and Creating X (featurevector) and y (labels)\n",
    "X_vec = []\n",
    "y_labl = []\n",
    "X_Axis = [0, 1, 2, 3]\n",
    "Y_Axis = [0]*len(X_Axis)\n",
    "for rid, rxn in subset_for_exp.iterrows():\n",
    "        Y_Axis[int(rxn['ReactionOrder'])] = Y_Axis[int(rxn['ReactionOrder'])] + 1\n",
    "        # Feature vectors got converted to string during our routine; converting them back to Numpy arrays\n",
    "        row_feat_vec = np.array(rxn['FeatureVector'].strip(' []').replace(\"\\n\", \"\").replace(\".\", \"\").split(), dtype=float)\n",
    "        X_vec.append(row_feat_vec)\n",
    "        y_labl.append(int(rxn['ReactionOrder']))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Performing Oversampling\n",
    "X_ror_vec, y_ror_labl = RandomOverSampler().fit_sample(X_vec, y_labl)\n",
    "X_smote_vec, y_smote_labl = SMOTE(kind='svm').fit_sample(X_vec, y_labl)\n",
    "axis_ror = (sorted(Counter(y_ror_labl).items()))\n",
    "axis_smote = (sorted(Counter(y_smote_labl).items()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b7fe65a160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Old and New Class Distributions\n",
    "\n",
    "# Gloabal\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Sub1\n",
    "plt.subplot(131)\n",
    "plt.bar(X_Axis[1:], Y_Axis[1:])\n",
    "plt.xlabel('Reaction Order')\n",
    "plt.ylabel('Count')\n",
    "plt.title(\"Imbalanced\")\n",
    "\n",
    "# Sub2\n",
    "plt.subplot(132)\n",
    "plt.bar(X_Axis[1:], [ele[1] for ele in axis_ror])\n",
    "plt.xlabel('Reaction Order')\n",
    "plt.title(\"ROR Balanced\")\n",
    "\n",
    "# Sub3\n",
    "plt.subplot(133)\n",
    "plt.bar(X_Axis[1:], [ele[1] for ele in axis_smote])\n",
    "plt.xlabel('Reaction Order')\n",
    "plt.title(\"SMOTE Balanced\")\n",
    "\n",
    "# Global\n",
    "ax.set_yscale('log')\n",
    "plt.suptitle('Class Imbalance in Gas Phase Reactions Subset')\n",
    "plt.subplots_adjust(wspace=0.4, top=0.8)\n",
    "plt.savefig('MLResultFigures/ReactionClasses.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Performing Dimensionality Reduction since we have a 42 dimensions\n",
    "\n",
    "# Initializing\n",
    "pca_imbalanced = PCA(svd_solver='full')\n",
    "pca_ror = PCA(svd_solver='full')\n",
    "pca_smote = PCA(svd_solver='full')\n",
    "\n",
    "# Fitting\n",
    "pca_imbalanced.fit(X_vec)\n",
    "pca_ror.fit(X_ror_vec)\n",
    "pca_smote.fit(X_smote_vec)\n",
    "\n",
    "# Scree Plots Data\n",
    "scree_imbalanced = pca_imbalanced.explained_variance_ratio_.cumsum()\n",
    "scree_ror = pca_ror.explained_variance_ratio_.cumsum()\n",
    "scree_smote = pca_smote.explained_variance_ratio_.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b78e3ee9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Old and Oversampled data's scree plot | Uncentered data\n",
    "\n",
    "# Gloabal\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "plt.plot(scree_imbalanced, linewidth=2.0, label=\"Imbalanced\")\n",
    "plt.plot(scree_ror, linewidth=2.0, label=\"ROR\")\n",
    "plt.plot(scree_smote, linewidth=2.0, label=\"SMOTE\")\n",
    "plt.xlabel('No. of Components')\n",
    "plt.ylabel('Variance Explained')\n",
    "plt.title(\"Imbalanced\")\n",
    "plt.legend()\n",
    "\n",
    "plt.title('Scree Plots of Unbalanced and Oversampled Data | Uncentered Data')\n",
    "plt.savefig('MLResultFigures/ScreePlotsUncentered.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trend in the scree plots is expected as appending rows to a data matrix is expected to either increase the singular values or keep them same as before. This can be proved at least for the largest and the smallest singular values (Refer GVL4 Problem 2.4.9). Hence, the variance explained by the principal components of a matrix  are expected to either increase or remain the same when we compare imbalanced and oversampled data. Note that the `variance explained` or the `eigen values of the covariance matrix` are just the square of the singular values of the centered data matrix.\n",
    "<hr>\n",
    "The above discussion reminds us of an important part of PCA, i.e. `CENTERING` (via mean-averaging). IMHO, it is so important that it is perhaps one of the reasons that earned PCA a distinct name; without centering, it might have been referred to as just the `Eigen Value Decomposition` of symmetric matrices. You may have already noticed that centering was not performed over our data, so we have not yet done any PCA. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standarding (centering + scaling) data matrix\n",
    "\n",
    "# Initializing\n",
    "centered_unbalanced = StandardScaler()\n",
    "centered_ror = StandardScaler()\n",
    "centered_smote = StandardScaler()\n",
    "\n",
    "# Standardizing\n",
    "X_vec_std = centered_unbalanced.fit_transform(X_vec)\n",
    "X_ror_vec_std = centered_unbalanced.fit_transform(X_ror_vec)\n",
    "X_smote_vec_std = centered_unbalanced.fit_transform(X_smote_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Performing Dimensionality Reduction since we have a 42 dimensions\n",
    "\n",
    "# Initializing\n",
    "pca_imbalanced_std = PCA(svd_solver='full')\n",
    "pca_ror_std = PCA(svd_solver='full')\n",
    "pca_smote_std = PCA(svd_solver='full')\n",
    "\n",
    "# Fitting\n",
    "pca_imbalanced_std.fit(X_vec_std)\n",
    "pca_ror_std.fit(X_ror_vec_std)\n",
    "pca_smote_std.fit(X_smote_vec_std)\n",
    "\n",
    "# Scree Plots Data\n",
    "scree_imbalanced_std = pca_imbalanced_std.explained_variance_ratio_.cumsum()\n",
    "scree_ror_std = pca_ror_std.explained_variance_ratio_.cumsum()\n",
    "scree_smote_std = pca_smote_std.explained_variance_ratio_.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b78e3eeef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Old and Oversampled data's scree plot | Centered data\n",
    "\n",
    "# Global\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "plt.plot(scree_imbalanced_std, linewidth=2.0, label=\"Imbalanced\")\n",
    "plt.plot(scree_ror_std, linewidth=2.0, label=\"ROR\")\n",
    "plt.plot(scree_smote_std, linewidth=2.0, label=\"SMOTE\")\n",
    "plt.xlabel('No. of Components')\n",
    "plt.ylabel('Variance Explained')\n",
    "plt.title(\"Imbalanced\")\n",
    "plt.legend()\n",
    "\n",
    "plt.title('Scree Plots of Unbalanced and Oversampled Data | Centered Data')\n",
    "plt.savefig('MLResultFigures/ScreePlotsCentered.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Classification via Random Forests (RF)\n",
    "\n",
    "# Initializing\n",
    "clf_unbalanced = RandomForestClassifier(criterion=\"entropy\")\n",
    "clf_ror = RandomForestClassifier(criterion=\"entropy\")\n",
    "clf_smote = RandomForestClassifier(criterion=\"entropy\")\n",
    "\n",
    "# Training and Cross validating\n",
    "scores_unbalanced = np.mean(cross_val_score(clf_unbalanced, X_vec_std, y_labl, cv=10))\n",
    "scores_ror = np.mean(cross_val_score(clf_ror, X_ror_vec_std, y_ror_labl, cv=10))\n",
    "scores_smote = np.mean(cross_val_score(clf_smote, X_smote_vec_std, y_smote_labl, cv=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b793c83b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Cross validation scores\n",
    "\n",
    "# Global\n",
    "fig, ax = plt.subplots(figsize=(5,5))\n",
    "plt.bar(['Unbalanced', 'ROR', 'SMOTE'], [scores_unbalanced, scores_ror, scores_smote])\n",
    "plt.xlabel('Data Type')\n",
    "plt.ylabel('Accuracy Scores')\n",
    "plt.title('Addressing Data Quality \\n Cross-validation Scores for Full Dimension Data')\n",
    "ax.set_ylim(ymin=0.8)\n",
    "plt.savefig('MLResultFigures/CVScoreFull.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two observations are worth discussing about: <span style=\"color:gray\">model trained over imbalanced data is performing better than that trained over ROR oversampled data</span>; and <span style=\"color:gray\">model trained over SMOTE data is performing better than the other 2 models</span>.\n",
    "<hr>\n",
    "Observation 1 is expected because due to disproportionate class distribution in the `Unbalanced` data, the model might be getting trained and tested over similar datasets, comprising majority of the $2^{nd}$ order data points/reactions. Observation 2 is more interesing; due to the `interpolation` component of the SMOTE algorithm, we might be getting a good representation of the minority classes and consequently, we might be obtaing a more robust random forest in each k-fold CV interation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perfoming k-Fold cross validation of Data with Reduced Dimension\n",
    "\n",
    "# Initializing PCA models\n",
    "pca_imbalanced_27 = PCA(n_components=27, svd_solver='full')\n",
    "pca_ror_27 = PCA(n_components=27, svd_solver='full')\n",
    "pca_smote_27 = PCA(n_components=27, svd_solver='full')\n",
    "\n",
    "# Getting tranformed data\n",
    "X_vec_std_27 = pca_imbalanced_27.fit_transform(X_vec_std)\n",
    "X_ror_vec_std_27 = pca_ror_27.fit_transform(X_ror_vec_std)\n",
    "X_smote_vec_std_27 = pca_smote_27.fit_transform(X_smote_vec_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "`27 out of 42` principal components are chosen because they explain more than `99%` variance.\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Classification via Random Forests (RF) | Reduced Dimension data\n",
    "\n",
    "# Initializing\n",
    "clf_unbalanced_27 = RandomForestClassifier(criterion=\"entropy\")\n",
    "clf_ror_27 = RandomForestClassifier(criterion=\"entropy\")\n",
    "clf_smote_27 = RandomForestClassifier(criterion=\"entropy\")\n",
    "\n",
    "# Training and Cross validating\n",
    "scores_unbalanced_27 = np.mean(cross_val_score(clf_unbalanced_27, X_vec_std_27, y_labl, cv=10))\n",
    "scores_ror_27 = np.mean(cross_val_score(clf_ror_27, X_ror_vec_std_27, y_ror_labl, cv=10))\n",
    "scores_smote_27 = np.mean(cross_val_score(clf_smote_27, X_smote_vec_std_27, y_smote_labl, cv=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OfD4eERuSao1nKj92KJp0RxmLzj6vFelkSI+LgA8C+5I6kp+ex38oj+tp6x6Tx7frgnE2sJG02HPmqt1vtutKsroPGvW6T5ZFRNxDqqn0nBR6mIZHU2WzgI3z7b6tYmh8H58l/bzt6Tp0aM97EBHzI+KYiHgNqTb2H5J27yDkWcAwSUM6jKNXkfqy+AwpEa+eR/fW7Wm7blRbdu+ZlztM+ekiDR4GvtqwzjUi4iLaf7Y69V4WdYW6LB4GbmyIda2IaOy1r6lmx2mTYrOofN7zHY3rsRw+83l5K5E+dz37Y4mOT0m7AP9J6pJ33fwl/yRt8kQRiTki7ie1BV6k9IyzVSStJumgVjWkSJfvXEp6xNEQpb5q/4N0MgdJ+2vR89fmkXbYQrXojrKX8C4mPfbnk+TacjaE1GzwOOkA+1qHm3srqVngKEmDJb2PxZ9A0a4ryVd039ij3T5ZEpK2yN/0I/PwxqQvqNtykf8DjpW0Xb7UcdO8vt+T9uvnlbq23I30wW7aF0SuWX8f+F9Jr8rr2kjSXvn1PnnZYlEXoW0v3Yp0i/EtwCn5s/RG4GMsQ5/DETGRlAgOz6NadntK+25UpwJvy7/UhgJfqKxnNqmZ5Eyl5wquLKknAXwf+ET+DEvSmpLelb+A2n22Wsq/ADeR9F1S09vSPhGm6ipgc0kH521YOR9/W3YQT6fH6U9I3b9uo/TE86+R2oMfXJbAc6xbkipm65P6FIElPz6HkN6TOcBgSSeQzt/0qojEnB3Fop8uT5B+Jr+XdCKolU+T3rQZpKsNfgKcm6dtD/xeqVliAqk99K/03h3lK+SD5FbSM9uq3UBekOd/hHQC5LZXzt10ec+TOksfn2M4kMWfA9euK8lvAx9Qevjnd5qsord9siTmk04w/V7S0zmWu0g1BiLiMtJZ6J/kslcCw/L2vYd0wvAx0hfuIbnG3cp/kporbss/D3/NoiaDzfLwAtL7cGakB6l24oOkXzKzgJ+R2jYndjhvK/+P9KWzavTS7Wm06UY1x3EJ6WqDKaQkVnUw6dfPPaSTfZ/N800mnbw9nfT5mU5+DmIHn61m3pKPkadI7aNrA9tHxJ873iMt5Gakd5CeRj6L1KTwddJJunY6Ok4j4nrgS6QuXGeTfsUdtAxhH5j3xxOkvPE4sF1EzMrTl/T4vJb0JXtf3o7n6KBJy31lmJkVpqQas5mZ4cRsZlYcJ2Yzs8I4MZuZFcaJ2cysMK161FrhDB8+PMaMGdPfYZjZADNlypTHImJE+5LLz4BJzGPGjGHy5Mn9HYaZDTCSlua29mXipgwzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDBOzGZmhXFiNjMrjBOzmVlhnJjNzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8LUlpglnSvpH5LuajFdkr4jabqkOyVtW5l2qKT789+hdcVoZlaiOmvM5wHjepn+TmCz/Hc4cBaApGHAicCOwA7AiZLWrTFOM7Oi1JaYI+ImYG4vRfYFLojkNmAdSRsAewETI2JuRMwDJtJ7gjczG1D6s415I+DhyvDMPK7VeDOzrtCfiVlNxkUv41+5AOlwSZMlTZ4zZ85yDc7MrL/0Z2KeCWxcGR4JzOpl/CtExDkRMTYixo4YMaK2QM3M+lJ/JuYJwCH56ow3A09GxGzgWuAdktbNJ/3ekceZmXWFwXUtWNJFwG7AcEkzSVdarAwQEd8Drgb2BqYDzwAfzdPmSvoycHte1MkR0dtJRDOzAaW2xBwRH2wzPYAjWkw7Fzi3jrjMzErnO//MzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDBOzGZmhXFiNjMrzOD+DsC6w5jjftnfIRTtwVPf1d8hWEFcYzYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDBOzGZmhXFiNjMrjBOzmVlhnJjNzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK8zg/g7AzJafMcf9sr9DKN6Dp76rv0NoyzVmM7PCODGbmRWm1sQsaZykeyVNl3Rck+mjJV0v6U5JkySNrExbKGlq/ptQZ5xmZiWprY1Z0iDgDGBPYCZwu6QJETGtUuw04IKIOF/S24FTgIPztGcjYpu64jMzK1WdNeYdgOkRMSMingcuBvZtKLMVcH1+fUOT6WZmXafOxLwR8HBleGYeV3UH8P78+r3AEEnr5eHVJE2WdJuk/ZqtQNLhuczkOXPmLM/Yzcz6TZ2JWU3GRcPwscCukv4E7Ao8AryYp42KiLHAh4BvSXrtKxYWcU5EjI2IsSNGjFiOoZuZ9Z86r2OeCWxcGR4JzKoWiIhZwPsAJK0FvD8inqxMIyJmSJoE/AvwQI3xmpkVoc4a8+3AZpI2kbQKcBCw2NUVkoZL6onhC8C5efy6klbtKQPsBFRPGpqZDVi1JeaIeBE4ErgW+AtwaUTcLelkSe/JxXYD7pV0H/Bq4Kt5/JbAZEl3kE4KntpwNYeZ2YDVtilD0v7ANRExX9LxwLbAVyLij+3mjYirgasbxp1QeX05cHmT+W4B3tA+fDOzgaeTGvOXclLeGdgLOB84q96wzMy6Vycn/xbm/+8CzoqIn0s6qb6Q+o47fGlvRejwxWyg6aTG/Iiks4EDgKvzSTn3sWFmVpNOEuwBpBN44yLiCWAY8LlaozIz62JtE3NEPAP8A9g5j3oRuL/OoMzMulnbxCzpROA/SdcZA6wM/KjOoMzMulknTRnvBd4DPA0v35E3pM6gzMy6WSeJ+fmICHI/F5LWrDckM7Pu1klivjRflbGOpI8Dvwa+X29YZmbdq+11zBFxmqQ9gaeA1wEnRMTE2iMzM+tSvSbm/BSSayNiD8DJ2MysD/TalBERC4FnJA3to3jMzLpeJ7dkPwf8WdJE8pUZABFxVG1RmZl1sU4S8y/zn5mZ9YFOTv6dnzu63zyPujciXqg3LDOz7tVJf8y7kbr6fJD0HL+NJR0aETfVG5qZWXfqpCnjm8A7IuJeAEmbAxcB29UZmJlZt+rkBpOVe5IyQETcR+ovw8zMatBJjXmypB8AF+bhDwNT6gvJzKy7dZKYPwkcARxFamO+CTizzqDMzLpZJ4l5MPDtiPgfePluwFVrjcrMrIt10sZ8PbB6ZXh1UkdGZmZWg04S82oRsaBnIL9eo76QzMy6WyeJ+WlJ2/YMSNoOeLa+kMzMulsnbcyfBS6TNCsPbwAcWF9IZmbdrZNbsm+XtAWpL2YB9/iWbDOz+rRsypC0vaT1AXIi3hb4CvBNScP6KD4zs67TWxvz2cDzAJLeBpwKXAA8CZxTf2hmZt2pt6aMQRExN78+EDgnIq4ArpA0tf7QzMy6U2815kGSehL37sBvKtM6OWloZmZLobcEexFwo6THSJfH3QwgaVNSc4aZmdWgZWKOiK9Kup50edx1ERF50krAp/siODOzbtRrk0RE3NZk3H31hWNmZp3c+WdmZn3IidnMrDBtE7OkIyWt2xfBmJlZZzXm9YHbJV0qaZwk1R2UmVk3a5uYI+J4YDPgB8B44H5JX5P02ppjMzPrSh21MedL5R7Nfy8C6wKXS/pGjbGZmXWltnfwSToKOBR4DPg/4HMR8YKklYD7gc/XG6KZWXfp5Nbq4cD7IuKh6siIeEnSPvWEZWbWvTppyrga6OnMCElDJO0IEBF/qSswM7Nu1UliPgtYUBl+Oo8zM7MadJKYVekng4h4CfcuZ2ZWm04S8wxJR0laOf99BphRd2BmZt2qk8T8CeCtwCPATGBH4PA6gzIz62adPIz1H8BBfRCLmZnR2XXMqwEfA7YGVusZHxGH1RiXmVnX6qQp40JSfxl7ATcCI4H5dQZlZtbNOknMm0bEl4CnI+J84F3AG+oNy8yse3WSmF/I/5+Q9HpgKDCmtojMzLpcJ4n5nNwf8/HABGAa8PVOFp67Cb1X0nRJxzWZPlrS9ZLulDRJ0sjKtEMl3Z//Du1we8zMVni9nvzLHRU9FRHzgJuA13S6YEmDgDOAPUmX2d0uaUJETKsUOw24ICLOl/R24BTgYEnDgBOBsUAAU/K885Zg28zMVki91pjzXX5HLuWydwCmR8SMiHgeuBjYt6HMVsD1+fUNlel7ARMjYm5OxhOBcUsZh5nZCqWTpoyJko6VtLGkYT1/Hcy3EfBwZXhmHld1B/D+/Pq9wBBJ63U4r5nZgNRJnxc91ysfURkXtG/WaPYIqmgYPhY4XdJ4UlPJI6SO+DuZF0mHk+9CHDVqVJtwzMxWDJ3c+bfJUi57JrBxZXgkMKth2bOA9wFIWgt4f0Q8KWkmsFvDvJOaxHYOcA7A2LFjX5G4zcxWRJ3c+XdIs/ERcUGbWW8HNpO0CakmfBDwoYZlDwfm5rbsLwDn5knXAl+rPJ37HXm6mdmA10lTxvaV16sBuwN/BHpNzBHxoqQjSUl2EHBuRNwt6WRgckRMINWKT5EUpKaMI/K8cyV9mZTcAU6OiLmvWImZ2QDUSVPGp6vDkoaSbtNuKyKuJj0BpTruhMrry4HLW8x7Lotq0GZmXaOjp2Q3eAbYbHkHYmZmSSdtzL9g0RURK5GuPb60zqDMzLpZJ23Mp1Vevwg8FBEza4rHzKzrdZKY/wbMjojnACStLmlMRDxYa2RmZl2qkzbmy4CXKsML8zgzM6tBJ4l5cO7rAoD8epX6QjIz626dJOY5kt7TMyBpX+Cx+kIyM+tunbQxfwL4saTT8/BMoOndgGZmtuw6ucHkAeDNuS8LRYSf92dmVqO2TRmSviZpnYhYEBHzJa0r6St9EZyZWTfqpI35nRHxRM9A7rh+7/pCMjPrbp0k5kGSVu0ZkLQ6sGov5c3MbBl0cvLvR8D1kn5IujX7MNr0LGdmZkuvk5N/35B0J7AH6ckiX46Ia2uPzMysS3VSYyYirgGuAZC0k6QzIuKINrOZmdlS6CgxS9oG+CBwIPBX4Kd1BmVm1s1aJmZJm5MeB/VB4HHgEtJ1zP/aR7GZmXWl3mrM9wA3A++OiOkAko7uk6jMzLpYb5fLvR94FLhB0vcl7U46+WdmZjVqmZgj4mcRcSCwBTAJOBp4taSzJL2jj+IzM+s6bW8wiYinI+LHEbEPMBKYChxXe2RmZl1qiR7GGhFzI+LsiHh7XQGZmXW7pXlKtpmZ1ciJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDBOzGZmhXFiNjMrjBOzmVlhnJjNzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWFqTcySxkm6V9J0Scc1mT5K0g2S/iTpTkl75/FjJD0raWr++16dcZqZlWRwXQuWNAg4A9gTmAncLmlCREyrFDseuDQizpK0FXA1MCZPeyAitqkrPjOzUtVZY94BmB4RMyLieeBiYN+GMgGsnV8PBWbVGI+Z2QqhzsS8EfBwZXhmHld1EvARSTNJteVPV6Ztkps4bpS0S41xmpkVpc7ErCbjomH4g8B5ETES2Bu4UNJKwGxgVET8C/AfwE8krd0wL5IOlzRZ0uQ5c+Ys5/DNzPpHnYl5JrBxZXgkr2yq+BhwKUBE3AqsBgyPiH9GxON5/BTgAWDzxhVExDkRMTYixo4YMaKGTTAz63t1Jubbgc0kbSJpFeAgYEJDmb8BuwNI2pKUmOdIGpFPHiLpNcBmwIwaYzUzK0ZtV2VExIuSjgSuBQYB50bE3ZJOBiZHxATgGOD7ko4mNXOMj4iQ9DbgZEkvAguBT0TE3LpiNTMrSW2JGSAiriad1KuOO6HA8cakAAAJgklEQVTyehqwU5P5rgCuqDM2M7NS+c4/M7PCODGbmRXGidnMrDBOzGZmhXFiNjMrjBOzmVlhnJjNzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDBOzGZmhXFiNjMrjBOzmVlhnJjNzArjxGxmVhgnZjOzwjgxm5kVxonZzKwwTsxmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyuME7OZWWGcmM3MCuPEbGZWGCdmM7PCODGbmRXGidnMrDC1JmZJ4yTdK2m6pOOaTB8l6QZJf5J0p6S9K9O+kOe7V9JedcZpZlaSwXUtWNIg4AxgT2AmcLukCRExrVLseODSiDhL0lbA1cCY/PogYGtgQ+DXkjaPiIV1xWtmVoo6a8w7ANMjYkZEPA9cDOzbUCaAtfProcCs/Hpf4OKI+GdE/BWYnpdnZjbg1ZmYNwIergzPzOOqTgI+Imkmqbb86SWY18xsQKqtKQNQk3HRMPxB4LyI+KaktwAXSnp9h/Mi6XDg8Dy4QNK9yxJwAYYDj/V3EFX6en9HUJui9vUA3s+w4u/r0TWE0as6E/NMYOPK8EgWNVX0+BgwDiAibpW0GulN7GReIuIc4JzlGHO/kjQ5Isb2dxzdwPu673hfL7k6mzJuBzaTtImkVUgn8yY0lPkbsDuApC2B1YA5udxBklaVtAmwGfCHGmM1MytGbTXmiHhR0pHAtcAg4NyIuFvSycDkiJgAHAN8X9LRpKaK8RERwN2SLgWmAS8CR/iKDDPrFkp50Eog6fDcPGM1877uO97XS86J2cysML4l28ysME7MfUTSQklTJd0l6ReS1qlM21rSbyTdJ+l+SV+SpDxtvKQ5ed57cnt815P0RUl351v5p0raUdIkSX/r2Xe53JWSFlSGm+5rSR/Ny5kq6XlJf86vT214D3r+tuqfLV82ksZIuqth3EmSju1lnvGSTl/C9TwoafjSxrm0libWEjkx951nI2KbiHg9MBc4AkDS6qSrUE6NiM2BNwFvBT5VmfeSiNgG2An4oqSN6WL5mvd9gG0j4o3AHiy6IekJ0n4if/ltUJmv5b6OiB/m92cb0qWZ/5qHe/p4uaRnev6rdi1gtlw5MfePW1l0J+OHgN9FxHUAEfEMcCTwik6fIuJx0u3pGzRO6zIbAI9FxD8BIuKxiOi5zv1i0qWZAO8DflqZr+N93Y3yL46vS/pD/kWxS2XyxpKuyZ2KnViZ50pJU/Kvl8ObLLZlGUkLJH1V0h2SbpP06jz+1ZJ+lsffIemtefxHcmxTJZ2d++Mh/9q5T9KN5C/lFZ0Tcx/LH6bdWXRN99bAlGqZiHgAWEvS2g3zjiJd631nH4RasutIieI+SWdK2rUy7XrgbXk/HwRcUpnW8b5u4sCGpozVl8N2lGhwROwAfBY4sTJ+B+DDwDbA/pJ6bhg5LCK2A8YCR0lar8kyW5VZE7gtIt4E3AR8PI//DnBjHr8t6fLZLYEDgZ3yr5qFwIclbQD8Nykh7wmskE1MjZyY+87qkqYCjwPDgIl5vGhyu3nWM/5ASXcDM4BvR8RztUZauIhYAGxHuh1/DnCJpPF58kLgt6SDePWIeLAyayf7upXGpoxnlzb+ftZu+3t+YUwBxlSmT4yIx/N2/xTYOY8/StIdwG2ku3U3a7LsVmWeB65qsr63A2cBRMTCiHiSVJnZjtRL5dQ8/BpgR2BSRMzJnaVVv4hXWE7MfefZ/E0/GliF3MYM3E2qSbxM0muABRExP4+6JCK2BnYBvilp/T6KuVj5gJ0UESeSmiPeX5l8MfBd4NKG2TrZ1wPd48C6DeOGsagvi3/m/wtZ/Aa0xoQeknYjte+/Jddu/0T6RfeyNmVeiEXX6zaur5GA8ytfjK+LiJNaxLbCc2LuY/nb/yjgWEkrAz8Gdpa0B7x8guo7wDeazHsrcCHwmb6LuDySXiepWjPbBnioMnwzcApwUcOsHe/rgSr/2pgtqacrhGGk/mp+22bWPSUNy/tsP+B3pK5650XEM5K2AN7cZL5OyjS6Hvhkjm9Qbma6HviApFf1xC1pNPB7YDdJ6+Xjaf8Oll88J+Z+EBF/Au4ADso/DfcFjlfqHe/PpH5GWl3y83Xgo5KG9EmwZVoLOF/SNEl3ktoVT+qZGMlpEbFYj2ZLsa+rGtuY37q8NqYfHELaB1OB3wD/ndvae/NbUqVgKnBFREwGrgEG5/fgy6SmikadlGn0GeBfJf2Z1MSxdb4K5njgurysicAGETGb9N7fCvwa+GMHyy+e7/wzMyuMa8xmZoVxYjYzK4wTs5lZYZyYzcwK48RsZlaYOp/5Z7ZUJC0kXcq2MukJNucD34qIl3qZZwzw1oj4SYfrWI90bSzA+qQbHObk4R3yXWRm/cKXy1lxJC2IiLXy61cBPyF1PnRiL/PsBhwbEfssxfpOIt39d9rSRWy2fLkpw4oWEf8g9YlxpJIxkm6W9Mf813Ojx6nALvnmj6N7KdeWpFMkHVEZ/rqkT0naQ9INube0aZLOkF7uN/udkm7N67pE0prLcz9Yd3GN2YpTrTFXxs0DtgDmAy9FxHP5tuyLImJsY41Z0hrNyrVY30lUasySXgtcHBHb517q7id1oLMdqVfArUj9P08k3dJ9C3AZ8M586/EXSTcgfm057hbrIm5jthVFz1NJVgZOl9TT9ePmLcp3Wu4VIuIBSfMlvYHU6dQfImJerhzf1tNjnaSLWdTL2lbALbnMKrTve8KsJSdmK17uAW4h8A9SH8F/Jz19ZCWgVReoR3dYrpUfAONJXVGeXRn/il7WSF8a10TEwUu4DrOm3MZsRZM0AvgecHruInIoMDtfoXEwMCgXnQ9UO3ZqVa5TVwDvJvVc9+vK+DdLGpWbOA4g1YxvAXbNXyBIWrOh9zuzJeIas5Wo56ECPZfLXQj8T552JnCFpP2BG4Cn8/g7gRdzh+zn9VKuI7lt+ibg0YbL9G4Bvkl6GsokYEJEhKSPkTrsXyWX+y9S27TZEvPJP7MmJK1E6uJyv4iYkcftARwZEfv1a3A24Lkpw6xBPun3AKndeEZ/x2PdxzVmM7PCuMZsZlYYJ2Yzs8I4MZuZFcaJ2cysME7MZmaFcWI2MyvM/weqMeX++fJhyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b793c95ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Cross validation scores | Reduced Dimension data\n",
    "\n",
    "# Global\n",
    "fig, ax = plt.subplots(figsize=(5,5))\n",
    "plt.bar(['Unbalanced', 'ROR', 'SMOTE'], [scores_unbalanced_27, scores_ror_27, scores_smote_27])\n",
    "plt.xlabel('Data Type')\n",
    "plt.ylabel('Accuracy Scores')\n",
    "plt.title('Addressing Data Quality \\n Cross-validation Scores for Reduced Dimension Data')\n",
    "ax.set_ylim(ymin=0.8)\n",
    "plt.savefig('MLResultFigures/CVScoreReduced.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above results are similar to what were obtained for the full dimensional data. Now we plot the covariance matrices of the reducted dimension data to look for covariance between individual dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b793cb1a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Covariance Matrices\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "seaborn.heatmap(np.cov(X_smote_vec_std_27.T), cmap=\"YlGnBu\", ax=ax)\n",
    "plt.title('Covariance Matrix Reduced Dimension SMOTE Data')\n",
    "plt.savefig('MLResultFigures/CovMat.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance matrix suggests that the standardized and reduced data matrix, `X_smote_vec_std_27.T`,  was orthogonal which is quite probably since we are dealing with sparse matrices. Further, typically, the presence of 1 type of chemical bond (say, C-H) is independent to the presence of another type of bond (say, C=O)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'criterion': 'gini'}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Since, SMOTE trained Random Forest performed the best, we now attempt to optmize it's hyper parameters to try and come up\n",
    "# more accurate model.\n",
    "param_grid = [{'criterion': ['gini', 'entropy']}]\n",
    "clf = GridSearchCV(clf_smote_27, param_grid, cv=10)\n",
    "clf.fit(X_smote_vec_std_27, y_smote_labl)\n",
    "clf.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b793c46208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here is the best criterion\n",
    "fig, ax = plt.subplots(figsize=(5,5))\n",
    "plt.bar(['Gini', 'Entropy'], clf.cv_results_['mean_test_score'])\n",
    "plt.xlabel('RF Criterion')\n",
    "plt.ylabel('Accuracy Scores')\n",
    "plt.title('Model Optimization | With Reduced SMOTE Data')\n",
    "ax.set_ylim(ymin=0.8)\n",
    "plt.savefig('MLResultFigures/RFOptimize.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finally, we perform complexity optmization to figure out the optmium number of tree and tree depth\n",
    "# We are using grid_search for complexity optimiztion\n",
    "param_grid_2 = [{'n_estimators': list(range(1,100,10)),\n",
    "                'max_depth': list(range(1,100,10)),\n",
    "                'criterion': ['gini']}]  # gini chosen because it was found to be better hyperparameter\n",
    "clf = GridSearchCV(clf_smote_27, param_grid_2, cv=10)\n",
    "clf.fit(X_smote_vec_std_27, y_smote_labl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plotting Score vs Complexity (No of Trees, Tree Depth) Plot\n",
    "x_val_opti_study = clf.cv_results_['params']\n",
    "y_val_opti_study = clf.cv_results_['mean_test_score']\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "for i in range(10):\n",
    "    plt.plot([ele['n_estimators'] for ele in x_val_opti_study[10*i:10*(i+1)]] , y_val_opti_study[10*i:10*(i+1)], \n",
    "             label=x_val_opti_study[10*i]['max_depth'])\n",
    "ax.set_xlabel('No. of Trees')\n",
    "ax.set_ylabel('10-Fold CV Score')\n",
    "plt.legend()\n",
    "plt.title(\"Optimizing Model Compelxity\")\n",
    "plt.savefig('MLResultFigures/ComplexityOptimize.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "For optimization, we chose to first minimize the number of tree and then the tree depth. We propose `11 trees with max_depth of 11` as the optmium complexity random forest.\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now, we set up a final RF model and split our data into test and train data for the final model evaluation\n",
    "clf_smote_27_std_opt = RandomForestClassifier(criterion=\"gini\", n_estimators=11, max_depth=11)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_smote_vec_std_27, y_smote_labl, test_size=0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training the model with optimal parameters\n",
    "clf_smote_27_std_opt.fit(X_train, y_train)\n",
    "y_pred = clf_smote_27_std_opt.predict(X_test)\n",
    "cnf_matrix = confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This function is adopted from http://scikit-learn.org/stable/auto_examples/model_selection/plot_confusion_matrix.html\n",
    "\n",
    "def plot_confusion_matrix(cm, classes,\n",
    "                          normalize=True,\n",
    "                          title='Confusion matrix',\n",
    "                          cmap=plt.cm.Blues):\n",
    "    \"\"\"\n",
    "    This function prints and plots the confusion matrix.\n",
    "    Normalization can be applied by setting `normalize=True`.\n",
    "    \"\"\"\n",
    "    if normalize:\n",
    "        cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]\n",
    "        print(\"Normalized confusion matrix\")\n",
    "    else:\n",
    "        print('Confusion matrix, without normalization')\n",
    "\n",
    "    print(cm)\n",
    "\n",
    "    plt.imshow(cm, interpolation='nearest', cmap=cmap)\n",
    "    plt.title(title)\n",
    "    plt.colorbar()\n",
    "    tick_marks = np.arange(len(classes))\n",
    "    plt.xticks(tick_marks, classes, rotation=45)\n",
    "    plt.yticks(tick_marks, classes)\n",
    "\n",
    "    fmt = '.2f' if normalize else 'd'\n",
    "    thresh = cm.max() / 2.\n",
    "    for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n",
    "        plt.text(j, i, format(cm[i, j], fmt),\n",
    "                 horizontalalignment=\"center\",\n",
    "                 color=\"white\" if cm[i, j] > thresh else \"black\")\n",
    "\n",
    "    plt.ylabel('True label')\n",
    "    plt.xlabel('Predicted label')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finally, here's the confusion matrix with optmium complexity model\n",
    "plt.figure()\n",
    "plot_confusion_matrix(cnf_matrix, classes=[1,2,3], title='Confusion matrix \\n SMOTE | Reduced, Stanadrdized Data')\n",
    "plt.savefig('ConfusionMatrix.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen from the figure above, we got a great accuracy of `33:67` Test:Train Split. This marks the end of our classification study. We got great results with Random Forest model and looking at the results, dimensionality reduction didn't hurt the accuracy much.\n",
    "<hr>\n",
    "\n",
    "#### Somes Notes for Future Researchers\n",
    "\n",
    "Our underlying assumption behind all the above experiments is that <strong>the reaction order can be predicted by observing the presence of certain species and, the formation and breaking of certain bonds in a reaction</strong>. This implies that the `reaction order` must be a property of that reaction. In homegenous reactions, this is a warranted case since the rate of reaction is typically represented in a polynomial form.\n",
    "\n",
    "Future Researchers are advised to check whether any catalytic or heterogeneous reactions are there in the database. However, this is not probable because NIST reports that their database contains gas phase reactions. In line with our assumption mentioned above, it is advised that all the catalytic/heterogenous reactions (if found) be removed from the training data. In heterogeneous reactions, mass transfer effects the rate of reaction and in catalytic reaction, catalyst have the same effect. The rate of reaction, therefore, generally acquires a complicated non-polynomial form. For instance, recall Langmuir Hinshelwood Kinetics for solid-gas catalytic reactions. So the term 'order' doesn't remain applicable to these reactions.\n",
    "<hr>\n",
    "Around 208 reactions in the NIST databse have an entity <em>M</em> in both reactant and product. These reactions are adopted from <a href=\"https://hal.archives-ouvertes.fr/hal-00295495/document\">Atkinson et al.</a>. Future researchers are advised to go through this work to figure out whether such reactions be removed from the training data. M can represent Air, $O_{2}$, $N_{2}$, etc.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "#### Acknowledgements\n",
    "\n",
    "1. Dr. Andrew J. Medford, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, USA\n",
    "2. Prof. Datta B. Dandge, Department of Petrochemical Engineering, Maharashtra Institute of Technology, Pune, India"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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