support_vector_classifier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Machine Learning: Support Vector Classifier"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import sklearn\n",
    "from sklearn import svm\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, precision_recall_fscore_support\n",
    "from IPython.display import display, Latex, Markdown\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "def cleanCases(gun_cases):\n",
    "    # gun violence cases dataset cleaned\n",
    "    cases = pd.read_csv(gun_cases)\n",
    "    cases = cases.loc[:, ['date', 'state', 'n_killed', 'n_injured']]\n",
    "\n",
    "    cases['date'] = pd.to_datetime(cases['date'])\n",
    "    cases['year'] = cases['date'].dt.year\n",
    "    cases['harmed'] = cases['n_killed'] + cases['n_injured']\n",
    "    cases = cases.drop(columns=['date', 'n_killed', 'n_injured'])\n",
    "    cases = cases[(cases['year'] > 2013) & (cases['year'] < 2018)]\n",
    "    cases = cases.groupby(['state', 'year']).agg('sum')\n",
    "    cases = cases.reset_index()\n",
    "    return cases\n",
    "\n",
    "def cleanLaws(gun_laws):\n",
    "    # gun laws dataset cleaned\n",
    "    laws = pd.read_csv(gun_laws)\n",
    "    laws = laws[(laws['year'] > 2014) & (laws['year'] < 2018)]\n",
    "    return laws\n",
    "\n",
    "def cleanPopulation(population):\n",
    "    # state population dataset cleaned\n",
    "    #importing state population counts from 2010 - 2019\n",
    "    state_populations = pd.read_csv(population)\n",
    "\n",
    "    #cleaning state population data\n",
    "    state_populations = state_populations.drop(columns=['2010', '2011', '2012', '2013', '2018', '2019'])\n",
    "    return state_populations\n",
    "\n",
    "def combineDatasets(gun_cases, gun_laws, population):\n",
    "    cases = cleanCases(gun_cases)\n",
    "    laws = cleanLaws(gun_laws)\n",
    "    state_population = cleanPopulation(population)\n",
    "    \n",
    "    # adding population counts to cases dataset by matching year and state\n",
    "    for i, row in cases.iterrows():\n",
    "        cases.at[i, ('population')] = float(state_population[state_population.state == row['state']][str(row['year'])])\n",
    "\n",
    "    #compute the proportion of harmed individuals due to a gun incident out of the state population \n",
    "    cases['proportion_harmed'] = cases['harmed']/cases['population']\n",
    "    cases.drop(columns=['harmed', 'population'], inplace=True)\n",
    "    # Check if gun cases were reduced based on previous year values (only valid for 2015-2017)\n",
    "    harmed = cases['proportion_harmed'].tolist()\n",
    "    decrease = list()\n",
    "\n",
    "    # False = (Decrease = 0), True = (Decrease = 1)\n",
    "    for i in range(0, len(harmed), 4):\n",
    "        decrease.append(False)                           # Year 2014; Temporary Place-Holder\n",
    "        decrease.append(harmed[i] > harmed[i+1])         # Year 2015\n",
    "        decrease.append(harmed[i+1] > harmed[i+2])       # Year 2016\n",
    "        decrease.append(harmed[i+2] > harmed[i+3])       # Year 2017\n",
    "\n",
    "    cases['decrease_in_gun_violence'] = pd.Series(decrease)\n",
    "    cases = cases.drop(labels=range(0, len(decrease), 4), axis=0)\n",
    "    cases = cases[(cases['state'] != 'District of Columbia')]\n",
    "    \n",
    "    # Combined dataset\n",
    "    data = cases.merge(laws, on=['state', 'year'], how='outer')\n",
    "    return data"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "gun_cases = 'gun-violence-data_01-2013_03-2018.csv'\n",
    "gun_laws = 'statefirearmlaws.csv'\n",
    "population = 'us_states_census.csv'\n",
    "data = combineDatasets(gun_cases, gun_laws, population)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "data.head(5)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "     state  year  proportion_harmed  decrease_in_gun_violence  felony  \\\n",
       "0  Alabama  2015           0.000195                     False       0   \n",
       "1  Alabama  2016           0.000257                     False       0   \n",
       "2  Alabama  2017           0.000287                     False       0   \n",
       "3   Alaska  2015           0.000209                     False       1   \n",
       "4   Alaska  2016           0.000258                     False       1   \n",
       "\n",
       "   invcommitment  invoutpatient  danger  drugmisdemeanor  alctreatment  ...  \\\n",
       "0              1              0       1                0             0  ...   \n",
       "1              1              0       1                0             0  ...   \n",
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       "\n",
       "   expartedating  dvrosurrender  dvrosurrendernoconditions  \\\n",
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       "   expartesurrenderdating  dvroremoval  stalking  lawtotal  \n",
       "0                       0            0         0        10  \n",
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       "2                       0            0         0        10  \n",
       "3                       0            0         0         3  \n",
       "4                       0            0         0         3  \n",
       "\n",
       "[5 rows x 139 columns]"
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     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Oversampling Dataset\n",
    "\n",
    "To balance out our decrease_in_gun_violence classes, we oversample from the decrease_in_gun_violence=1 class. \n",
    "\n",
    "Oversampling= replicating some points from the minority class in order to increase its cardinality [handling imbalanced datasets](https://towardsdatascience.com/handling-imbalanced-datasets-in-machine-learning-7a0e84220f28)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "oversampled_rows = data[data.decrease_in_gun_violence == True].copy(deep=True)\n",
    "balanced_data = pd.concat([data, oversampled_rows], ignore_index=True)\n",
    "\n",
    "print(f'Shape: {balanced_data.shape}')\n",
    "print(f'Number of examples in our balanced dataset where decrease_in_gun_violence=0: {len(balanced_data[balanced_data.decrease_in_gun_violence == False])}')\n",
    "print(f'Number of examples in our balanced dataset where decrease_in_gun_violence=1: {len(balanced_data[balanced_data.decrease_in_gun_violence == True])}')"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Shape: (199, 139)\n",
      "Number of examples in our balanced dataset where decrease_in_gun_violence=0: 101\n",
      "Number of examples in our balanced dataset where decrease_in_gun_violence=1: 98\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Create the features and labels for classification."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "def create_features_labels(dataset): \n",
    "    X = dataset.drop(columns = ['decrease_in_gun_violence', 'state', 'year']) #keep all law reform info as features, as well as the proportion of individuals harmed\n",
    "    y = dataset['decrease_in_gun_violence']   # Labels are if the number of cases reduced\n",
    "    y = y.replace({True: 1, False: 0})\n",
    "    return X, y\n",
    "\n",
    "# X, y = create_features_labels(data)\n",
    "X, y = create_features_labels(balanced_data)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "#checking proportion of classes w.r.t 'decrease'\n",
    "print(f'Number of examples in our entire dataset where decrease_in_gun_violence=0: {len(y[y == 0])}')\n",
    "print(f'Number of examples in our entire dataset where decrease_in_gun_violence=1: {len(y[y == 1])}')"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of examples in our entire dataset where decrease_in_gun_violence=0: 101\n",
      "Number of examples in our entire dataset where decrease_in_gun_violence=1: 98\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Baseline Classifier"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Create a baseline classifier `MajorityLabelClassifier` to test our classifier against. This will always predict the class equal to the mode of the labels."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "class MajorityLabelClassifier():\n",
    "    # Initialize parameter for the classifier\n",
    "    def __init__(self):\n",
    "        self.mode = 0\n",
    "    \n",
    "    # Fit the data by taking training data X and their labels y and storing the learned parameter\n",
    "    def fit(self, X, y):\n",
    "        modes = dict()           # Stores all the modes of the training data\n",
    "        y = y.tolist()\n",
    "        for i in range(len(X)):\n",
    "            if y[i] in modes.keys():\n",
    "                modes[y[i]] += 1\n",
    "            else:\n",
    "                modes[y[i]] = 1\n",
    "                \n",
    "        # Find the most frequent mode and store it\n",
    "        total = 0\n",
    "        for key in modes:\n",
    "            if modes[key] > total:\n",
    "                total = modes[key]\n",
    "                self.mode = key\n",
    "    \n",
    "    # Predict the label for each instance X as the learned parameter\n",
    "    def predict(self, X):\n",
    "        labels = list()\n",
    "        for i in X:\n",
    "            labels.append(self.mode)\n",
    "        return labels\n",
    "    \n",
    "    # Calculate the accuracy of our classifier using the true and predicted labels\n",
    "    def evaluate_accuracy(self, y, y_predict):\n",
    "        accurate_pred = 0\n",
    "        total = len(y_predict)\n",
    "        true_labels = y.tolist()\n",
    "        \n",
    "        for i in range(total):\n",
    "            if true_labels[i] == y_predict[i]:\n",
    "                accurate_pred += 1\n",
    "        return accurate_pred/total"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "baseline = MajorityLabelClassifier()\n",
    "baseline.fit(X, y)\n",
    "labels = baseline.predict(X)\n",
    "print(baseline.evaluate_accuracy(y, labels))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.6838235294117647\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Support Vector Classifier"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Evaluate the `SupportVectorClassifier()` by training, fitting, and predicting on the data."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "`we should use cross validation to fine tune some of our parameters and try to increase our accuracy up to 80%`"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "def learn_classifier(X_train, y_train, kernel):\n",
    "    \"\"\" learns a classifier from the input features and labels using the kernel function supplied\n",
    "    Inputs:\n",
    "        X_train: scipy.sparse.csr.csr_matrix: sparse matrix of features, output of create_features()\n",
    "        y_train: numpy.ndarray(int): dense binary vector of class labels, output of create_labels()\n",
    "        kernel: str: kernel function to be used with classifier. [linear|poly|rbf|sigmoid]\n",
    "    Outputs:\n",
    "        sklearn.svm.SVC: classifier learnt from data\n",
    "    \"\"\"\n",
    "    \n",
    "    # svc =  sklearn.svm.SVC(kernel = kernel)\n",
    "    svc =  svm.SVC(kernel = kernel)\n",
    "    return svc.fit(X_train, y_train)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "#fit svc model + predict on test set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2,random_state=1) #changed split to 80% train, 20% test\n",
    "clf_model = learn_classifier(X_train, y_train, 'linear')  \n",
    "y_predict = clf_model.predict(X_test)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "#evaluation metrics\n",
    "train_accuracy = clf_model.score(X,y)  #this gives training accuracy\n",
    "test_accuracy = accuracy_score(y_test, y_predict) #this gives testing accuracy\n",
    "\n",
    "print(f'Train Accuracy: {train_accuracy}')\n",
    "print(f'Test Accuracy: {test_accuracy}')\n",
    "\n",
    "cm = confusion_matrix(y_test, y_predict) #confusion matrix\n",
    "precision, recall, f1, support =  precision_recall_fscore_support(y_test, y_predict) #precision, recall, f1 score, and support for each class (decrease_in_gun_violence=0 and decrease_in_gun_violence=1)\n",
    "\n",
    "print(f'precision: {precision}')\n",
    "print(f'recall   : {recall}')\n",
    "print(f'f1 score : {f1}')\n",
    "\n",
    "#plot confusion matrix\n",
    "sns.heatmap(cm, annot = True, fmt = \".3f\", square = True, cmap = plt.cm.Blues);\n",
    "plt.ylabel('True');\n",
    "plt.xlabel('Predicted');\n",
    "plt.title('Support Vector Classifier Confusion Matrix');\n",
    "plt.tight_layout();"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Train Accuracy: 0.6633165829145728\n",
      "Test Accuracy: 0.4\n",
      "precision: [0.47058824 0.34782609]\n",
      "recall   : [0.34782609 0.47058824]\n",
      "f1 score : [0.4 0.4]\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Results from linear SVC aren't very good. While our predictions for both classes are well-balanced, we only obtained a test accuracy of 40%, and low precision, recall, and f1 scores. In the next steps, we'll do some cross-validation to tune the parameters of our SVC model and hopefully increase the accuracy."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Cross-Validation for SVC Parameter Tuning"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "def evaluate_classifier(classifier, X_validation, y_validation):\n",
    "    \"\"\" evaluates a classifier based on a supplied validation data\n",
    "    Inputs:\n",
    "        classifier: sklearn.svm.classes.SVC: classifer to evaluate\n",
    "        X_validation: scipy.sparse.csr.csr_matrix: sparse matrix of features\n",
    "        y_validation: numpy.ndarray(int): dense binary vector of class labels\n",
    "    Outputs:\n",
    "        double: accuracy of classifier on the validation data\n",
    "    \"\"\"\n",
    "    y_pred = classifier.predict(X_validation)\n",
    "    return sklearn.metrics.accuracy_score(y_validation, y_pred)\n",
    "\n",
    "def best_model_selection(kf, X, y):\n",
    "    \"\"\"\n",
    "    Select the kernel giving best results using k-fold cross-validation.\n",
    "    Other parameters should be left default.\n",
    "    Input:\n",
    "    kf (sklearn.model_selection.KFold): kf object defined above\n",
    "    X (scipy.sparse.csr.csr_matrix): training data\n",
    "    y (array(int)): training labels\n",
    "    Return:\n",
    "    best_kernel (string)\n",
    "    \"\"\"\n",
    "    kernel_accuracies = dict()\n",
    "    for kernel in ['linear', 'rbf', 'poly', 'sigmoid']:\n",
    "        fold_accuracies = []\n",
    "        for train_index, test_index in kf.split(X):\n",
    "            \n",
    "            # Use the documentation of KFold cross-validation to split\n",
    "            # training data and test data from create_features() and create_labels()\n",
    "            X_train, y_train = X.loc[train_index], y.loc[train_index]\n",
    "            X_test,  y_test  = X.loc[test_index] , y.loc[test_index]\n",
    "            \n",
    "            # call learn_classifer() using training split of kth fold\n",
    "            classifier = learn_classifier(X_train, y_train, kernel)\n",
    "            \n",
    "            # evaluate on the test split of kth fold\n",
    "            fold_accuracy = evaluate_classifier(classifier, X_test, y_test)\n",
    "            fold_accuracies.append(fold_accuracy)\n",
    "\n",
    "        # record avg accuracies and determine best model (kernel)\n",
    "        avg_fold_accuracy = np.mean(fold_accuracies)\n",
    "        kernel_accuracies[kernel] = avg_fold_accuracy\n",
    "\n",
    "    # return best kernel as string\n",
    "    print(kernel_accuracies)\n",
    "    best_kernel = max(kernel_accuracies, key = kernel_accuracies.get)\n",
    "    return best_kernel"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "kf = sklearn.model_selection.KFold(n_splits=4, random_state=1, shuffle=True) #5-fold cross validation\n",
    "kf"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "KFold(n_splits=4, random_state=1, shuffle=True)"
      ]
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "source": [
    "#reset indices of X_train and y_train to avoid indexing errors during CV\n",
    "X_train.reset_index(inplace=True, drop=True)\n",
    "y_train.reset_index(inplace=True, drop=True)\n",
    "\n",
    "#use CV to find the best_kernel for our SVC model\n",
    "best_kernel = best_model_selection(kf, X_train, y_train)\n",
    "print(f'Best kernel selected via cross-validation: {best_kernel}')\n",
    "\n",
    "#train and predict classifier\n",
    "classifier = learn_classifier(X_train, y_train, kernel=best_kernel)\n",
    "y_predict = clf_model.predict(X_test)\n",
    "\n",
    "classifier"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'linear': 0.5407051282051282, 'rbf': 0.452724358974359, 'poly': 0.49022435897435895, 'sigmoid': 0.515224358974359}\n",
      "Best kernel selected via cross-validation: linear\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "SVC(kernel='linear')"
      ]
     },
     "metadata": {},
     "execution_count": 41
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "source": [
    "#evaluation metrics\n",
    "train_accuracy = classifier.score(X,y)  #this gives training accuracy\n",
    "test_accuracy = accuracy_score(y_test, y_predict) #this gives testing accuracy\n",
    "\n",
    "print(f'Train Accuracy: {train_accuracy}')\n",
    "print(f'Test Accuracy: {test_accuracy}')\n",
    "\n",
    "cm = confusion_matrix(y_test, y_predict) #confusion matrix\n",
    "precision, recall, f1, support =  precision_recall_fscore_support(y_test, y_predict) #precision, recall, f1 score, and support for each class (decrease_in_gun_violence=0 and decrease_in_gun_violence=1)\n",
    "\n",
    "print(f'precision: {precision}')\n",
    "print(f'recall   : {recall}')\n",
    "print(f'f1 score : {f1}')\n",
    "\n",
    "#plot confusion matrix\n",
    "sns.heatmap(cm, annot = True, fmt = \".3f\", square = True, cmap = plt.cm.Blues);\n",
    "plt.ylabel('True');\n",
    "plt.xlabel('Predicted');\n",
    "plt.title('Support Vector Classifier (After Cross Validation) Confusion Matrix');\n",
    "plt.tight_layout();"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Train Accuracy: 0.6633165829145728\n",
      "Test Accuracy: 0.4\n",
      "precision: [0.47058824 0.34782609]\n",
      "recall   : [0.34782609 0.47058824]\n",
      "f1 score : [0.4 0.4]\n"
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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Cross Validation selects the best kernel to be 'linear' , which gives the same performance results as without using cross validation to select the best kernel. No improvement in model performance after using cross validation to select best kernel for SVC model."
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "87eb1506ace0c76867aaab3383ec0484b429857f88291368ffd3c4acf06de760"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.9.7 64-bit ('cs418env': conda)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}