{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classifier accuracy\n",
    "\n",
    "In this notebook we'll explore the classifier confusion matrix and ROC/PR curves.\n",
    "\n",
    "See:\n",
    "http://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html and\n",
    "http://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_curve.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 62,  18],\n",
       "       [ 10, 138]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('bmh')\n",
    "from sklearn import cross_validation\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import confusion_matrix\n",
    " \n",
    "# first let's load some data\n",
    "\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "data = load_breast_cancer()\n",
    "X = data.data[:,:10]\n",
    "y = data.target * 2 - 1\n",
    "\n",
    "X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.4, random_state=1)\n",
    " \n",
    "classifier = LogisticRegression(C=0.1)\n",
    "_ = classifier.fit(X_train, y_train)\n",
    "y_pred = classifier.predict(X_test)\n",
    " \n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The confusion matrix is a matrix $C$ such that $C_{i, j}$ is equal to the\n",
    "number of observations known to be in group $i$ but predicted to be in group $j$.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron :\n",
    " \n",
    "    \"\"\"An implementation of the perceptron algorithm.\n",
    "    Note that this implementation does not include a bias term\"\"\"\n",
    " \n",
    "    def __init__(self, max_iterations=100, learning_rate=0.2) :\n",
    " \n",
    "        self.max_iterations = max_iterations\n",
    "        self.learning_rate = learning_rate\n",
    " \n",
    "    def fit(self, X, y) :\n",
    "        \"\"\"\n",
    "        Train a classifier using the perceptron training algorithm.\n",
    "        After training the attribute 'w' will contain the perceptron weight vector.\n",
    " \n",
    "        Parameters\n",
    "        ----------\n",
    " \n",
    "        X : ndarray, shape (num_examples, n_features)\n",
    "        Training data.\n",
    " \n",
    "        y : ndarray, shape (n_examples,)\n",
    "        Array of labels.\n",
    " \n",
    "        \"\"\"\n",
    "        self.w = np.zeros(len(X[0]))\n",
    "        converged = False\n",
    "        iterations = 0\n",
    "        while (not converged and iterations <= self.max_iterations) :\n",
    "            converged = True\n",
    "            for i in range(len(X)) :\n",
    "                if y[i] * self.decision_function(X[i]) <= 0 :\n",
    "                    self.w = self.w + y[i] * self.learning_rate * X[i]\n",
    "                    converged = False\n",
    "            iterations += 1\n",
    "        self.converged = converged\n",
    "        if converged :\n",
    "            print ('converged in %d iterations ' % iterations)\n",
    " \n",
    "    def decision_function(self, x) :\n",
    "        return np.inner(self.w, x)\n",
    " \n",
    "    def predict(self, X) :\n",
    "        \"\"\"\n",
    "        make predictions using a trained linear classifier\n",
    " \n",
    "        Parameters\n",
    "        ----------\n",
    " \n",
    "        X : ndarray, shape (num_examples, n_features)\n",
    "        Training data.\n",
    "        \"\"\"\n",
    " \n",
    "        scores = np.inner(self.w, X)\n",
    "        return np.sign(scores)\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ROC curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E53NpOJqjIi5cfRa9cv7r/ms/d2JYzhFq1h7rEeqyOHr0qM/n46GisO+Fh5VF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\nkpKSOHXqFIsWLSI3N5fk5GQ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5rrvuOubNm8egQYNKVF4m9iTknUVJOrRzc3OZPn2630xl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\nmICssjDGGBPQ/wOCpkj8pTdPCAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ce1cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "\n",
    "classifiers = {'Perceptron' : Perceptron(),\n",
    "            'logistic regression C=0.1': LogisticRegression(C=0.1),\n",
    "            'logistic regression C=10': LogisticRegression(C=10),\n",
    "            'logistic regression C=100': LogisticRegression(C=100),\n",
    "              }\n",
    "# note that the parameter C of\n",
    "# the scikit-learn LogisticRegression class is inversely\n",
    "# proportional to the strength of regularization\n",
    "\n",
    "results = {}\n",
    "for description,classifier in classifiers.items() :\n",
    "    _ = classifier.fit(X_train, y_train)\n",
    "    scores=classifier.decision_function(X_test)\n",
    "    fpr, tpr, _ = roc_curve(y_test, scores)\n",
    "    results[description] = (fpr, tpr)\n",
    "    \n",
    "plt.figure()\n",
    "plt.plot([0, 1], [0, 1], 'k--');\n",
    "for c in results :\n",
    "    fpr, tpr = results[c]\n",
    "    plt.plot(fpr, tpr, label=c);\n",
    "\n",
    "plt.xlabel('False positive rate');\n",
    "plt.ylabel('True positive rate');\n",
    "plt.title('ROC curve');\n",
    "plt.legend(loc='best');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pn4U94no1VKINen69LftZOqp7tfcxZcoU1q1bxz/+8Q8Ahg0bxpQpU3j44Yd5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f809f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_recall_curve\n",
    "\n",
    "results = {}\n",
    "for description,classifier in classifiers.items() :\n",
    "    _ = classifier.fit(X_train, y_train)\n",
    "    scores = classifier.decision_function(X_test)\n",
    "    precision, recall, _ = precision_recall_curve(y_test, scores)\n",
    "    results[description] = (precision, recall)\n",
    "    \n",
    "\n",
    "plt.figure()\n",
    "for c in results :\n",
    "    precision, recall = results[c]\n",
    "    #plt.plot(precision, recall, label=c);\n",
    "    plt.step(recall, precision, where='post', label=c)\n",
    "\n",
    "plt.xlabel('Recall');\n",
    "plt.ylabel('Precision');\n",
    "plt.title('PR curve');\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}