Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/Shrey-Viradiya/HandsOnMachineLearning/blob/master/Classification.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'DESCR', 'details', 'categories', 'url'])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist = fetch_openml('mnist_784', version=1)\n",
    "mnist.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = mnist['data']\n",
    "y = mnist['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 784)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "some_digit = X[0]\n",
    "some_digit_image = some_digit.reshape(28,28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(some_digit_image, cmap='binary')\n",
    "plt.axis(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'5'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.astype(np.uint8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = X[:60000], X[60000:], y[:60000], y[60000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_5 = (y_train == 5)  # True for all 5s, False for all other digits\n",
    "y_test_5 = (y_test == 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "sgd_clf = SGDClassifier(n_jobs = -1,random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDClassifier(alpha=0.0001, average=False, class_weight=None,\n",
       "              early_stopping=False, epsilon=0.1, eta0=0.0, fit_intercept=True,\n",
       "              l1_ratio=0.15, learning_rate='optimal', loss='hinge',\n",
       "              max_iter=1000, n_iter_no_change=5, n_jobs=-1, penalty='l2',\n",
       "              power_t=0.5, random_state=42, shuffle=True, tol=0.001,\n",
       "              validation_fraction=0.1, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.fit(X_train,y_train_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.96416667, 0.95866667, 0.96416667, 0.95833333, 0.96733333,\n",
       "       0.96933333, 0.96433333, 0.96583333, 0.9575    , 0.96566667])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(sgd_clf, X_train, y_train_5, cv = 10, n_jobs = -1,scoring='accuracy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.95035, 0.96035, 0.9604 ])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(sgd_clf, X_train, y_train_5, cv = 3,n_jobs = -1, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator\n",
    "\n",
    "class Never5Classifier(BaseEstimator):\n",
    "    def fit(self,X,y=None):\n",
    "        return self\n",
    "    def predict(self, X):\n",
    "        return np.zeros((len(X),1), dtype=bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "n5c = Never5Classifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.91125, 0.90855, 0.90915])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(n5c, X_train, y_train_5, cv=3, scoring=\"accuracy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# confusion Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = cross_val_predict(sgd_clf, X_train, y_train_5,n_jobs = -1, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, ...,  True, False, False])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[53892,   687],\n",
       "       [ 1891,  3530]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train_5,y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_score, recall_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8370879772350012"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6511713705958311"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import f1_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7325171197343846"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1_score(y_train_5,y_train_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Precision/Recall Trade-off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2164.22030239])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_scores = sgd_clf.decision_function([some_digit])\n",
    "y_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_some_digit_pred = (y_scores > threshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_some_digit_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshold = 8000\n",
    "y_some_digit_pred = (y_scores > threshold)\n",
    "y_some_digit_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_scores = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3,method=\"decision_function\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1200.93051237, -26883.79202424, -33072.03475406, ...,\n",
       "        13272.12718981,  -7258.47203373, -16877.50840447])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_recall_curve\n",
    "\n",
    "precisions, recalls, thresholds = precision_recall_curve(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 9.99815532e-01, 9.99815532e-01, ...,\n",
       "       3.68935621e-04, 1.84467810e-04, 0.00000000e+00])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recalls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-106527.45300471, -105763.22240074, -105406.2965229 , ...,\n",
       "         38871.26391927,   42216.05562787,   49441.43765905])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_precision_recall_vs_threshold(precisions, recalls, thresholds):\n",
    "    fig = plt.figure(figsize= (16,9))\n",
    "    plt.plot(thresholds, precisions[:-1], \"b--\", label=\"Precision\")\n",
    "    plt.plot(thresholds, recalls[:-1], \"g-\", label=\"Recall\")\n",
    "    plt.grid(True)\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_precision_recall_vs_threshold(precisions, recalls, thresholds)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold_90_precision = thresholds[np.argmax(precisions >= 0.90)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred_90 = (y_scores >= threshold_90_precision)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3370.0194991439557"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshold_90_precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ...,  True, False, False])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_pred_90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9000345901072293"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_train_5, y_train_pred_90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4799852425751706"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_train_5, y_train_pred_90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ROC curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The receiver operating characteristic (ROC) curve is another common tool used with binary classifiers. It is very similar to the precision/recall curve, but instead of plotting precision versus recall, the ROC curve plots the true positive rate (another name for recall) against the false positive rate (FPR). The FPR is the ratio of negative instances that are incorrectly classified as positive. It is equal to 1 – the true negative rate (TNR), which is the ratio of negative instances that are correctly classified as negative. The TNR is also called specificity. Hence, the ROC curve plots sensitivity (recall) versus 1 – specificity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_roc_curve(fpr, tpr, label=None):\n",
    "    fig = plt.figure(figsize = (16,9))\n",
    "    plt.plot(fpr, tpr, linewidth=2, label=label)\n",
    "    plt.plot([0, 1], [0, 1], 'k--') # Dashed diagonal\n",
    "    plt.grid(True)\n",
    "\n",
    "plot_roc_curve(fpr, tpr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way to compare classifiers is to measure the area under the curve (AUC). A perfect classifier will have a ROC AUC equal to 1, whereas a purely random classifier will have a ROC AUC equal to 0.5. Scikit-Learn provides a function to compute the ROC AUC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9604938554008616"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_auc_score(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiclass Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_clf = SVC()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "some_digit_score = svm_clf.decision_function([some_digit])\n",
    "some_digit_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.argmax(some_digit_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_clf.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.multiclass import OneVsRestClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ovr_clf = OneVsRestClassifier(SVC(),n_jobs = -1)\n",
    "ovr_clf.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ovr_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ovr_clf.decision_function([some_digit])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training SGD Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgd_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgd_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgd_clf.decision_function([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cross_val_score(sgd_clf, X_train, y_train, cv=3, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pre-processing and increasing accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "scaler = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_scaled = scaler.fit_transform(X_train.astype(np.float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = cross_val_predict(sgd_clf, X_train_scaled, y_train, cv = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "conf_mx = confusion_matrix(y_train, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.matshow(conf_mx)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s focus the plot on the errors. First, you need to divide each value in the confusion matrix by the number of images in the corresponding class so that you can compare error rates instead of absolute numbers of errors (which would make abundant classes look unfairly bad):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "row_sums = conf_mx.sum(axis = 1, keepdims = True)\n",
    "norm_conf_mx = conf_mx / row_sums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.fill_diagonal(norm_conf_mx,0)\n",
    "plt.matshow(norm_conf_mx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_digits(instances, images_per_row=10, **options):\n",
    "    size = 28\n",
    "    images_per_row = min(len(instances), images_per_row)\n",
    "    images = [instance.reshape(size,size) for instance in instances]\n",
    "    n_rows = (len(instances) - 1) // images_per_row + 1\n",
    "    row_images = []\n",
    "    n_empty = n_rows * images_per_row - len(instances)\n",
    "    images.append(np.zeros((size, size * n_empty)))\n",
    "    for row in range(n_rows):\n",
    "        rimages = images[row * images_per_row : (row + 1) * images_per_row]\n",
    "        row_images.append(np.concatenate(rimages, axis=1))\n",
    "    image = np.concatenate(row_images, axis=0)\n",
    "    plt.imshow(image, cmap = matplotlib.cm.binary, **options)\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cl_a, cl_b = 3, 5\n",
    "X_aa = X_train[(y_train == cl_a) & (y_train_pred == cl_a)]\n",
    "X_ab = X_train[(y_train == cl_a) & (y_train_pred == cl_b)]\n",
    "X_ba = X_train[(y_train == cl_b) & (y_train_pred == cl_a)]\n",
    "X_bb = X_train[(y_train == cl_b) & (y_train_pred == cl_b)]\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.subplot(221); plot_digits(X_aa[:25], images_per_row=5)\n",
    "plt.subplot(222); plot_digits(X_ab[:25], images_per_row=5)\n",
    "plt.subplot(223); plot_digits(X_ba[:25], images_per_row=5)\n",
    "plt.subplot(224); plot_digits(X_bb[:25], images_per_row=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multilabel Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Until now each instance has always been assigned to just one class. In some cases you may want your classifier to output multiple classes for each instance. Consider a face-recognition classifier: what should it do if it recognizes several people in the same picture? It should attach one tag per person it recognizes. Say the classifier has been trained to recognize three faces, Alice, Bob, and Charlie. Then when the classifier is shown a picture of Alice and Charlie, it should output [1, 0, 1] (meaning “Alice yes, Bob no, Charlie yes”). Such a classification system that outputs multiple binary tags is called a multilabel classification system.\n",
    "\n",
    "We won’t go into face recognition just yet, but let’s look at a simpler example, just for illustration purposes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_large = (y_train >= 7)\n",
    "y_train_large"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_odd = (y_train %2 == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_multilabel = np.c_[y_train_large, y_train_odd]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_clf = KNeighborsClassifier(n_jobs = -1)\n",
    "knn_clf.fit(X_train,y_multilabel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_knn_pred = cross_val_predict(knn_clf, X_train, y_multilabel, cv=3)\n",
    "f1_score(y_multilabel, y_train_knn_pred, average = 'macro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multioutput–Multiclass classification (or simply Multioutput classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = np.random.randint(0,100,(len(X_train),784))\n",
    "X_train_mod = X_train + noise\n",
    "noise = np.random.randint(0,100,(len(X_test),784))\n",
    "X_test_mod = X_test + noise\n",
    "y_train_mod = X_train\n",
    "y_test_mod = X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "some_index = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_digit = X_train_mod[some_index]\n",
    "noice_digit_image = noise_digit.reshape(28,28)\n",
    "plt.imshow(noice_digit_image, cmap='binary')\n",
    "plt.axis(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clean_digit = X_train[some_index]\n",
    "clean_digit_image = clean_digit.reshape(28,28)\n",
    "plt.imshow(clean_digit_image, cmap='binary')\n",
    "plt.axis(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_clf.fit(X_train_mod, y_train_mod)\n",
    "clean_digit = knn_clf.predict([X_test_mod[some_index]])\n",
    "plot_digits(clean_digit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_digits([noice_digit_image, clean_digit_image])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_digits([X_test_mod[some_index],clean_digit])"
   ]
  }
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