MNIST-Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "51518093",
   "metadata": {},
   "source": [
    "## Loading datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6dd08874",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_openml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8c87b1bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist = fetch_openml('mnist_784' , as_frame=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8adbea9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x , y = mnist['data'],mnist['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "80345cd8",
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2d9c2346",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 784)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "22f4f9c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4257c348",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fbcf49c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "some_digit=x[2000]\n",
    "some_digit_image=some_digit.reshape(28,28) # necessary to reshape the array to get an image as output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3d02cb74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 27.5, 27.5, -0.5)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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=matplotlib.cm.binary,interpolation=\"nearest\")\n",
    "plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "de0e6ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'5'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[2000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0099482f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#MNIST datset has already been divided into test and train data sets where first 60000 datasets are training data\n",
    "x_train , x_test = x[:60000] , x[60000:]\n",
    "y_train , y_test = y[:60000] , y[60000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1abc10c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#We use shuffle to optimize the results \n",
    "import numpy as np\n",
    "shuffle_index = np.random.permutation(60000)\n",
    "x_train , y_train = x_train[shuffle_index] , y_train[shuffle_index]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "163f5d6a",
   "metadata": {},
   "source": [
    "## Creating a specific number detector(7 in my case)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "705b66b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train=y_train.astype(np.int8) # converting str to int\n",
    "y_test7=y_test.astype(np.int8)\n",
    "y_train_7=(y_train==7)\n",
    "y_test_7=(y_test==7)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "72fbade5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([False, False, False, ..., False, False, False]),\n",
       " array([False, False, False, ..., False, False, False]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_7 , y_test_7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "22deeefd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-6 {color: black;background-color: white;}#sk-container-id-6 pre{padding: 0;}#sk-container-id-6 div.sk-toggleable {background-color: white;}#sk-container-id-6 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-6 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-6 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-6 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-6 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-6 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-6 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-6 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-6 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-6 div.sk-item {position: relative;z-index: 1;}#sk-container-id-6 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-6 div.sk-item::before, #sk-container-id-6 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-6 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-6 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-6 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-6 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-6 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-6 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-6 div.sk-label-container {text-align: center;}#sk-container-id-6 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-6 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestClassifier()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestClassifier</label><div class=\"sk-toggleable__content\"><pre>RandomForestClassifier()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "RandomForestClassifier()"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  we need a binary classifier that detects if the number is a 7\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.linear_model import SGDClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "# model = LogisticRegression(solver='lbfgs')\n",
    "# model = SGDClassifier()\n",
    "# model = DecisionTreeClassifier()\n",
    "model = RandomForestClassifier()\n",
    "model.fit(x_train,y_train_7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "25826290",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "4781775f",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Cross Validation \n",
    "from sklearn.model_selection import cross_val_score\n",
    "a=cross_val_score(model,x_train,y_train_7,cv=3,scoring='accuracy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "962277b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9891333333333333"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "98ad7990",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict\n",
    "y_train_pred=cross_val_predict(model,x_train,y_train_7,cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "545c35af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc182ec1",
   "metadata": {},
   "source": [
    "## Calculating confusion matrix\n",
    "takes actual labels and predicted labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "6a633796",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix , ConfusionMatrixDisplay\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "85fcb9e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[53657,    78],\n",
       "       [  606,  5659]], dtype=int64)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train_7,y_train_pred) # This is not a perfect prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "9147a2c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "disp = ConfusionMatrixDisplay.from_predictions(y_train_7,y_train_pred)\n",
    "disp.plot()\n",
    "plt.xlabel=(\"Predicted\")\n",
    "plt.ylabel=(\"Actual\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "546df110",
   "metadata": {},
   "source": [
    "## Precision and Recall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "24534617",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_score , recall_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "34ba64b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9864040439253966"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_train_7,y_train_pred) #this is my precision score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "83468301",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9032721468475658"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_train_7,y_train_pred) # This is my recall score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bff7688c",
   "metadata": {},
   "source": [
    "## Now calculating F1 score \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f0264dca",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import f1_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "f5e13c75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9430094984169306"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1_score(y_train_7,y_train_pred) #This is my f1 score which is a better way to evaluate classifiers "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "448c0478",
   "metadata": {},
   "source": [
    "## Precision - Recall curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "913bbfe5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_recall_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "8b8f9023",
   "metadata": {},
   "outputs": [],
   "source": [
    "## we need to calculate the decision function which gives us the threshold value for the model\n",
    "#y_Scores=cross_val_predict(model,x_train,y_train_7,cv=3,method='decision_function')\n",
    "y_Scores = model.predict_proba(x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "32bf8b08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [1., 0.],\n",
       "       [1., 0.],\n",
       "       ...,\n",
       "       [1., 0.],\n",
       "       [1., 0.],\n",
       "       [1., 0.]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_Scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "f3a6ef2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "precisions , recalls , thresholds = precision_recall_curve(y_train_7, y_Scores[:,-1] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "943e5b0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.10441667, 0.30242325, 0.47879251, 0.61409528, 0.71649131,\n",
       "       0.78587556, 0.83656029, 0.87219825, 0.90312815, 0.92308826,\n",
       "       0.93815514, 0.95140471, 0.96074222, 0.96697021, 0.97161911,\n",
       "       0.97524907, 0.97967162, 0.98212886, 0.98568282, 0.98754729,\n",
       "       0.99020073, 0.99145434, 0.99349826, 0.99444444, 0.99491822,\n",
       "       0.99555061, 0.99618381, 0.99729386, 0.99761146, 0.99824729,\n",
       "       0.99904321, 0.99920255, 0.99936194, 0.99968087, 0.99984041,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        ])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precisions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "ee4af813",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       1.        , 0.99984038, 0.99968077, 0.99952115, 0.99936153,\n",
       "       0.99872306, 0.99840383, 0.99728651, 0.99648843, 0.99600958,\n",
       "       0.99409417, 0.99138069, 0.99010375, 0.98659218, 0.98324022,\n",
       "       0.97940942, 0.97557861, 0.97174781, 0.96632083, 0.96169194,\n",
       "       0.95626496, 0.95291301, 0.94684757, 0.93998404, 0.93312051,\n",
       "       0.92609737, 0.91747805, 0.90901836, 0.89656824, 0.88699122,\n",
       "       0.87470072, 0.86464485, 0.85155626, 0.83798883, 0.82298484,\n",
       "       0.80558659, 0.7811652 , 0.76025539, 0.7377494 , 0.7056664 ,\n",
       "       0.67310455, 0.63144453, 0.57717478, 0.49704709, 0.35993615,\n",
       "       0.        ])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recalls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "3aecd56e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,\n",
       "       0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,\n",
       "       0.22, 0.23, 0.24, 0.25, 0.26, 0.28, 0.29, 0.3 , 0.32, 0.33, 0.35,\n",
       "       0.37, 0.38, 0.53, 0.56, 0.57, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64,\n",
       "       0.65, 0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75,\n",
       "       0.76, 0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86,\n",
       "       0.87, 0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97,\n",
       "       0.98, 0.99, 1.  ])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thresholds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b57e3c5",
   "metadata": {},
   "source": [
    "## Plotting the precision-recall curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "f5d44681",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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.plot(thresholds,precisions[:-1],\"b--\",label=\"Precision\") # slicing and removing last values because they are just default values and we want to avoid error\n",
    "plt.plot(thresholds,recalls[:-1],\"g-\",label=\"Recall\")\n",
    "plt.xlabel(\"Thresholds\")\n",
    "plt.legend(loc='upper left')    \n",
    "plt.ylim([0,1])\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ffe1288",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}