machinelearning/knn/07-FeatureScaling/FeatureScaling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 07 数据归一化处理"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:25.566054Z",
     "start_time": "2024-08-24T08:39:25.246766Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最值归一化 Normalization"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:30.454126Z",
     "start_time": "2024-08-24T08:39:30.431443Z"
    }
   },
   "source": [
    "x = np.random.randint(0, 100, 100) "
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:32.774244Z",
     "start_time": "2024-08-24T08:39:32.765828Z"
    }
   },
   "source": [
    "x"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([92, 79, 59, 84, 56,  4, 71, 13,  7,  7, 75, 76, 59, 18, 84, 46,  7,\n",
       "       87, 77, 35, 86, 94, 19, 76, 15, 74,  5, 20, 72, 88, 84, 66, 49, 82,\n",
       "       25, 55,  1, 53, 61, 22, 92, 94, 78, 84, 58, 74, 87, 75, 99, 84, 70,\n",
       "       88, 52, 92, 16, 61,  4, 80, 44, 61, 12, 16, 84, 50, 31, 91, 94, 28,\n",
       "       84, 31, 86, 28, 25, 86, 61, 55, 25, 72, 56, 22,  3, 59, 85, 14, 24,\n",
       "       45, 91, 82, 63, 76, 80, 67, 53, 52, 28, 50, 37,  8, 52, 43])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "归一化 公式"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:37.761764Z",
     "start_time": "2024-08-24T08:39:37.755076Z"
    }
   },
   "source": [
    "(x - np.min(x)) / (np.max(x) - np.min(x))"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92857143, 0.79591837, 0.59183673, 0.84693878, 0.56122449,\n",
       "       0.03061224, 0.71428571, 0.12244898, 0.06122449, 0.06122449,\n",
       "       0.75510204, 0.76530612, 0.59183673, 0.17346939, 0.84693878,\n",
       "       0.45918367, 0.06122449, 0.87755102, 0.7755102 , 0.34693878,\n",
       "       0.86734694, 0.94897959, 0.18367347, 0.76530612, 0.14285714,\n",
       "       0.74489796, 0.04081633, 0.19387755, 0.7244898 , 0.8877551 ,\n",
       "       0.84693878, 0.66326531, 0.48979592, 0.82653061, 0.24489796,\n",
       "       0.55102041, 0.        , 0.53061224, 0.6122449 , 0.21428571,\n",
       "       0.92857143, 0.94897959, 0.78571429, 0.84693878, 0.58163265,\n",
       "       0.74489796, 0.87755102, 0.75510204, 1.        , 0.84693878,\n",
       "       0.70408163, 0.8877551 , 0.52040816, 0.92857143, 0.15306122,\n",
       "       0.6122449 , 0.03061224, 0.80612245, 0.43877551, 0.6122449 ,\n",
       "       0.1122449 , 0.15306122, 0.84693878, 0.5       , 0.30612245,\n",
       "       0.91836735, 0.94897959, 0.2755102 , 0.84693878, 0.30612245,\n",
       "       0.86734694, 0.2755102 , 0.24489796, 0.86734694, 0.6122449 ,\n",
       "       0.55102041, 0.24489796, 0.7244898 , 0.56122449, 0.21428571,\n",
       "       0.02040816, 0.59183673, 0.85714286, 0.13265306, 0.23469388,\n",
       "       0.44897959, 0.91836735, 0.82653061, 0.63265306, 0.76530612,\n",
       "       0.80612245, 0.67346939, 0.53061224, 0.52040816, 0.2755102 ,\n",
       "       0.5       , 0.36734694, 0.07142857, 0.52040816, 0.42857143])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:45.320017Z",
     "start_time": "2024-08-24T08:39:45.316320Z"
    }
   },
   "source": [
    "X = np.random.randint(0, 100, (50, 2))"
   ],
   "outputs": [],
   "execution_count": 6
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:52.531365Z",
     "start_time": "2024-08-24T08:39:52.527958Z"
    }
   },
   "source": [
    "X = np.array(X, dtype=float)"
   ],
   "outputs": [],
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:39:55.544770Z",
     "start_time": "2024-08-24T08:39:55.539561Z"
    }
   },
   "source": [
    "X[:10,:]"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[13., 32.],\n",
       "       [90., 72.],\n",
       "       [58., 93.],\n",
       "       [94., 93.],\n",
       "       [62., 17.],\n",
       "       [27., 71.],\n",
       "       [56., 62.],\n",
       "       [57., 67.],\n",
       "       [47., 83.],\n",
       "       [32., 48.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:40:32.678355Z",
     "start_time": "2024-08-24T08:40:32.672229Z"
    }
   },
   "source": [
    "X[:,0] = (X[:,0] - np.min(X[:,0])) / (np.max(X[:,0]) - np.min(X[:,0]))\n",
    "X[:,1] = (X[:,1] - np.min(X[:,1])) / (np.max(X[:,1]) - np.min(X[:,1]))"
   ],
   "outputs": [],
   "execution_count": 9
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:40:35.023140Z",
     "start_time": "2024-08-24T08:40:35.018668Z"
    }
   },
   "source": [
    "X[:10,:]"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.13265306, 0.23529412],\n",
       "       [0.91836735, 0.70588235],\n",
       "       [0.59183673, 0.95294118],\n",
       "       [0.95918367, 0.95294118],\n",
       "       [0.63265306, 0.05882353],\n",
       "       [0.2755102 , 0.69411765],\n",
       "       [0.57142857, 0.58823529],\n",
       "       [0.58163265, 0.64705882],\n",
       "       [0.47959184, 0.83529412],\n",
       "       [0.32653061, 0.42352941]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:41:03.111721Z",
     "start_time": "2024-08-24T08:41:03.028596Z"
    }
   },
   "source": [
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:41:08.781641Z",
     "start_time": "2024-08-24T08:41:08.776611Z"
    }
   },
   "source": [
    "np.mean(X[:,0])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.4948979591836735)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:41:10.766947Z",
     "start_time": "2024-08-24T08:41:10.763414Z"
    }
   },
   "source": [
    "np.std(X[:,0])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.27495976760715785)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:41:13.333978Z",
     "start_time": "2024-08-24T08:41:13.327767Z"
    }
   },
   "source": [
    "np.mean(X[:,1])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.5007058823529412)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:41:15.621163Z",
     "start_time": "2024-08-24T08:41:15.616635Z"
    }
   },
   "source": [
    "np.std(X[:,1])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.295190138712457)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 15
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 均值方差归一化 Standardization"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:42:10.813445Z",
     "start_time": "2024-08-24T08:42:10.810390Z"
    }
   },
   "source": [
    "X2 = np.random.randint(0, 100, (50, 2))"
   ],
   "outputs": [],
   "execution_count": 16
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:42:12.526934Z",
     "start_time": "2024-08-24T08:42:12.516740Z"
    }
   },
   "source": [
    "X2 = np.array(X2, dtype=float)"
   ],
   "outputs": [],
   "execution_count": 17
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:42:14.252858Z",
     "start_time": "2024-08-24T08:42:14.245754Z"
    }
   },
   "source": [
    "X2[:10,:]"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[52., 32.],\n",
       "       [54., 19.],\n",
       "       [43., 52.],\n",
       "       [49., 87.],\n",
       "       [20., 62.],\n",
       "       [85., 70.],\n",
       "       [49., 92.],\n",
       "       [56., 76.],\n",
       "       [ 8.,  2.],\n",
       "       [14., 14.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 18
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:12.255507Z",
     "start_time": "2024-08-24T08:43:12.252153Z"
    }
   },
   "source": [
    "X2[:,0] = (X2[:,0] - np.mean(X2[:,0])) / np.std(X2[:,0])\n",
    "X2[:,1] = (X2[:,1] - np.mean(X2[:,1])) / np.std(X2[:,1])"
   ],
   "outputs": [],
   "execution_count": 19
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:14.991682Z",
     "start_time": "2024-08-24T08:43:14.910165Z"
    }
   },
   "source": [
    "plt.scatter(X2[:,0], X2[:,1])\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 20
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:18.264822Z",
     "start_time": "2024-08-24T08:43:18.257974Z"
    }
   },
   "source": [
    "np.mean(X2[:,0])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(-1.0880185641326534e-16)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:20.170553Z",
     "start_time": "2024-08-24T08:43:20.165737Z"
    }
   },
   "source": [
    "np.std(X2[:,0])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999999999)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 22
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:22.455281Z",
     "start_time": "2024-08-24T08:43:22.449333Z"
    }
   },
   "source": [
    "np.mean(X2[:,1])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(-6.439293542825907e-17)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 23
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-24T08:43:25.632784Z",
     "start_time": "2024-08-24T08:43:25.626811Z"
    }
   },
   "source": [
    "np.std(X2[:,1])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999999999)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 24
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}