特征选择，处理.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据探索和样本构造"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 针对label值做异常值处理往往很有效"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn import preprocessing as prepc\n",
    "from sklearn import feature_selection as fselect\n",
    "from sklearn.datasets import load_iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2],\n",
       "       [5.4, 3.9, 1.7, 0.4],\n",
       "       [4.6, 3.4, 1.4, 0.3],\n",
       "       [5. , 3.4, 1.5, 0.2],\n",
       "       [4.4, 2.9, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5.4, 3.7, 1.5, 0.2],\n",
       "       [4.8, 3.4, 1.6, 0.2],\n",
       "       [4.8, 3. , 1.4, 0.1],\n",
       "       [4.3, 3. , 1.1, 0.1],\n",
       "       [5.8, 4. , 1.2, 0.2],\n",
       "       [5.7, 4.4, 1.5, 0.4],\n",
       "       [5.4, 3.9, 1.3, 0.4],\n",
       "       [5.1, 3.5, 1.4, 0.3],\n",
       "       [5.7, 3.8, 1.7, 0.3],\n",
       "       [5.1, 3.8, 1.5, 0.3],\n",
       "       [5.4, 3.4, 1.7, 0.2],\n",
       "       [5.1, 3.7, 1.5, 0.4],\n",
       "       [4.6, 3.6, 1. , 0.2],\n",
       "       [5.1, 3.3, 1.7, 0.5],\n",
       "       [4.8, 3.4, 1.9, 0.2],\n",
       "       [5. , 3. , 1.6, 0.2],\n",
       "       [5. , 3.4, 1.6, 0.4],\n",
       "       [5.2, 3.5, 1.5, 0.2],\n",
       "       [5.2, 3.4, 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.6, 0.2],\n",
       "       [4.8, 3.1, 1.6, 0.2],\n",
       "       [5.4, 3.4, 1.5, 0.4],\n",
       "       [5.2, 4.1, 1.5, 0.1],\n",
       "       [5.5, 4.2, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5. , 3.2, 1.2, 0.2],\n",
       "       [5.5, 3.5, 1.3, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [4.4, 3. , 1.3, 0.2],\n",
       "       [5.1, 3.4, 1.5, 0.2],\n",
       "       [5. , 3.5, 1.3, 0.3],\n",
       "       [4.5, 2.3, 1.3, 0.3],\n",
       "       [4.4, 3.2, 1.3, 0.2],\n",
       "       [5. , 3.5, 1.6, 0.6],\n",
       "       [5.1, 3.8, 1.9, 0.4],\n",
       "       [4.8, 3. , 1.4, 0.3],\n",
       "       [5.1, 3.8, 1.6, 0.2],\n",
       "       [4.6, 3.2, 1.4, 0.2],\n",
       "       [5.3, 3.7, 1.5, 0.2],\n",
       "       [5. , 3.3, 1.4, 0.2],\n",
       "       [7. , 3.2, 4.7, 1.4],\n",
       "       [6.4, 3.2, 4.5, 1.5],\n",
       "       [6.9, 3.1, 4.9, 1.5],\n",
       "       [5.5, 2.3, 4. , 1.3],\n",
       "       [6.5, 2.8, 4.6, 1.5],\n",
       "       [5.7, 2.8, 4.5, 1.3],\n",
       "       [6.3, 3.3, 4.7, 1.6],\n",
       "       [4.9, 2.4, 3.3, 1. ],\n",
       "       [6.6, 2.9, 4.6, 1.3],\n",
       "       [5.2, 2.7, 3.9, 1.4],\n",
       "       [5. , 2. , 3.5, 1. ],\n",
       "       [5.9, 3. , 4.2, 1.5],\n",
       "       [6. , 2.2, 4. , 1. ],\n",
       "       [6.1, 2.9, 4.7, 1.4],\n",
       "       [5.6, 2.9, 3.6, 1.3],\n",
       "       [6.7, 3.1, 4.4, 1.4],\n",
       "       [5.6, 3. , 4.5, 1.5],\n",
       "       [5.8, 2.7, 4.1, 1. ],\n",
       "       [6.2, 2.2, 4.5, 1.5],\n",
       "       [5.6, 2.5, 3.9, 1.1],\n",
       "       [5.9, 3.2, 4.8, 1.8],\n",
       "       [6.1, 2.8, 4. , 1.3],\n",
       "       [6.3, 2.5, 4.9, 1.5],\n",
       "       [6.1, 2.8, 4.7, 1.2],\n",
       "       [6.4, 2.9, 4.3, 1.3],\n",
       "       [6.6, 3. , 4.4, 1.4],\n",
       "       [6.8, 2.8, 4.8, 1.4],\n",
       "       [6.7, 3. , 5. , 1.7],\n",
       "       [6. , 2.9, 4.5, 1.5],\n",
       "       [5.7, 2.6, 3.5, 1. ],\n",
       "       [5.5, 2.4, 3.8, 1.1],\n",
       "       [5.5, 2.4, 3.7, 1. ],\n",
       "       [5.8, 2.7, 3.9, 1.2],\n",
       "       [6. , 2.7, 5.1, 1.6],\n",
       "       [5.4, 3. , 4.5, 1.5],\n",
       "       [6. , 3.4, 4.5, 1.6],\n",
       "       [6.7, 3.1, 4.7, 1.5],\n",
       "       [6.3, 2.3, 4.4, 1.3],\n",
       "       [5.6, 3. , 4.1, 1.3],\n",
       "       [5.5, 2.5, 4. , 1.3],\n",
       "       [5.5, 2.6, 4.4, 1.2],\n",
       "       [6.1, 3. , 4.6, 1.4],\n",
       "       [5.8, 2.6, 4. , 1.2],\n",
       "       [5. , 2.3, 3.3, 1. ],\n",
       "       [5.6, 2.7, 4.2, 1.3],\n",
       "       [5.7, 3. , 4.2, 1.2],\n",
       "       [5.7, 2.9, 4.2, 1.3],\n",
       "       [6.2, 2.9, 4.3, 1.3],\n",
       "       [5.1, 2.5, 3. , 1.1],\n",
       "       [5.7, 2.8, 4.1, 1.3],\n",
       "       [6.3, 3.3, 6. , 2.5],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [7.1, 3. , 5.9, 2.1],\n",
       "       [6.3, 2.9, 5.6, 1.8],\n",
       "       [6.5, 3. , 5.8, 2.2],\n",
       "       [7.6, 3. , 6.6, 2.1],\n",
       "       [4.9, 2.5, 4.5, 1.7],\n",
       "       [7.3, 2.9, 6.3, 1.8],\n",
       "       [6.7, 2.5, 5.8, 1.8],\n",
       "       [7.2, 3.6, 6.1, 2.5],\n",
       "       [6.5, 3.2, 5.1, 2. ],\n",
       "       [6.4, 2.7, 5.3, 1.9],\n",
       "       [6.8, 3. , 5.5, 2.1],\n",
       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = load_iris()\n",
    "X = iris.data\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
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       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = iris.target\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 离散特征 one Hot Encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = prepc.OneHotEncoder().fit_transform(y.reshape((-1, 1))).toarray()\n",
    "X_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 特征标准化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        -1.18150376e+00],\n",
       "       [-5.37177559e-01,  8.00654259e-01, -1.17067529e+00,\n",
       "        -1.31297673e+00],\n",
       "       [-9.00681170e-01,  1.49486315e+00, -1.28440670e+00,\n",
       "        -1.05003079e+00],\n",
       "       [-1.50652052e+00,  1.26346019e+00, -1.56873522e+00,\n",
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       "        -1.31297673e+00],\n",
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       "        -1.31297673e+00],\n",
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       "        -1.31297673e+00],\n",
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       "         3.96171883e-01],\n",
       "       [-4.16009689e-01, -1.74477836e+00,  1.37235899e-01,\n",
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       "       [ 7.95669016e-01, -5.87763531e-01,  4.78430123e-01,\n",
       "         3.96171883e-01],\n",
       "       [-1.73673948e-01, -5.87763531e-01,  4.21564419e-01,\n",
       "         1.33225943e-01],\n",
       "       [ 5.53333275e-01,  5.69251294e-01,  5.35295827e-01,\n",
       "         5.27644853e-01],\n",
       "       [-1.14301691e+00, -1.51337539e+00, -2.60824029e-01,\n",
       "        -2.61192967e-01],\n",
       "       [ 9.16836886e-01, -3.56360566e-01,  4.78430123e-01,\n",
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       "       [-7.79513300e-01, -8.19166497e-01,  8.03701950e-02,\n",
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       "       [-1.02184904e+00, -2.43898725e+00, -1.47092621e-01,\n",
       "        -2.61192967e-01],\n",
       "       [ 6.86617933e-02, -1.24957601e-01,  2.50967307e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 1.89829664e-01, -1.97618132e+00,  1.37235899e-01,\n",
       "        -2.61192967e-01],\n",
       "       [ 3.10997534e-01, -3.56360566e-01,  5.35295827e-01,\n",
       "         2.64698913e-01],\n",
       "       [-2.94841818e-01, -3.56360566e-01, -9.02269170e-02,\n",
       "         1.33225943e-01],\n",
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       "         2.64698913e-01],\n",
       "       [-2.94841818e-01, -1.24957601e-01,  4.21564419e-01,\n",
       "         3.96171883e-01],\n",
       "       [-5.25060772e-02, -8.19166497e-01,  1.94101603e-01,\n",
       "        -2.61192967e-01],\n",
       "       [ 4.32165405e-01, -1.97618132e+00,  4.21564419e-01,\n",
       "         3.96171883e-01],\n",
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       "       [ 6.86617933e-02,  3.37848329e-01,  5.92161531e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 3.10997534e-01, -5.87763531e-01,  1.37235899e-01,\n",
       "         1.33225943e-01],\n",
       "       [ 5.53333275e-01, -1.28197243e+00,  6.49027235e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 3.10997534e-01, -5.87763531e-01,  5.35295827e-01,\n",
       "         1.75297293e-03],\n",
       "       [ 6.74501145e-01, -3.56360566e-01,  3.07833011e-01,\n",
       "         1.33225943e-01],\n",
       "       [ 9.16836886e-01, -1.24957601e-01,  3.64698715e-01,\n",
       "         2.64698913e-01],\n",
       "       [ 1.15917263e+00, -5.87763531e-01,  5.92161531e-01,\n",
       "         2.64698913e-01],\n",
       "       [ 1.03800476e+00, -1.24957601e-01,  7.05892939e-01,\n",
       "         6.59117823e-01],\n",
       "       [ 1.89829664e-01, -3.56360566e-01,  4.21564419e-01,\n",
       "         3.96171883e-01],\n",
       "       [-1.73673948e-01, -1.05056946e+00, -1.47092621e-01,\n",
       "        -2.61192967e-01],\n",
       "       [-4.16009689e-01, -1.51337539e+00,  2.35044910e-02,\n",
       "        -1.29719997e-01],\n",
       "       [-4.16009689e-01, -1.51337539e+00, -3.33612130e-02,\n",
       "        -2.61192967e-01],\n",
       "       [-5.25060772e-02, -8.19166497e-01,  8.03701950e-02,\n",
       "         1.75297293e-03],\n",
       "       [ 1.89829664e-01, -8.19166497e-01,  7.62758643e-01,\n",
       "         5.27644853e-01],\n",
       "       [-5.37177559e-01, -1.24957601e-01,  4.21564419e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 1.89829664e-01,  8.00654259e-01,  4.21564419e-01,\n",
       "         5.27644853e-01],\n",
       "       [ 1.03800476e+00,  1.06445364e-01,  5.35295827e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 5.53333275e-01, -1.74477836e+00,  3.64698715e-01,\n",
       "         1.33225943e-01],\n",
       "       [-2.94841818e-01, -1.24957601e-01,  1.94101603e-01,\n",
       "         1.33225943e-01],\n",
       "       [-4.16009689e-01, -1.28197243e+00,  1.37235899e-01,\n",
       "         1.33225943e-01],\n",
       "       [-4.16009689e-01, -1.05056946e+00,  3.64698715e-01,\n",
       "         1.75297293e-03],\n",
       "       [ 3.10997534e-01, -1.24957601e-01,  4.78430123e-01,\n",
       "         2.64698913e-01],\n",
       "       [-5.25060772e-02, -1.05056946e+00,  1.37235899e-01,\n",
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       "        -2.61192967e-01],\n",
       "       [-2.94841818e-01, -8.19166497e-01,  2.50967307e-01,\n",
       "         1.33225943e-01],\n",
       "       [-1.73673948e-01, -1.24957601e-01,  2.50967307e-01,\n",
       "         1.75297293e-03],\n",
       "       [-1.73673948e-01, -3.56360566e-01,  2.50967307e-01,\n",
       "         1.33225943e-01],\n",
       "       [ 4.32165405e-01, -3.56360566e-01,  3.07833011e-01,\n",
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       "       [-9.00681170e-01, -1.28197243e+00, -4.31421141e-01,\n",
       "        -1.29719997e-01],\n",
       "       [-1.73673948e-01, -5.87763531e-01,  1.94101603e-01,\n",
       "         1.33225943e-01],\n",
       "       [ 5.53333275e-01,  5.69251294e-01,  1.27454998e+00,\n",
       "         1.71090158e+00],\n",
       "       [-5.25060772e-02, -8.19166497e-01,  7.62758643e-01,\n",
       "         9.22063763e-01],\n",
       "       [ 1.52267624e+00, -1.24957601e-01,  1.21768427e+00,\n",
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       "       [ 5.53333275e-01, -3.56360566e-01,  1.04708716e+00,\n",
       "         7.90590793e-01],\n",
       "       [ 7.95669016e-01, -1.24957601e-01,  1.16081857e+00,\n",
       "         1.31648267e+00],\n",
       "       [ 2.12851559e+00, -1.24957601e-01,  1.61574420e+00,\n",
       "         1.18500970e+00],\n",
       "       [-1.14301691e+00, -1.28197243e+00,  4.21564419e-01,\n",
       "         6.59117823e-01],\n",
       "       [ 1.76501198e+00, -3.56360566e-01,  1.44514709e+00,\n",
       "         7.90590793e-01],\n",
       "       [ 1.03800476e+00, -1.28197243e+00,  1.16081857e+00,\n",
       "         7.90590793e-01],\n",
       "       [ 1.64384411e+00,  1.26346019e+00,  1.33141568e+00,\n",
       "         1.71090158e+00],\n",
       "       [ 7.95669016e-01,  3.37848329e-01,  7.62758643e-01,\n",
       "         1.05353673e+00],\n",
       "       [ 6.74501145e-01, -8.19166497e-01,  8.76490051e-01,\n",
       "         9.22063763e-01],\n",
       "       [ 1.15917263e+00, -1.24957601e-01,  9.90221459e-01,\n",
       "         1.18500970e+00],\n",
       "       [-1.73673948e-01, -1.28197243e+00,  7.05892939e-01,\n",
       "         1.05353673e+00],\n",
       "       [-5.25060772e-02, -5.87763531e-01,  7.62758643e-01,\n",
       "         1.57942861e+00],\n",
       "       [ 6.74501145e-01,  3.37848329e-01,  8.76490051e-01,\n",
       "         1.44795564e+00],\n",
       "       [ 7.95669016e-01, -1.24957601e-01,  9.90221459e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 2.24968346e+00,  1.72626612e+00,  1.67260991e+00,\n",
       "         1.31648267e+00],\n",
       "       [ 2.24968346e+00, -1.05056946e+00,  1.78634131e+00,\n",
       "         1.44795564e+00],\n",
       "       [ 1.89829664e-01, -1.97618132e+00,  7.05892939e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 1.28034050e+00,  3.37848329e-01,  1.10395287e+00,\n",
       "         1.44795564e+00],\n",
       "       [-2.94841818e-01, -5.87763531e-01,  6.49027235e-01,\n",
       "         1.05353673e+00],\n",
       "       [ 2.24968346e+00, -5.87763531e-01,  1.67260991e+00,\n",
       "         1.05353673e+00],\n",
       "       [ 5.53333275e-01, -8.19166497e-01,  6.49027235e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 1.03800476e+00,  5.69251294e-01,  1.10395287e+00,\n",
       "         1.18500970e+00],\n",
       "       [ 1.64384411e+00,  3.37848329e-01,  1.27454998e+00,\n",
       "         7.90590793e-01],\n",
       "       [ 4.32165405e-01, -5.87763531e-01,  5.92161531e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 3.10997534e-01, -1.24957601e-01,  6.49027235e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 6.74501145e-01, -5.87763531e-01,  1.04708716e+00,\n",
       "         1.18500970e+00],\n",
       "       [ 1.64384411e+00, -1.24957601e-01,  1.16081857e+00,\n",
       "         5.27644853e-01],\n",
       "       [ 1.88617985e+00, -5.87763531e-01,  1.33141568e+00,\n",
       "         9.22063763e-01],\n",
       "       [ 2.49201920e+00,  1.72626612e+00,  1.50201279e+00,\n",
       "         1.05353673e+00],\n",
       "       [ 6.74501145e-01, -5.87763531e-01,  1.04708716e+00,\n",
       "         1.31648267e+00],\n",
       "       [ 5.53333275e-01, -5.87763531e-01,  7.62758643e-01,\n",
       "         3.96171883e-01],\n",
       "       [ 3.10997534e-01, -1.05056946e+00,  1.04708716e+00,\n",
       "         2.64698913e-01],\n",
       "       [ 2.24968346e+00, -1.24957601e-01,  1.33141568e+00,\n",
       "         1.44795564e+00],\n",
       "       [ 5.53333275e-01,  8.00654259e-01,  1.04708716e+00,\n",
       "         1.57942861e+00],\n",
       "       [ 6.74501145e-01,  1.06445364e-01,  9.90221459e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 1.89829664e-01, -1.24957601e-01,  5.92161531e-01,\n",
       "         7.90590793e-01],\n",
       "       [ 1.28034050e+00,  1.06445364e-01,  9.33355755e-01,\n",
       "         1.18500970e+00],\n",
       "       [ 1.03800476e+00,  1.06445364e-01,  1.04708716e+00,\n",
       "         1.57942861e+00],\n",
       "       [ 1.28034050e+00,  1.06445364e-01,  7.62758643e-01,\n",
       "         1.44795564e+00],\n",
       "       [-5.25060772e-02, -8.19166497e-01,  7.62758643e-01,\n",
       "         9.22063763e-01],\n",
       "       [ 1.15917263e+00,  3.37848329e-01,  1.21768427e+00,\n",
       "         1.44795564e+00],\n",
       "       [ 1.03800476e+00,  5.69251294e-01,  1.10395287e+00,\n",
       "         1.71090158e+00],\n",
       "       [ 1.03800476e+00, -1.24957601e-01,  8.19624347e-01,\n",
       "         1.44795564e+00],\n",
       "       [ 5.53333275e-01, -1.28197243e+00,  7.05892939e-01,\n",
       "         9.22063763e-01],\n",
       "       [ 7.95669016e-01, -1.24957601e-01,  8.19624347e-01,\n",
       "         1.05353673e+00],\n",
       "       [ 4.32165405e-01,  8.00654259e-01,  9.33355755e-01,\n",
       "         1.44795564e+00],\n",
       "       [ 6.86617933e-02, -1.24957601e-01,  7.62758643e-01,\n",
       "         7.90590793e-01]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = prepc.StandardScaler().fit_transform(X)\n",
    "X_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.22222222, 0.625     , 0.06779661, 0.04166667],\n",
       "       [0.16666667, 0.41666667, 0.06779661, 0.04166667],\n",
       "       [0.11111111, 0.5       , 0.05084746, 0.04166667],\n",
       "       [0.08333333, 0.45833333, 0.08474576, 0.04166667],\n",
       "       [0.19444444, 0.66666667, 0.06779661, 0.04166667],\n",
       "       [0.30555556, 0.79166667, 0.11864407, 0.125     ],\n",
       "       [0.08333333, 0.58333333, 0.06779661, 0.08333333],\n",
       "       [0.19444444, 0.58333333, 0.08474576, 0.04166667],\n",
       "       [0.02777778, 0.375     , 0.06779661, 0.04166667],\n",
       "       [0.16666667, 0.45833333, 0.08474576, 0.        ],\n",
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       "       [0.30555556, 0.79166667, 0.05084746, 0.125     ],\n",
       "       [0.22222222, 0.625     , 0.06779661, 0.08333333],\n",
       "       [0.38888889, 0.75      , 0.11864407, 0.08333333],\n",
       "       [0.22222222, 0.75      , 0.08474576, 0.08333333],\n",
       "       [0.30555556, 0.58333333, 0.11864407, 0.04166667],\n",
       "       [0.22222222, 0.70833333, 0.08474576, 0.125     ],\n",
       "       [0.08333333, 0.66666667, 0.        , 0.04166667],\n",
       "       [0.22222222, 0.54166667, 0.11864407, 0.16666667],\n",
       "       [0.13888889, 0.58333333, 0.15254237, 0.04166667],\n",
       "       [0.19444444, 0.41666667, 0.10169492, 0.04166667],\n",
       "       [0.19444444, 0.58333333, 0.10169492, 0.125     ],\n",
       "       [0.25      , 0.625     , 0.08474576, 0.04166667],\n",
       "       [0.25      , 0.58333333, 0.06779661, 0.04166667],\n",
       "       [0.11111111, 0.5       , 0.10169492, 0.04166667],\n",
       "       [0.13888889, 0.45833333, 0.10169492, 0.04166667],\n",
       "       [0.30555556, 0.58333333, 0.08474576, 0.125     ],\n",
       "       [0.25      , 0.875     , 0.08474576, 0.        ],\n",
       "       [0.33333333, 0.91666667, 0.06779661, 0.04166667],\n",
       "       [0.16666667, 0.45833333, 0.08474576, 0.        ],\n",
       "       [0.19444444, 0.5       , 0.03389831, 0.04166667],\n",
       "       [0.33333333, 0.625     , 0.05084746, 0.04166667],\n",
       "       [0.16666667, 0.45833333, 0.08474576, 0.        ],\n",
       "       [0.02777778, 0.41666667, 0.05084746, 0.04166667],\n",
       "       [0.22222222, 0.58333333, 0.08474576, 0.04166667],\n",
       "       [0.19444444, 0.625     , 0.05084746, 0.08333333],\n",
       "       [0.05555556, 0.125     , 0.05084746, 0.08333333],\n",
       "       [0.02777778, 0.5       , 0.05084746, 0.04166667],\n",
       "       [0.19444444, 0.625     , 0.10169492, 0.20833333],\n",
       "       [0.22222222, 0.75      , 0.15254237, 0.125     ],\n",
       "       [0.13888889, 0.41666667, 0.06779661, 0.08333333],\n",
       "       [0.22222222, 0.75      , 0.10169492, 0.04166667],\n",
       "       [0.08333333, 0.5       , 0.06779661, 0.04166667],\n",
       "       [0.27777778, 0.70833333, 0.08474576, 0.04166667],\n",
       "       [0.19444444, 0.54166667, 0.06779661, 0.04166667],\n",
       "       [0.75      , 0.5       , 0.62711864, 0.54166667],\n",
       "       [0.58333333, 0.5       , 0.59322034, 0.58333333],\n",
       "       [0.72222222, 0.45833333, 0.66101695, 0.58333333],\n",
       "       [0.33333333, 0.125     , 0.50847458, 0.5       ],\n",
       "       [0.61111111, 0.33333333, 0.61016949, 0.58333333],\n",
       "       [0.38888889, 0.33333333, 0.59322034, 0.5       ],\n",
       "       [0.55555556, 0.54166667, 0.62711864, 0.625     ],\n",
       "       [0.16666667, 0.16666667, 0.38983051, 0.375     ],\n",
       "       [0.63888889, 0.375     , 0.61016949, 0.5       ],\n",
       "       [0.25      , 0.29166667, 0.49152542, 0.54166667],\n",
       "       [0.19444444, 0.        , 0.42372881, 0.375     ],\n",
       "       [0.44444444, 0.41666667, 0.54237288, 0.58333333],\n",
       "       [0.47222222, 0.08333333, 0.50847458, 0.375     ],\n",
       "       [0.5       , 0.375     , 0.62711864, 0.54166667],\n",
       "       [0.36111111, 0.375     , 0.44067797, 0.5       ],\n",
       "       [0.66666667, 0.45833333, 0.57627119, 0.54166667],\n",
       "       [0.36111111, 0.41666667, 0.59322034, 0.58333333],\n",
       "       [0.41666667, 0.29166667, 0.52542373, 0.375     ],\n",
       "       [0.52777778, 0.08333333, 0.59322034, 0.58333333],\n",
       "       [0.36111111, 0.20833333, 0.49152542, 0.41666667],\n",
       "       [0.44444444, 0.5       , 0.6440678 , 0.70833333],\n",
       "       [0.5       , 0.33333333, 0.50847458, 0.5       ],\n",
       "       [0.55555556, 0.20833333, 0.66101695, 0.58333333],\n",
       "       [0.5       , 0.33333333, 0.62711864, 0.45833333],\n",
       "       [0.58333333, 0.375     , 0.55932203, 0.5       ],\n",
       "       [0.63888889, 0.41666667, 0.57627119, 0.54166667],\n",
       "       [0.69444444, 0.33333333, 0.6440678 , 0.54166667],\n",
       "       [0.66666667, 0.41666667, 0.6779661 , 0.66666667],\n",
       "       [0.47222222, 0.375     , 0.59322034, 0.58333333],\n",
       "       [0.38888889, 0.25      , 0.42372881, 0.375     ],\n",
       "       [0.33333333, 0.16666667, 0.47457627, 0.41666667],\n",
       "       [0.33333333, 0.16666667, 0.45762712, 0.375     ],\n",
       "       [0.41666667, 0.29166667, 0.49152542, 0.45833333],\n",
       "       [0.47222222, 0.29166667, 0.69491525, 0.625     ],\n",
       "       [0.30555556, 0.41666667, 0.59322034, 0.58333333],\n",
       "       [0.47222222, 0.58333333, 0.59322034, 0.625     ],\n",
       "       [0.66666667, 0.45833333, 0.62711864, 0.58333333],\n",
       "       [0.55555556, 0.125     , 0.57627119, 0.5       ],\n",
       "       [0.36111111, 0.41666667, 0.52542373, 0.5       ],\n",
       "       [0.33333333, 0.20833333, 0.50847458, 0.5       ],\n",
       "       [0.33333333, 0.25      , 0.57627119, 0.45833333],\n",
       "       [0.5       , 0.41666667, 0.61016949, 0.54166667],\n",
       "       [0.41666667, 0.25      , 0.50847458, 0.45833333],\n",
       "       [0.19444444, 0.125     , 0.38983051, 0.375     ],\n",
       "       [0.36111111, 0.29166667, 0.54237288, 0.5       ],\n",
       "       [0.38888889, 0.41666667, 0.54237288, 0.45833333],\n",
       "       [0.38888889, 0.375     , 0.54237288, 0.5       ],\n",
       "       [0.52777778, 0.375     , 0.55932203, 0.5       ],\n",
       "       [0.22222222, 0.20833333, 0.33898305, 0.41666667],\n",
       "       [0.38888889, 0.33333333, 0.52542373, 0.5       ],\n",
       "       [0.55555556, 0.54166667, 0.84745763, 1.        ],\n",
       "       [0.41666667, 0.29166667, 0.69491525, 0.75      ],\n",
       "       [0.77777778, 0.41666667, 0.83050847, 0.83333333],\n",
       "       [0.55555556, 0.375     , 0.77966102, 0.70833333],\n",
       "       [0.61111111, 0.41666667, 0.81355932, 0.875     ],\n",
       "       [0.91666667, 0.41666667, 0.94915254, 0.83333333],\n",
       "       [0.16666667, 0.20833333, 0.59322034, 0.66666667],\n",
       "       [0.83333333, 0.375     , 0.89830508, 0.70833333],\n",
       "       [0.66666667, 0.20833333, 0.81355932, 0.70833333],\n",
       "       [0.80555556, 0.66666667, 0.86440678, 1.        ],\n",
       "       [0.61111111, 0.5       , 0.69491525, 0.79166667],\n",
       "       [0.58333333, 0.29166667, 0.72881356, 0.75      ],\n",
       "       [0.69444444, 0.41666667, 0.76271186, 0.83333333],\n",
       "       [0.38888889, 0.20833333, 0.6779661 , 0.79166667],\n",
       "       [0.41666667, 0.33333333, 0.69491525, 0.95833333],\n",
       "       [0.58333333, 0.5       , 0.72881356, 0.91666667],\n",
       "       [0.61111111, 0.41666667, 0.76271186, 0.70833333],\n",
       "       [0.94444444, 0.75      , 0.96610169, 0.875     ],\n",
       "       [0.94444444, 0.25      , 1.        , 0.91666667],\n",
       "       [0.47222222, 0.08333333, 0.6779661 , 0.58333333],\n",
       "       [0.72222222, 0.5       , 0.79661017, 0.91666667],\n",
       "       [0.36111111, 0.33333333, 0.66101695, 0.79166667],\n",
       "       [0.94444444, 0.33333333, 0.96610169, 0.79166667],\n",
       "       [0.55555556, 0.29166667, 0.66101695, 0.70833333],\n",
       "       [0.66666667, 0.54166667, 0.79661017, 0.83333333],\n",
       "       [0.80555556, 0.5       , 0.84745763, 0.70833333],\n",
       "       [0.52777778, 0.33333333, 0.6440678 , 0.70833333],\n",
       "       [0.5       , 0.41666667, 0.66101695, 0.70833333],\n",
       "       [0.58333333, 0.33333333, 0.77966102, 0.83333333],\n",
       "       [0.80555556, 0.41666667, 0.81355932, 0.625     ],\n",
       "       [0.86111111, 0.33333333, 0.86440678, 0.75      ],\n",
       "       [1.        , 0.75      , 0.91525424, 0.79166667],\n",
       "       [0.58333333, 0.33333333, 0.77966102, 0.875     ],\n",
       "       [0.55555556, 0.33333333, 0.69491525, 0.58333333],\n",
       "       [0.5       , 0.25      , 0.77966102, 0.54166667],\n",
       "       [0.94444444, 0.41666667, 0.86440678, 0.91666667],\n",
       "       [0.55555556, 0.58333333, 0.77966102, 0.95833333],\n",
       "       [0.58333333, 0.45833333, 0.76271186, 0.70833333],\n",
       "       [0.47222222, 0.41666667, 0.6440678 , 0.70833333],\n",
       "       [0.72222222, 0.45833333, 0.74576271, 0.83333333],\n",
       "       [0.66666667, 0.45833333, 0.77966102, 0.95833333],\n",
       "       [0.72222222, 0.45833333, 0.69491525, 0.91666667],\n",
       "       [0.41666667, 0.29166667, 0.69491525, 0.75      ],\n",
       "       [0.69444444, 0.5       , 0.83050847, 0.91666667],\n",
       "       [0.66666667, 0.54166667, 0.79661017, 1.        ],\n",
       "       [0.66666667, 0.41666667, 0.71186441, 0.91666667],\n",
       "       [0.55555556, 0.20833333, 0.6779661 , 0.75      ],\n",
       "       [0.61111111, 0.41666667, 0.71186441, 0.79166667],\n",
       "       [0.52777778, 0.58333333, 0.74576271, 0.91666667],\n",
       "       [0.44444444, 0.41666667, 0.69491525, 0.70833333]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_minmax = prepc.MinMaxScaler().fit_transform(X)\n",
    "X_minmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据变换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多项式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  5.1 ,  3.5 , ...,  1.96,  0.28,  0.04],\n",
       "       [ 1.  ,  4.9 ,  3.  , ...,  1.96,  0.28,  0.04],\n",
       "       [ 1.  ,  4.7 ,  3.2 , ...,  1.69,  0.26,  0.04],\n",
       "       ...,\n",
       "       [ 1.  ,  6.5 ,  3.  , ..., 27.04, 10.4 ,  4.  ],\n",
       "       [ 1.  ,  6.2 ,  3.4 , ..., 29.16, 12.42,  5.29],\n",
       "       [ 1.  ,  5.9 ,  3.  , ..., 26.01,  9.18,  3.24]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prepc.PolynomialFeatures(degree=2).fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n多项式\\nX1, X2, X3, X4\\n获取幂次为0： 1\\n幂次为1: X1, X2, X3, X4，\\n幂次为2： X1^2, X1*X2, X1*X3,....\\n变成这么多加起来的特征\\n用处：FM模型\\n'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "多项式\n",
    "X1, X2, X3, X4\n",
    "获取幂次为0： 1\n",
    "幂次为1: X1, X2, X3, X4，\n",
    "幂次为2： X1^2, X1*X2, X1*X3,....\n",
    "变成这么多加起来的特征\n",
    "用处：FM模型\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 对数log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### log1p: log(1+x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n应用： 长尾分布\\n很少的值占据了很多的比例 eg 大部分人收入很低\\n“越大的值被压缩的越厉害”\\n'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "应用： 长尾分布\n",
    "很少的值占据了很多的比例 eg 大部分人收入很低\n",
    "“越大的值被压缩的越厉害”\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.80828877, 1.5040774 , 0.87546874, 0.18232156],\n",
       "       [1.77495235, 1.38629436, 0.87546874, 0.18232156],\n",
       "       [1.74046617, 1.43508453, 0.83290912, 0.18232156],\n",
       "       [1.7227666 , 1.41098697, 0.91629073, 0.18232156],\n",
       "       [1.79175947, 1.5260563 , 0.87546874, 0.18232156],\n",
       "       [1.85629799, 1.58923521, 0.99325177, 0.33647224],\n",
       "       [1.7227666 , 1.48160454, 0.87546874, 0.26236426],\n",
       "       [1.79175947, 1.48160454, 0.91629073, 0.18232156],\n",
       "       [1.68639895, 1.36097655, 0.87546874, 0.18232156],\n",
       "       [1.77495235, 1.41098697, 0.91629073, 0.09531018],\n",
       "       [1.85629799, 1.54756251, 0.91629073, 0.18232156],\n",
       "       [1.75785792, 1.48160454, 0.95551145, 0.18232156],\n",
       "       [1.75785792, 1.38629436, 0.87546874, 0.09531018],\n",
       "       [1.66770682, 1.38629436, 0.74193734, 0.09531018],\n",
       "       [1.91692261, 1.60943791, 0.78845736, 0.18232156],\n",
       "       [1.90210753, 1.68639895, 0.91629073, 0.33647224],\n",
       "       [1.85629799, 1.58923521, 0.83290912, 0.33647224],\n",
       "       [1.80828877, 1.5040774 , 0.87546874, 0.26236426],\n",
       "       [1.90210753, 1.56861592, 0.99325177, 0.26236426],\n",
       "       [1.80828877, 1.56861592, 0.91629073, 0.26236426],\n",
       "       [1.85629799, 1.48160454, 0.99325177, 0.18232156],\n",
       "       [1.80828877, 1.54756251, 0.91629073, 0.33647224],\n",
       "       [1.7227666 , 1.5260563 , 0.69314718, 0.18232156],\n",
       "       [1.80828877, 1.45861502, 0.99325177, 0.40546511],\n",
       "       [1.75785792, 1.48160454, 1.06471074, 0.18232156],\n",
       "       [1.79175947, 1.38629436, 0.95551145, 0.18232156],\n",
       "       [1.79175947, 1.48160454, 0.95551145, 0.33647224],\n",
       "       [1.82454929, 1.5040774 , 0.91629073, 0.18232156],\n",
       "       [1.82454929, 1.48160454, 0.87546874, 0.18232156],\n",
       "       [1.74046617, 1.43508453, 0.95551145, 0.18232156],\n",
       "       [1.75785792, 1.41098697, 0.95551145, 0.18232156],\n",
       "       [1.85629799, 1.48160454, 0.91629073, 0.33647224],\n",
       "       [1.82454929, 1.62924054, 0.91629073, 0.09531018],\n",
       "       [1.87180218, 1.64865863, 0.87546874, 0.18232156],\n",
       "       [1.77495235, 1.41098697, 0.91629073, 0.09531018],\n",
       "       [1.79175947, 1.43508453, 0.78845736, 0.18232156],\n",
       "       [1.87180218, 1.5040774 , 0.83290912, 0.18232156],\n",
       "       [1.77495235, 1.41098697, 0.91629073, 0.09531018],\n",
       "       [1.68639895, 1.38629436, 0.83290912, 0.18232156],\n",
       "       [1.80828877, 1.48160454, 0.91629073, 0.18232156],\n",
       "       [1.79175947, 1.5040774 , 0.83290912, 0.26236426],\n",
       "       [1.70474809, 1.19392247, 0.83290912, 0.26236426],\n",
       "       [1.68639895, 1.43508453, 0.83290912, 0.18232156],\n",
       "       [1.79175947, 1.5040774 , 0.95551145, 0.47000363],\n",
       "       [1.80828877, 1.56861592, 1.06471074, 0.33647224],\n",
       "       [1.75785792, 1.38629436, 0.87546874, 0.26236426],\n",
       "       [1.80828877, 1.56861592, 0.95551145, 0.18232156],\n",
       "       [1.7227666 , 1.43508453, 0.87546874, 0.18232156],\n",
       "       [1.84054963, 1.54756251, 0.91629073, 0.18232156],\n",
       "       [1.79175947, 1.45861502, 0.87546874, 0.18232156],\n",
       "       [2.07944154, 1.43508453, 1.74046617, 0.87546874],\n",
       "       [2.00148   , 1.43508453, 1.70474809, 0.91629073],\n",
       "       [2.06686276, 1.41098697, 1.77495235, 0.91629073],\n",
       "       [1.87180218, 1.19392247, 1.60943791, 0.83290912],\n",
       "       [2.01490302, 1.33500107, 1.7227666 , 0.91629073],\n",
       "       [1.90210753, 1.33500107, 1.70474809, 0.83290912],\n",
       "       [1.98787435, 1.45861502, 1.74046617, 0.95551145],\n",
       "       [1.77495235, 1.22377543, 1.45861502, 0.69314718],\n",
       "       [2.02814825, 1.36097655, 1.7227666 , 0.83290912],\n",
       "       [1.82454929, 1.30833282, 1.58923521, 0.87546874],\n",
       "       [1.79175947, 1.09861229, 1.5040774 , 0.69314718],\n",
       "       [1.93152141, 1.38629436, 1.64865863, 0.91629073],\n",
       "       [1.94591015, 1.16315081, 1.60943791, 0.69314718],\n",
       "       [1.96009478, 1.36097655, 1.74046617, 0.87546874],\n",
       "       [1.88706965, 1.36097655, 1.5260563 , 0.83290912],\n",
       "       [2.04122033, 1.41098697, 1.68639895, 0.87546874],\n",
       "       [1.88706965, 1.38629436, 1.70474809, 0.91629073],\n",
       "       [1.91692261, 1.30833282, 1.62924054, 0.69314718],\n",
       "       [1.97408103, 1.16315081, 1.70474809, 0.91629073],\n",
       "       [1.88706965, 1.25276297, 1.58923521, 0.74193734],\n",
       "       [1.93152141, 1.43508453, 1.75785792, 1.02961942],\n",
       "       [1.96009478, 1.33500107, 1.60943791, 0.83290912],\n",
       "       [1.98787435, 1.25276297, 1.77495235, 0.91629073],\n",
       "       [1.96009478, 1.33500107, 1.74046617, 0.78845736],\n",
       "       [2.00148   , 1.36097655, 1.66770682, 0.83290912],\n",
       "       [2.02814825, 1.38629436, 1.68639895, 0.87546874],\n",
       "       [2.05412373, 1.33500107, 1.75785792, 0.87546874],\n",
       "       [2.04122033, 1.38629436, 1.79175947, 0.99325177],\n",
       "       [1.94591015, 1.36097655, 1.70474809, 0.91629073],\n",
       "       [1.90210753, 1.28093385, 1.5040774 , 0.69314718],\n",
       "       [1.87180218, 1.22377543, 1.56861592, 0.74193734],\n",
       "       [1.87180218, 1.22377543, 1.54756251, 0.69314718],\n",
       "       [1.91692261, 1.30833282, 1.58923521, 0.78845736],\n",
       "       [1.94591015, 1.30833282, 1.80828877, 0.95551145],\n",
       "       [1.85629799, 1.38629436, 1.70474809, 0.91629073],\n",
       "       [1.94591015, 1.48160454, 1.70474809, 0.95551145],\n",
       "       [2.04122033, 1.41098697, 1.74046617, 0.91629073],\n",
       "       [1.98787435, 1.19392247, 1.68639895, 0.83290912],\n",
       "       [1.88706965, 1.38629436, 1.62924054, 0.83290912],\n",
       "       [1.87180218, 1.25276297, 1.60943791, 0.83290912],\n",
       "       [1.87180218, 1.28093385, 1.68639895, 0.78845736],\n",
       "       [1.96009478, 1.38629436, 1.7227666 , 0.87546874],\n",
       "       [1.91692261, 1.28093385, 1.60943791, 0.78845736],\n",
       "       [1.79175947, 1.19392247, 1.45861502, 0.69314718],\n",
       "       [1.88706965, 1.30833282, 1.64865863, 0.83290912],\n",
       "       [1.90210753, 1.38629436, 1.64865863, 0.78845736],\n",
       "       [1.90210753, 1.36097655, 1.64865863, 0.83290912],\n",
       "       [1.97408103, 1.36097655, 1.66770682, 0.83290912],\n",
       "       [1.80828877, 1.25276297, 1.38629436, 0.74193734],\n",
       "       [1.90210753, 1.33500107, 1.62924054, 0.83290912],\n",
       "       [1.98787435, 1.45861502, 1.94591015, 1.25276297],\n",
       "       [1.91692261, 1.30833282, 1.80828877, 1.06471074],\n",
       "       [2.09186406, 1.38629436, 1.93152141, 1.13140211],\n",
       "       [1.98787435, 1.36097655, 1.88706965, 1.02961942],\n",
       "       [2.01490302, 1.38629436, 1.91692261, 1.16315081],\n",
       "       [2.1517622 , 1.38629436, 2.02814825, 1.13140211],\n",
       "       [1.77495235, 1.25276297, 1.70474809, 0.99325177],\n",
       "       [2.11625551, 1.36097655, 1.98787435, 1.02961942],\n",
       "       [2.04122033, 1.25276297, 1.91692261, 1.02961942],\n",
       "       [2.10413415, 1.5260563 , 1.96009478, 1.25276297],\n",
       "       [2.01490302, 1.43508453, 1.80828877, 1.09861229],\n",
       "       [2.00148   , 1.30833282, 1.84054963, 1.06471074],\n",
       "       [2.05412373, 1.38629436, 1.87180218, 1.13140211],\n",
       "       [1.90210753, 1.25276297, 1.79175947, 1.09861229],\n",
       "       [1.91692261, 1.33500107, 1.80828877, 1.22377543],\n",
       "       [2.00148   , 1.43508453, 1.84054963, 1.19392247],\n",
       "       [2.01490302, 1.38629436, 1.87180218, 1.02961942],\n",
       "       [2.16332303, 1.56861592, 2.04122033, 1.16315081],\n",
       "       [2.16332303, 1.28093385, 2.06686276, 1.19392247],\n",
       "       [1.94591015, 1.16315081, 1.79175947, 0.91629073],\n",
       "       [2.06686276, 1.43508453, 1.90210753, 1.19392247],\n",
       "       [1.88706965, 1.33500107, 1.77495235, 1.09861229],\n",
       "       [2.16332303, 1.33500107, 2.04122033, 1.09861229],\n",
       "       [1.98787435, 1.30833282, 1.77495235, 1.02961942],\n",
       "       [2.04122033, 1.45861502, 1.90210753, 1.13140211],\n",
       "       [2.10413415, 1.43508453, 1.94591015, 1.02961942],\n",
       "       [1.97408103, 1.33500107, 1.75785792, 1.02961942],\n",
       "       [1.96009478, 1.38629436, 1.77495235, 1.02961942],\n",
       "       [2.00148   , 1.33500107, 1.88706965, 1.13140211],\n",
       "       [2.10413415, 1.38629436, 1.91692261, 0.95551145],\n",
       "       [2.12823171, 1.33500107, 1.96009478, 1.06471074],\n",
       "       [2.18605128, 1.56861592, 2.00148   , 1.09861229],\n",
       "       [2.00148   , 1.33500107, 1.88706965, 1.16315081],\n",
       "       [1.98787435, 1.33500107, 1.80828877, 0.91629073],\n",
       "       [1.96009478, 1.28093385, 1.88706965, 0.87546874],\n",
       "       [2.16332303, 1.38629436, 1.96009478, 1.19392247],\n",
       "       [1.98787435, 1.48160454, 1.88706965, 1.22377543],\n",
       "       [2.00148   , 1.41098697, 1.87180218, 1.02961942],\n",
       "       [1.94591015, 1.38629436, 1.75785792, 1.02961942],\n",
       "       [2.06686276, 1.41098697, 1.85629799, 1.13140211],\n",
       "       [2.04122033, 1.41098697, 1.88706965, 1.22377543],\n",
       "       [2.06686276, 1.41098697, 1.80828877, 1.19392247],\n",
       "       [1.91692261, 1.30833282, 1.80828877, 1.06471074],\n",
       "       [2.05412373, 1.43508453, 1.93152141, 1.19392247],\n",
       "       [2.04122033, 1.45861502, 1.90210753, 1.25276297],\n",
       "       [2.04122033, 1.38629436, 1.82454929, 1.19392247],\n",
       "       [1.98787435, 1.25276297, 1.79175947, 1.06471074],\n",
       "       [2.01490302, 1.38629436, 1.82454929, 1.09861229],\n",
       "       [1.97408103, 1.48160454, 1.85629799, 1.19392247],\n",
       "       [1.93152141, 1.38629436, 1.80828877, 1.02961942]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prepc.FunctionTransformer(np.log1p, validate=True).fit_transform(X)\n",
    "# validate 看是否合法 取log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二值化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 把一些连续的值变成离散的值，使得特征更好解释"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [1., 1., 1., 0.],\n",
       "       [1., 0., 1., 0.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prepc.Binarizer(threshold=3).fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 特征筛选"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "1. 统计相关性\n",
    "2. 基于正则L1\n",
    "3. 基于树的重要性\n",
    "4. 前向后向\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 统计相关性\n",
    "方差： 标准化之前用，方差大的特征好\n",
    "Chi-square 卡方检验\n",
    "相关系数\n",
    "互信息"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 方差\n",
    "fselect.VarianceThreshold(threshold=0.5).fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 卡方 k=2, 保留两个\n",
    "fselect.SelectKBest(fselect.chi2, k=2).fit_transform(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.基于正则\n",
    "对参数的惩罚\n",
    "LR = Sigmoid(wx), 损失函数为log loss (or Sigmoid cross entropy)\n",
    "-(ylog(fit)+(1-y)log(1-fit)) + Omega\n",
    "###  L1 引起稀疏化， 系数容易变成0了， 说明这个对应的特征没有用了\n",
    "why L1 正则容易稀疏化呢？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 3.5, 1.4],\n",
       "       [4.9, 3. , 1.4],\n",
       "       [4.7, 3.2, 1.3],\n",
       "       [4.6, 3.1, 1.5],\n",
       "       [5. , 3.6, 1.4],\n",
       "       [5.4, 3.9, 1.7],\n",
       "       [4.6, 3.4, 1.4],\n",
       "       [5. , 3.4, 1.5],\n",
       "       [4.4, 2.9, 1.4],\n",
       "       [4.9, 3.1, 1.5],\n",
       "       [5.4, 3.7, 1.5],\n",
       "       [4.8, 3.4, 1.6],\n",
       "       [4.8, 3. , 1.4],\n",
       "       [4.3, 3. , 1.1],\n",
       "       [5.8, 4. , 1.2],\n",
       "       [5.7, 4.4, 1.5],\n",
       "       [5.4, 3.9, 1.3],\n",
       "       [5.1, 3.5, 1.4],\n",
       "       [5.7, 3.8, 1.7],\n",
       "       [5.1, 3.8, 1.5],\n",
       "       [5.4, 3.4, 1.7],\n",
       "       [5.1, 3.7, 1.5],\n",
       "       [4.6, 3.6, 1. ],\n",
       "       [5.1, 3.3, 1.7],\n",
       "       [4.8, 3.4, 1.9],\n",
       "       [5. , 3. , 1.6],\n",
       "       [5. , 3.4, 1.6],\n",
       "       [5.2, 3.5, 1.5],\n",
       "       [5.2, 3.4, 1.4],\n",
       "       [4.7, 3.2, 1.6],\n",
       "       [4.8, 3.1, 1.6],\n",
       "       [5.4, 3.4, 1.5],\n",
       "       [5.2, 4.1, 1.5],\n",
       "       [5.5, 4.2, 1.4],\n",
       "       [4.9, 3.1, 1.5],\n",
       "       [5. , 3.2, 1.2],\n",
       "       [5.5, 3.5, 1.3],\n",
       "       [4.9, 3.1, 1.5],\n",
       "       [4.4, 3. , 1.3],\n",
       "       [5.1, 3.4, 1.5],\n",
       "       [5. , 3.5, 1.3],\n",
       "       [4.5, 2.3, 1.3],\n",
       "       [4.4, 3.2, 1.3],\n",
       "       [5. , 3.5, 1.6],\n",
       "       [5.1, 3.8, 1.9],\n",
       "       [4.8, 3. , 1.4],\n",
       "       [5.1, 3.8, 1.6],\n",
       "       [4.6, 3.2, 1.4],\n",
       "       [5.3, 3.7, 1.5],\n",
       "       [5. , 3.3, 1.4],\n",
       "       [7. , 3.2, 4.7],\n",
       "       [6.4, 3.2, 4.5],\n",
       "       [6.9, 3.1, 4.9],\n",
       "       [5.5, 2.3, 4. ],\n",
       "       [6.5, 2.8, 4.6],\n",
       "       [5.7, 2.8, 4.5],\n",
       "       [6.3, 3.3, 4.7],\n",
       "       [4.9, 2.4, 3.3],\n",
       "       [6.6, 2.9, 4.6],\n",
       "       [5.2, 2.7, 3.9],\n",
       "       [5. , 2. , 3.5],\n",
       "       [5.9, 3. , 4.2],\n",
       "       [6. , 2.2, 4. ],\n",
       "       [6.1, 2.9, 4.7],\n",
       "       [5.6, 2.9, 3.6],\n",
       "       [6.7, 3.1, 4.4],\n",
       "       [5.6, 3. , 4.5],\n",
       "       [5.8, 2.7, 4.1],\n",
       "       [6.2, 2.2, 4.5],\n",
       "       [5.6, 2.5, 3.9],\n",
       "       [5.9, 3.2, 4.8],\n",
       "       [6.1, 2.8, 4. ],\n",
       "       [6.3, 2.5, 4.9],\n",
       "       [6.1, 2.8, 4.7],\n",
       "       [6.4, 2.9, 4.3],\n",
       "       [6.6, 3. , 4.4],\n",
       "       [6.8, 2.8, 4.8],\n",
       "       [6.7, 3. , 5. ],\n",
       "       [6. , 2.9, 4.5],\n",
       "       [5.7, 2.6, 3.5],\n",
       "       [5.5, 2.4, 3.8],\n",
       "       [5.5, 2.4, 3.7],\n",
       "       [5.8, 2.7, 3.9],\n",
       "       [6. , 2.7, 5.1],\n",
       "       [5.4, 3. , 4.5],\n",
       "       [6. , 3.4, 4.5],\n",
       "       [6.7, 3.1, 4.7],\n",
       "       [6.3, 2.3, 4.4],\n",
       "       [5.6, 3. , 4.1],\n",
       "       [5.5, 2.5, 4. ],\n",
       "       [5.5, 2.6, 4.4],\n",
       "       [6.1, 3. , 4.6],\n",
       "       [5.8, 2.6, 4. ],\n",
       "       [5. , 2.3, 3.3],\n",
       "       [5.6, 2.7, 4.2],\n",
       "       [5.7, 3. , 4.2],\n",
       "       [5.7, 2.9, 4.2],\n",
       "       [6.2, 2.9, 4.3],\n",
       "       [5.1, 2.5, 3. ],\n",
       "       [5.7, 2.8, 4.1],\n",
       "       [6.3, 3.3, 6. ],\n",
       "       [5.8, 2.7, 5.1],\n",
       "       [7.1, 3. , 5.9],\n",
       "       [6.3, 2.9, 5.6],\n",
       "       [6.5, 3. , 5.8],\n",
       "       [7.6, 3. , 6.6],\n",
       "       [4.9, 2.5, 4.5],\n",
       "       [7.3, 2.9, 6.3],\n",
       "       [6.7, 2.5, 5.8],\n",
       "       [7.2, 3.6, 6.1],\n",
       "       [6.5, 3.2, 5.1],\n",
       "       [6.4, 2.7, 5.3],\n",
       "       [6.8, 3. , 5.5],\n",
       "       [5.7, 2.5, 5. ],\n",
       "       [5.8, 2.8, 5.1],\n",
       "       [6.4, 3.2, 5.3],\n",
       "       [6.5, 3. , 5.5],\n",
       "       [7.7, 3.8, 6.7],\n",
       "       [7.7, 2.6, 6.9],\n",
       "       [6. , 2.2, 5. ],\n",
       "       [6.9, 3.2, 5.7],\n",
       "       [5.6, 2.8, 4.9],\n",
       "       [7.7, 2.8, 6.7],\n",
       "       [6.3, 2.7, 4.9],\n",
       "       [6.7, 3.3, 5.7],\n",
       "       [7.2, 3.2, 6. ],\n",
       "       [6.2, 2.8, 4.8],\n",
       "       [6.1, 3. , 4.9],\n",
       "       [6.4, 2.8, 5.6],\n",
       "       [7.2, 3. , 5.8],\n",
       "       [7.4, 2.8, 6.1],\n",
       "       [7.9, 3.8, 6.4],\n",
       "       [6.4, 2.8, 5.6],\n",
       "       [6.3, 2.8, 5.1],\n",
       "       [6.1, 2.6, 5.6],\n",
       "       [7.7, 3. , 6.1],\n",
       "       [6.3, 3.4, 5.6],\n",
       "       [6.4, 3.1, 5.5],\n",
       "       [6. , 3. , 4.8],\n",
       "       [6.9, 3.1, 5.4],\n",
       "       [6.7, 3.1, 5.6],\n",
       "       [6.9, 3.1, 5.1],\n",
       "       [5.8, 2.7, 5.1],\n",
       "       [6.8, 3.2, 5.9],\n",
       "       [6.7, 3.3, 5.7],\n",
       "       [6.7, 3. , 5.2],\n",
       "       [6.3, 2.5, 5. ],\n",
       "       [6.5, 3. , 5.2],\n",
       "       [6.2, 3.4, 5.4],\n",
       "       [5.9, 3. , 5.1]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression(penalty=\"l1\", C=0.1, multi_class='ovr', solver='liblinear').fit(X, y)\n",
    "model = fselect.SelectFromModel(lr, prefit=True)\n",
    "model.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 基于树的特征重要程度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import GradientBoostingClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.4, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [1.3, 0.2],\n",
       "       [1.5, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [1.7, 0.4],\n",
       "       [1.4, 0.3],\n",
       "       [1.5, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [1.5, 0.1],\n",
       "       [1.5, 0.2],\n",
       "       [1.6, 0.2],\n",
       "       [1.4, 0.1],\n",
       "       [1.1, 0.1],\n",
       "       [1.2, 0.2],\n",
       "       [1.5, 0.4],\n",
       "       [1.3, 0.4],\n",
       "       [1.4, 0.3],\n",
       "       [1.7, 0.3],\n",
       "       [1.5, 0.3],\n",
       "       [1.7, 0.2],\n",
       "       [1.5, 0.4],\n",
       "       [1. , 0.2],\n",
       "       [1.7, 0.5],\n",
       "       [1.9, 0.2],\n",
       "       [1.6, 0.2],\n",
       "       [1.6, 0.4],\n",
       "       [1.5, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [1.6, 0.2],\n",
       "       [1.6, 0.2],\n",
       "       [1.5, 0.4],\n",
       "       [1.5, 0.1],\n",
       "       [1.4, 0.2],\n",
       "       [1.5, 0.1],\n",
       "       [1.2, 0.2],\n",
       "       [1.3, 0.2],\n",
       "       [1.5, 0.1],\n",
       "       [1.3, 0.2],\n",
       "       [1.5, 0.2],\n",
       "       [1.3, 0.3],\n",
       "       [1.3, 0.3],\n",
       "       [1.3, 0.2],\n",
       "       [1.6, 0.6],\n",
       "       [1.9, 0.4],\n",
       "       [1.4, 0.3],\n",
       "       [1.6, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [1.5, 0.2],\n",
       "       [1.4, 0.2],\n",
       "       [4.7, 1.4],\n",
       "       [4.5, 1.5],\n",
       "       [4.9, 1.5],\n",
       "       [4. , 1.3],\n",
       "       [4.6, 1.5],\n",
       "       [4.5, 1.3],\n",
       "       [4.7, 1.6],\n",
       "       [3.3, 1. ],\n",
       "       [4.6, 1.3],\n",
       "       [3.9, 1.4],\n",
       "       [3.5, 1. ],\n",
       "       [4.2, 1.5],\n",
       "       [4. , 1. ],\n",
       "       [4.7, 1.4],\n",
       "       [3.6, 1.3],\n",
       "       [4.4, 1.4],\n",
       "       [4.5, 1.5],\n",
       "       [4.1, 1. ],\n",
       "       [4.5, 1.5],\n",
       "       [3.9, 1.1],\n",
       "       [4.8, 1.8],\n",
       "       [4. , 1.3],\n",
       "       [4.9, 1.5],\n",
       "       [4.7, 1.2],\n",
       "       [4.3, 1.3],\n",
       "       [4.4, 1.4],\n",
       "       [4.8, 1.4],\n",
       "       [5. , 1.7],\n",
       "       [4.5, 1.5],\n",
       "       [3.5, 1. ],\n",
       "       [3.8, 1.1],\n",
       "       [3.7, 1. ],\n",
       "       [3.9, 1.2],\n",
       "       [5.1, 1.6],\n",
       "       [4.5, 1.5],\n",
       "       [4.5, 1.6],\n",
       "       [4.7, 1.5],\n",
       "       [4.4, 1.3],\n",
       "       [4.1, 1.3],\n",
       "       [4. , 1.3],\n",
       "       [4.4, 1.2],\n",
       "       [4.6, 1.4],\n",
       "       [4. , 1.2],\n",
       "       [3.3, 1. ],\n",
       "       [4.2, 1.3],\n",
       "       [4.2, 1.2],\n",
       "       [4.2, 1.3],\n",
       "       [4.3, 1.3],\n",
       "       [3. , 1.1],\n",
       "       [4.1, 1.3],\n",
       "       [6. , 2.5],\n",
       "       [5.1, 1.9],\n",
       "       [5.9, 2.1],\n",
       "       [5.6, 1.8],\n",
       "       [5.8, 2.2],\n",
       "       [6.6, 2.1],\n",
       "       [4.5, 1.7],\n",
       "       [6.3, 1.8],\n",
       "       [5.8, 1.8],\n",
       "       [6.1, 2.5],\n",
       "       [5.1, 2. ],\n",
       "       [5.3, 1.9],\n",
       "       [5.5, 2.1],\n",
       "       [5. , 2. ],\n",
       "       [5.1, 2.4],\n",
       "       [5.3, 2.3],\n",
       "       [5.5, 1.8],\n",
       "       [6.7, 2.2],\n",
       "       [6.9, 2.3],\n",
       "       [5. , 1.5],\n",
       "       [5.7, 2.3],\n",
       "       [4.9, 2. ],\n",
       "       [6.7, 2. ],\n",
       "       [4.9, 1.8],\n",
       "       [5.7, 2.1],\n",
       "       [6. , 1.8],\n",
       "       [4.8, 1.8],\n",
       "       [4.9, 1.8],\n",
       "       [5.6, 2.1],\n",
       "       [5.8, 1.6],\n",
       "       [6.1, 1.9],\n",
       "       [6.4, 2. ],\n",
       "       [5.6, 2.2],\n",
       "       [5.1, 1.5],\n",
       "       [5.6, 1.4],\n",
       "       [6.1, 2.3],\n",
       "       [5.6, 2.4],\n",
       "       [5.5, 1.8],\n",
       "       [4.8, 1.8],\n",
       "       [5.4, 2.1],\n",
       "       [5.6, 2.4],\n",
       "       [5.1, 2.3],\n",
       "       [5.1, 1.9],\n",
       "       [5.9, 2.3],\n",
       "       [5.7, 2.5],\n",
       "       [5.2, 2.3],\n",
       "       [5. , 1.9],\n",
       "       [5.2, 2. ],\n",
       "       [5.4, 2.3],\n",
       "       [5.1, 1.8]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fselect.SelectFromModel(GradientBoostingClassifier()).fit_transform(iris.data, iris.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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",
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 },
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