pandas_ex.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Load lib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import numpy as np;\n",
    "import pandas as pd;\n",
    "import matplotlib.pyplot as plt;\n",
    "import seaborn as sns;\n",
    "%matplotlib inline\n",
    "\n",
    "from collections import Counter;\n",
    "# RF, Adaboost,GBDT, Extratree, Voting.\n",
    "from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier, GradientBoostingClassifier, ExtraTreesClassifier, VotingClassifier;\n",
    "#LDA\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis;\n",
    "#LR\n",
    "from sklearn.linear_model import LogisticRegression;\n",
    "#KNN\n",
    "from sklearn.neighbors import KNeighborsClassifier;\n",
    "#DT\n",
    "from sklearn.tree import DecisionTreeClassifier;\n",
    "#full nn?\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "#svm\n",
    "from sklearn.svm import SVC\n",
    "# K折线 学习曲线 \n",
    "from sklearn.model_selection import GridSearchCV, cross_val_score, StratifiedKFold, learning_curve\n",
    "\n",
    "sns.set(style='white', context='notebook', palette='deep');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  \n",
       "0      0         A/5 21171   7.2500   NaN        S  \n",
       "1      0          PC 17599  71.2833   C85        C  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train = pd.read_csv(\"../data/titanic/train.csv\")\n",
    "test = pd.read_csv(\"../data/titanic/test.csv\")\n",
    "train.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PassengerId      0\n",
       "Survived         0\n",
       "Pclass           0\n",
       "Name             0\n",
       "Sex              0\n",
       "Age            177\n",
       "SibSp            0\n",
       "Parch            0\n",
       "Ticket           0\n",
       "Fare             0\n",
       "Cabin          687\n",
       "Embarked         2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 891 entries, 0 to 890\n",
      "Data columns (total 12 columns):\n",
      "PassengerId    891 non-null int64\n",
      "Survived       891 non-null int64\n",
      "Pclass         891 non-null int64\n",
      "Name           891 non-null object\n",
      "Sex            891 non-null object\n",
      "Age            714 non-null float64\n",
      "SibSp          891 non-null int64\n",
      "Parch          891 non-null int64\n",
      "Ticket         891 non-null object\n",
      "Fare           891 non-null float64\n",
      "Cabin          204 non-null object\n",
      "Embarked       889 non-null object\n",
      "dtypes: float64(2), int64(5), object(5)\n",
      "memory usage: 83.6+ KB\n"
     ]
    }
   ],
   "source": [
    "train.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(891, 12)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PassengerId      int64\n",
       "Survived         int64\n",
       "Pclass           int64\n",
       "Name            object\n",
       "Sex             object\n",
       "Age            float64\n",
       "SibSp            int64\n",
       "Parch            int64\n",
       "Ticket          object\n",
       "Fare           float64\n",
       "Cabin           object\n",
       "Embarked        object\n",
       "dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 2])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train['Pclass'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>714.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>446.000000</td>\n",
       "      <td>0.383838</td>\n",
       "      <td>2.308642</td>\n",
       "      <td>29.699118</td>\n",
       "      <td>0.523008</td>\n",
       "      <td>0.381594</td>\n",
       "      <td>32.204208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>257.353842</td>\n",
       "      <td>0.486592</td>\n",
       "      <td>0.836071</td>\n",
       "      <td>14.526497</td>\n",
       "      <td>1.102743</td>\n",
       "      <td>0.806057</td>\n",
       "      <td>49.693429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>223.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>20.125000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.910400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>446.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>14.454200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>668.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>891.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>512.329200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       PassengerId    Survived      Pclass         Age       SibSp  \\\n",
       "count   891.000000  891.000000  891.000000  714.000000  891.000000   \n",
       "mean    446.000000    0.383838    2.308642   29.699118    0.523008   \n",
       "std     257.353842    0.486592    0.836071   14.526497    1.102743   \n",
       "min       1.000000    0.000000    1.000000    0.420000    0.000000   \n",
       "25%     223.500000    0.000000    2.000000   20.125000    0.000000   \n",
       "50%     446.000000    0.000000    3.000000   28.000000    0.000000   \n",
       "75%     668.500000    1.000000    3.000000   38.000000    1.000000   \n",
       "max     891.000000    1.000000    3.000000   80.000000    8.000000   \n",
       "\n",
       "            Parch        Fare  \n",
       "count  891.000000  891.000000  \n",
       "mean     0.381594   32.204208  \n",
       "std      0.806057   49.693429  \n",
       "min      0.000000    0.000000  \n",
       "25%      0.000000    7.910400  \n",
       "50%      0.000000   14.454200  \n",
       "75%      0.000000   31.000000  \n",
       "max      6.000000  512.329200  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.096067</td>\n",
       "      <td>-0.308247</td>\n",
       "      <td>0.096067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fare</th>\n",
       "      <td>0.096067</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.159651</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SibSp</th>\n",
       "      <td>-0.308247</td>\n",
       "      <td>0.159651</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.159651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fare</th>\n",
       "      <td>0.096067</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.159651</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "            Age      Fare     SibSp      Fare\n",
       "Age    1.000000  0.096067 -0.308247  0.096067\n",
       "Fare   0.096067  1.000000  0.159651  1.000000\n",
       "SibSp -0.308247  0.159651  1.000000  0.159651\n",
       "Fare   0.096067  1.000000  0.159651  1.000000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train[['Age','Fare','SibSp','Fare']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  \n",
       "0      0         A/5 21171   7.2500   NaN        S  \n",
       "1      0          PC 17599  71.2833   C85        C  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "3      0            113803  53.1000  C123        S  \n",
       "4      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "      <th>Name_len</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "      <td>51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  Name_len  \n",
       "0      0         A/5 21171   7.2500   NaN        S        23  \n",
       "1      0          PC 17599  71.2833   C85        C        51  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S        22  \n",
       "3      0            113803  53.1000  C123        S        44  \n",
       "4      0            373450   8.0500   NaN        S        24  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# apply 输入函数对象，类似map，相当与批处理\n",
    "train['Name_len']=train['Name'].apply(len);\n",
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Cut and Qcut"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "\n",
    "都是把数值型的集合划分为离散的段.\n",
    "\n",
    "cut默认按给定的值均匀划分。\n",
    "qcut默认下，保证划分到每个段的个数相等，然后再去选取分段点;\n",
    "\n",
    "用高斯分布来理解:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import numpy as np;\n",
    "import pandas as pd;\n",
    "import seaborn as sns;\n",
    "import matplotlib.pyplot as plt;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>f</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.650985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.509034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.436448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12.681229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.662605</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           f\n",
       "0   7.650985\n",
       "1  12.509034\n",
       "2   7.436448\n",
       "3  12.681229\n",
       "4   7.662605"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu =10;\n",
    "std = 1.5;\n",
    "f1 = (std*(np.random.randn(1000,))+mu).tolist();\n",
    "gaussian = pd.DataFrame({\"f\":f1})\n",
    "gaussian.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd99368abe0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(gaussian['f'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussian['cut'] = pd.cut(gaussian['f'],5)\n",
    "sns.countplot(x=\"cut\",data = gaussian);\n",
    "splits = gaussian['cut'].unique().sort_values();\n",
    "# sns.factorplot(x=\"cut\", y = \"f\",data = gaussian, kind=\"bar\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### Categorical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "\n",
    "注意cut后的分段为一个pandas Categorical类，每个Categorical 包含了的段的类型是Interval\n",
    "\n",
    "用`get_split_points`得到分段点,然后画到原来的图形上，展示分段效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.arrays.categorical.Categorical"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(splits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas._libs.interval.Interval"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(splits[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_split_points(sp):\n",
    "    points = []\n",
    "    for i,interval in enumerate(sp):\n",
    "        points.append(interval.left);\n",
    "        if i == len(sp)-1:\n",
    "            points.append(interval.right)\n",
    "    return points\n",
    "\n",
    "l = get_split_points(splits)\n",
    "# 用ax将seanborn的图画在一起a\n",
    "fig, ax = plt.subplots()\n",
    "sns.distplot(gaussian['f'],ax=ax);\n",
    "maxi = 0.25;\n",
    "lines=100;\n",
    "for i in l:\n",
    "    plt.plot([i]*lines, np.linspace(0, maxi, lines))\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussian['qcut'] = pd.qcut(gaussian['f'],5)\n",
    "sns.countplot(x=\"qcut\",data = gaussian);\n",
    "splits = gaussian['qcut'].unique().sort_values();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = get_split_points(splits)\n",
    "# 用ax将seanborn的图画在一起a\n",
    "fig, ax = plt.subplots()\n",
    "sns.distplot(gaussian['f'],ax=ax);\n",
    "maxi = 0.25;\n",
    "lines=100;\n",
    "for i in l:\n",
    "    plt.plot([i]*lines, np.linspace(0, maxi, lines))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 结论\n",
    "可以明显看出qcut和cut区别，qcut为了保证每个段元素相等，在元素分布密集的中间区域，范围比较债，而在分布稀疏的边缘，范围比较宽，cut的则是均匀分布，每个区域内的元素个数不一样。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Groupby"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>one</td>\n",
       "      <td>-1.116273</td>\n",
       "      <td>-0.990068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>a</td>\n",
       "      <td>two</td>\n",
       "      <td>1.685549</td>\n",
       "      <td>0.506476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>b</td>\n",
       "      <td>one</td>\n",
       "      <td>-0.321567</td>\n",
       "      <td>0.957115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>b</td>\n",
       "      <td>two</td>\n",
       "      <td>1.190307</td>\n",
       "      <td>0.511386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>one</td>\n",
       "      <td>-0.814202</td>\n",
       "      <td>0.310887</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key1 key2     data1     data2\n",
       "0    a  one -1.116273 -0.990068\n",
       "1    a  two  1.685549  0.506476\n",
       "2    b  one -0.321567  0.957115\n",
       "3    b  two  1.190307  0.511386\n",
       "4    a  one -0.814202  0.310887"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'key1':['a','a','b','b','a'],'key2':['one','two','one','two','one'],'data1':np.random.randn(5),'data2':np.random.randn(5)})  \n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.groupby.DataFrameGroupBy object at 0x7fd9959d8668>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp = df.groupby(['key1','key2']); gp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### see group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('a', 'one'): Int64Index([0, 4], dtype='int64'),\n",
       " ('a', 'two'): Int64Index([1], dtype='int64'),\n",
       " ('b', 'one'): Int64Index([2], dtype='int64'),\n",
       " ('b', 'two'): Int64Index([3], dtype='int64')}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp.groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### show items in  groups "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(('a', 'one'),   key1 key2     data1     data2\n",
      "0    a  one -1.116273 -0.990068\n",
      "4    a  one -0.814202  0.310887)\n",
      "(('a', 'two'),   key1 key2     data1     data2\n",
      "1    a  two  1.685549  0.506476)\n",
      "(('b', 'one'),   key1 key2     data1     data2\n",
      "2    b  one -0.321567  0.957115)\n",
      "(('b', 'two'),   key1 key2     data1     data2\n",
      "3    b  two  1.190307  0.511386)\n"
     ]
    }
   ],
   "source": [
    "for g in gp: print(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### staticis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1  key2\n",
       "a     one     2\n",
       "      two     1\n",
       "b     one     1\n",
       "      two     1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>one</th>\n",
       "      <td>-1.930475</td>\n",
       "      <td>-0.679181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>1.685549</td>\n",
       "      <td>0.506476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>one</th>\n",
       "      <td>-0.321567</td>\n",
       "      <td>0.957115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>1.190307</td>\n",
       "      <td>0.511386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              data1     data2\n",
       "key1 key2                    \n",
       "a    one  -1.930475 -0.679181\n",
       "     two   1.685549  0.506476\n",
       "b    one  -0.321567  0.957115\n",
       "     two   1.190307  0.511386"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>one</th>\n",
       "      <td>-0.965237</td>\n",
       "      <td>-0.339591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>1.685549</td>\n",
       "      <td>0.506476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>one</th>\n",
       "      <td>-0.321567</td>\n",
       "      <td>0.957115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>1.190307</td>\n",
       "      <td>0.511386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              data1     data2\n",
       "key1 key2                    \n",
       "a    one  -0.965237 -0.339591\n",
       "     two   1.685549  0.506476\n",
       "b    one  -0.321567  0.957115\n",
       "     two   1.190307  0.511386"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### app agg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "agg some function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1  key2\n",
       "a     one    -0.965237\n",
       "      two     1.685549\n",
       "b     one    -0.321567\n",
       "      two     1.190307\n",
       "Name: data1, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp['data1'].agg('mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "apply self definition function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   -0.116273\n",
       "1    2.685549\n",
       "2    0.678433\n",
       "3    2.190307\n",
       "4    0.185798\n",
       "Name: data1, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp['data1'].apply( lambda x: x+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Pivot_table (透视表)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>small</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>2</td>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>2</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>foo</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>3</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>foo</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>3</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>bar</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>bar</td>\n",
       "      <td>one</td>\n",
       "      <td>small</td>\n",
       "      <td>5</td>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>bar</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>6</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>bar</td>\n",
       "      <td>two</td>\n",
       "      <td>large</td>\n",
       "      <td>7</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A    B      C  D   E\n",
       "0  foo  one  small  1  10\n",
       "1  foo  one  large  2  82\n",
       "2  foo  one  large  2  92\n",
       "3  foo  two  small  3  35\n",
       "4  foo  two  small  3  42\n",
       "5  bar  one  large  4  15\n",
       "6  bar  one  small  5  61\n",
       "7  bar  two  small  6  27\n",
       "8  bar  two  large  7  43"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({\"A\": [\"foo\", \"foo\", \"foo\", \"foo\", \"foo\",\n",
    "                         \"bar\", \"bar\", \"bar\", \"bar\"],\n",
    "                    \"B\": [\"one\", \"one\", \"one\", \"two\", \"two\",\n",
    "                         \"one\", \"one\", \"two\", \"two\"],\n",
    "                  \"C\": [\"small\", \"large\", \"large\", \"small\",\n",
    "                       \"small\", \"large\", \"small\", \"small\",\n",
    "                        \"large\"],\n",
    "                 \"D\": [1, 2, 2, 3, 3, 4, 5, 6, 7],  \"E\": [10, 82, 92, 35, 42, 15, 61, 27,43]})\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    object\n",
       "B    object\n",
       "C    object\n",
       "D     int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`聚集函数`计算只和numeric的列有关 , 默认计算方式是 numpy.mean 可以通过aggfun来指定新的统计指标\n",
    "index指定cat行，colums指定cat列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>5.5</td>\n",
       "      <td>36.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>2.2</td>\n",
       "      <td>52.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       D     E\n",
       "A             \n",
       "bar  5.5  36.5\n",
       "foo  2.2  52.2"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,index=['A'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "margin 增加一行来统计行列的sum的信息"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>D</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>5.500000</td>\n",
       "      <td>36.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>2.200000</td>\n",
       "      <td>52.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>3.666667</td>\n",
       "      <td>45.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            D          E\n",
       "A                       \n",
       "bar  5.500000  36.500000\n",
       "foo  2.200000  52.200000\n",
       "All  3.666667  45.222222"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,index=['A'],margins=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "values指定被统计的numeric 列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>5.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>2.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>3.666667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            D\n",
       "A            \n",
       "bar  5.500000\n",
       "foo  2.200000\n",
       "All  3.666667"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,values=['D'],index=['A'],margins=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "index 和columns分别指定表的行和列\n",
    "可以通过列名，分组，index等方式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"3\" halign=\"left\">D</th>\n",
       "      <th colspan=\"3\" halign=\"left\">E</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>All</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
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       "      <th>A</th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>4.500000</td>\n",
       "      <td>6.50</td>\n",
       "      <td>5.500000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>35.00</td>\n",
       "      <td>36.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>1.666667</td>\n",
       "      <td>3.00</td>\n",
       "      <td>2.200000</td>\n",
       "      <td>61.333333</td>\n",
       "      <td>38.50</td>\n",
       "      <td>52.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>2.800000</td>\n",
       "      <td>4.75</td>\n",
       "      <td>3.666667</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>36.75</td>\n",
       "      <td>45.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            D                          E                  \n",
       "B         one   two       All        one    two        All\n",
       "A                                                         \n",
       "bar  4.500000  6.50  5.500000  38.000000  35.00  36.500000\n",
       "foo  1.666667  3.00  2.200000  61.333333  38.50  52.200000\n",
       "All  2.800000  4.75  3.666667  52.000000  36.75  45.222222"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,index=['A'],columns=['B'],margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
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       "      <td>10</td>\n",
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       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>82</td>\n",
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       "      <td>27</td>\n",
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       "      <th>8</th>\n",
       "      <td>7</td>\n",
       "      <td>43</td>\n",
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      ],
      "text/plain": [
       "   D   E\n",
       "0  1  10\n",
       "1  2  82\n",
       "2  2  92\n",
       "3  3  35\n",
       "4  3  42\n",
       "5  4  15\n",
       "6  5  61\n",
       "7  6  27\n",
       "8  7  43"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,index=range(0,9) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>D</th>\n",
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       "      <th>e</th>\n",
       "      <td>3</td>\n",
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       "      <th>f</th>\n",
       "      <td>4</td>\n",
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       "      <th>g</th>\n",
       "      <td>5</td>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h</th>\n",
       "      <td>6</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>i</th>\n",
       "      <td>7</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   D   E\n",
       "a  1  10\n",
       "b  2  82\n",
       "c  2  92\n",
       "d  3  35\n",
       "e  3  42\n",
       "f  4  15\n",
       "g  5  61\n",
       "h  6  27\n",
       "i  7  43"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,index=['a','b','c','d','e','f','g','h','i'] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "aggfun指定新的统计指标"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def variance(a):\n",
    "    return np.square (a- np.mean(a) ) / len(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">D</th>\n",
       "      <th colspan=\"2\" halign=\"left\">E</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>9</td>\n",
       "      <td>13</td>\n",
       "      <td>76</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>184</td>\n",
       "      <td>77</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      D        E    \n",
       "B   one two  one two\n",
       "A                   \n",
       "bar   9  13   76  70\n",
       "foo   5   6  184  77"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df,values=['D','E'],index=['A'],columns=['B'],aggfunc=deviration )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### Crosstab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>small</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>2</td>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>2</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>foo</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>3</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>foo</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>3</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>bar</td>\n",
       "      <td>one</td>\n",
       "      <td>large</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>bar</td>\n",
       "      <td>one</td>\n",
       "      <td>small</td>\n",
       "      <td>5</td>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>bar</td>\n",
       "      <td>two</td>\n",
       "      <td>small</td>\n",
       "      <td>6</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>bar</td>\n",
       "      <td>two</td>\n",
       "      <td>large</td>\n",
       "      <td>7</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A    B      C  D   E\n",
       "0  foo  one  small  1  10\n",
       "1  foo  one  large  2  82\n",
       "2  foo  one  large  2  92\n",
       "3  foo  two  small  3  35\n",
       "4  foo  two  small  3  42\n",
       "5  bar  one  large  4  15\n",
       "6  bar  one  small  5  61\n",
       "7  bar  two  small  6  27\n",
       "8  bar  two  large  7  43"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({\"A\": [\"foo\", \"foo\", \"foo\", \"foo\", \"foo\",\n",
    "                         \"bar\", \"bar\", \"bar\", \"bar\"],\n",
    "                    \"B\": [\"one\", \"one\", \"one\", \"two\", \"two\",\n",
    "                         \"one\", \"one\", \"two\", \"two\"],\n",
    "                  \"C\": [\"small\", \"large\", \"large\", \"small\",\n",
    "                       \"small\", \"large\", \"small\", \"small\",\n",
    "                        \"large\"],\n",
    "                 \"D\": [1, 2, 2, 3, 3, 4, 5, 6, 7],  \"E\": [10, 82, 92, 35, 42, 15, 61, 27,43]})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "统计不同数据间(crosstab的含义)，各类情况出现的频数，下例就是想看看A[ bar foo] 与B [ one two] 组合后4种情况出现的次数统计\n",
    "\n",
    "这里就不区分num和cat了,反正是统计频率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>B</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "B    one  two\n",
       "A            \n",
       "bar    2    2\n",
       "foo    3    2"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(index=df['A'],columns=df['B'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "也可以指定aggfun,但是只针对numeric数据，因此需要用value来指定\n",
    "统计A,B各种组合下，D的累加的情况:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>B</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bar</th>\n",
       "      <td>9</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foo</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "B    one  two\n",
       "A            \n",
       "bar    9   13\n",
       "foo    5    6"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(df.A,df.B,values=df['D'] ,aggfunc=np.sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "重点看fast ai 里的movielen例子，是如何把数据拼接成最终想要的表的"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "###  KFold,stratifiedKFold,StratifiedShuffleSplit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "都是用来生成**cross validation data**的\n",
    "\n",
    "`KFold`是分成n坨，shuffle指的是拿做cv set 的那坨的顺序是随机的,若false,则按顺序抽一坨为cv set.  但不分层(即按分类的比例来构造每一坨), \n",
    "`StratifiedKFold`和KFold的区别是为分层，比如y中0和1为1:1,则分坨时，每坨0和1的比例也是1:1\n",
    "\n",
    "以上两种属于`不放回抽样`，即每坨的元素都是不重复的，所以的坨加起来就是原来的集合\n",
    "\n",
    "\n",
    "`ShuffleSplit` 和`StratifiedShuffleSplit` 则是`放回抽样`，同样分10次，每次都放回. 意味着可能10次的cv set里，元素可能重复\n",
    "\n",
    "`train_and_test_split`\n",
    "前面都是给出index，这个函数直接根据dataset给出分好的train set and cv set.不是\n",
    "Fold算法，只给出一个train和1个test, 调用多次的效果类似于`ShuffleSplit`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KFold shuffle=false\n",
      "TRAIN: [2 3 4 5 6 7 8 9] TEST: [0 1]\n",
      "TRAIN: [0 1 4 5 6 7 8 9] TEST: [2 3]\n",
      "TRAIN: [0 1 2 3 6 7 8 9] TEST: [4 5]\n",
      "TRAIN: [0 1 2 3 4 5 8 9] TEST: [6 7]\n",
      "TRAIN: [0 1 2 3 4 5 6 7] TEST: [8 9]\n",
      "KFold shuffle=true\n",
      "TRAIN: [0 1 2 4 5 6 7 8] TEST: [3 9]\n",
      "TRAIN: [0 1 2 3 4 5 7 9] TEST: [6 8]\n",
      "TRAIN: [0 1 3 4 6 7 8 9] TEST: [2 5]\n",
      "TRAIN: [0 2 3 4 5 6 8 9] TEST: [1 7]\n",
      "TRAIN: [1 2 3 5 6 7 8 9] TEST: [0 4]\n",
      "StratifiedKFold shuffle =false\n",
      "TRAIN: [1 2 3 4 6 7 8 9] TEST: [0 5]\n",
      "TRAIN: [0 2 3 4 5 7 8 9] TEST: [1 6]\n",
      "TRAIN: [0 1 3 4 5 6 8 9] TEST: [2 7]\n",
      "TRAIN: [0 1 2 4 5 6 7 9] TEST: [3 8]\n",
      "TRAIN: [0 1 2 3 5 6 7 8] TEST: [4 9]\n",
      "StratifiedKFold shuffle =true\n",
      "TRAIN: [0 2 3 4 5 7 8 9] TEST: [1 6]\n",
      "TRAIN: [0 1 2 3 5 6 7 8] TEST: [4 9]\n",
      "TRAIN: [0 1 3 4 5 6 8 9] TEST: [2 7]\n",
      "TRAIN: [1 2 3 4 6 7 8 9] TEST: [0 5]\n",
      "TRAIN: [0 1 2 4 5 6 7 9] TEST: [3 8]\n",
      "Shuffle Split\n",
      "TRAIN: [5 0 7 2 9 4 3 6] TEST: [8 1]\n",
      "TRAIN: [8 5 3 4 7 9 6 2] TEST: [0 1]\n",
      "TRAIN: [0 6 8 5 3 7 1 4] TEST: [9 2]\n",
      "TRAIN: [6 2 8 0 3 4 5 9] TEST: [1 7]\n",
      "TRAIN: [4 8 0 7 6 3 2 9] TEST: [1 5]\n",
      "Stratified Shuffle Split\n",
      "TRAIN: [8 4 1 0 6 5 7 2] TEST: [3 9]\n",
      "TRAIN: [7 0 3 9 4 5 1 6] TEST: [8 2]\n",
      "TRAIN: [1 2 5 6 4 8 9 0] TEST: [3 7]\n",
      "TRAIN: [4 6 7 8 3 5 1 2] TEST: [9 0]\n",
      "TRAIN: [7 2 6 5 4 3 0 9] TEST: [1 8]\n",
      "train_test_split:\n",
      "[7, 3, 2, 9, 6, 1, 4, 5] [1, 0, 0, 1, 1, 0, 0, 1] [8, 0] [1, 0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2026: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified.\n",
      "  FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "splits = 5\n",
    "\n",
    "tx = range(10)\n",
    "ty = [0] * 5 + [1] * 5\n",
    "\n",
    "from sklearn.model_selection import StratifiedShuffleSplit, StratifiedKFold,KFold,ShuffleSplit\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import datasets\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "print(\"KFold shuffle=false\")\n",
    "kFold = KFold(n_splits=splits, shuffle=False, random_state=42)\n",
    "for train_index, test_index in kFold.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "    \n",
    "print(\"KFold shuffle=true\")\n",
    "kFold = KFold(n_splits=splits, shuffle=True, random_state=43)\n",
    "for train_index, test_index in kFold.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "\n",
    "print(\"StratifiedKFold shuffle =false\")\n",
    "stratifiedKFold = StratifiedKFold(n_splits=splits, shuffle=False, random_state=42)\n",
    "for train_index, test_index in stratifiedKFold.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "    \n",
    "print(\"StratifiedKFold shuffle =true\")\n",
    "stratifiedKFold = StratifiedKFold(n_splits=splits, shuffle=True, random_state=42)\n",
    "for train_index, test_index in stratifiedKFold.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "\n",
    "print(\"Shuffle Split\")\n",
    "shuffleSplit = ShuffleSplit(n_splits=splits, random_state=42, test_size=2)\n",
    "for train_index, test_index in shuffleSplit.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "    \n",
    "print(\"Stratified Shuffle Split\")\n",
    "stratifiedShuffleSplit = StratifiedShuffleSplit(n_splits=splits, random_state=42, test_size=2)\n",
    "for train_index, test_index in stratifiedShuffleSplit.split(tx, ty):\n",
    "    print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
    "    \n",
    "    \n",
    "print('train_test_split:')\n",
    "\n",
    "X_train, X_vld, y_train,y_vld = train_test_split(tx,ty,train_size=0.8,shuffle=True)\n",
    "print(X_train,y_train,X_vld,y_vld)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### One-hot encoding using pandas or sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "[参考](https://blog.csdn.net/hshuihui/article/details/53259710)\n",
    "\n",
    "category 怎么处理\n",
    "数值型特征怎么处理.\n",
    "\n",
    "目前比较熟悉的有pandas里的get_dummies做one-hot encoding.\n",
    "\n",
    "sklearn里也有很多特征编码方法.\n",
    "\n",
    "下面的例子是要把数值型或者字符型都用sklearn 来one-hot encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.preprocessing import LabelBinarizer\n",
    "from sklearn.preprocessing import MultiLabelBinarizer\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.preprocessing import * \n",
    "import numpy as np\n",
    "\n",
    "dataset = pd.DataFrame({'pet': ['cat', 'dog', 'dog', 'fish'],                         \n",
    "'age': [4 , 6, 3, 3],                        \n",
    "'salary':[4, 5, 1, 1],\n",
    "'lvl':[4, 5, pd.np.nan, 1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pet</th>\n",
       "      <th>age</th>\n",
       "      <th>salary</th>\n",
       "      <th>lvl</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>cat</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dog</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>dog</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fish</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    pet  age  salary  lvl\n",
       "0   cat    4       4  4.0\n",
       "1   dog    6       5  5.0\n",
       "2   dog    3       1  NaN\n",
       "3  fish    3       1  1.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.preprocessing import LabelBinarizer\n",
    "from sklearn.preprocessing import MultiLabelBinarizer\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.preprocessing import * \n",
    "import numpy as np\n",
    "\n",
    "dataset = pd.DataFrame({'pet': ['cat', 'dog', 'dog', 'fish'],                         \n",
    "'age': [4 , 6, 3, 3],                        \n",
    "'salary':[4, 5, 1, 1],\n",
    "'lvl':[4, 5, pd.np.nan, 1]})\n",
    "dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### pandas get_dummies for one-hot encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age_3</th>\n",
       "      <th>age_4</th>\n",
       "      <th>age_6</th>\n",
       "      <th>salary_1</th>\n",
       "      <th>salary_4</th>\n",
       "      <th>salary_5</th>\n",
       "      <th>pet_cat</th>\n",
       "      <th>pet_dog</th>\n",
       "      <th>pet_fish</th>\n",
       "      <th>lvl_1.0</th>\n",
       "      <th>lvl_4.0</th>\n",
       "      <th>lvl_5.0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age_3  age_4  age_6  salary_1  salary_4  salary_5  pet_cat  pet_dog  \\\n",
       "0      0      1      0         0         1         0        1        0   \n",
       "1      0      0      1         0         0         1        0        1   \n",
       "2      1      0      0         1         0         0        0        1   \n",
       "3      1      0      0         1         0         0        0        0   \n",
       "\n",
       "   pet_fish  lvl_1.0  lvl_4.0  lvl_5.0  \n",
       "0         0        0        1        0  \n",
       "1         0        0        0        1  \n",
       "2         0        0        0        0  \n",
       "3         1        1        0        0  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d =  pd.get_dummies(dataset,columns=['age','salary','pet','lvl']);\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "NaN也可以当做一类，如果需要的话"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age_3.0</th>\n",
       "      <th>age_4.0</th>\n",
       "      <th>age_6.0</th>\n",
       "      <th>age_nan</th>\n",
       "      <th>salary_1.0</th>\n",
       "      <th>salary_4.0</th>\n",
       "      <th>salary_5.0</th>\n",
       "      <th>salary_nan</th>\n",
       "      <th>pet_cat</th>\n",
       "      <th>pet_dog</th>\n",
       "      <th>pet_fish</th>\n",
       "      <th>pet_nan</th>\n",
       "      <th>lvl_1.0</th>\n",
       "      <th>lvl_4.0</th>\n",
       "      <th>lvl_5.0</th>\n",
       "      <th>lvl_nan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age_3.0  age_4.0  age_6.0  age_nan  salary_1.0  salary_4.0  salary_5.0  \\\n",
       "0        0        1        0        0           0           1           0   \n",
       "1        0        0        1        0           0           0           1   \n",
       "2        1        0        0        0           1           0           0   \n",
       "3        1        0        0        0           1           0           0   \n",
       "\n",
       "   salary_nan  pet_cat  pet_dog  pet_fish  pet_nan  lvl_1.0  lvl_4.0  lvl_5.0  \\\n",
       "0           0        1        0         0        0        0        1        0   \n",
       "1           0        0        1         0        0        0        0        1   \n",
       "2           0        0        1         0        0        0        0        0   \n",
       "3           0        0        0         1        0        1        0        0   \n",
       "\n",
       "   lvl_nan  \n",
       "0        0  \n",
       "1        0  \n",
       "2        1  \n",
       "3        0  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d =  pd.get_dummies(dataset,columns=['age','salary','pet','lvl'],dummy_na=True);\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### sklearn preprocessing for one-hot encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "*  Nan不能处理\n",
    "* 只能处理成np.array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0., 1., 0.],\n",
       "       [0., 0., 1., 0., 0., 1.],\n",
       "       [1., 0., 0., 1., 0., 0.],\n",
       "       [1., 0., 0., 1., 0., 0.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age= OneHotEncoder(sparse = False).fit_transform( dataset[['age']])\n",
    "# pet= OneHotEncoder(sparse = False).fit_transform( dataset[['pet']])\n",
    "salary= OneHotEncoder(sparse = False).fit_transform( dataset[['salary']])\n",
    "# lvl = OneHotEncoder(sparse = False).fit_transform( dataset[['lvl']])\n",
    "d = np.hstack( (age,salary));d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "LabelEncoder 针对字符型label. ['a','b','c']--->[0,1,2]\n",
    "先LabelEncoder ,再OneHotEncoder才能达到最终的效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 1 2]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/sklearn/preprocessing/label.py:111: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numi_pet = LabelEncoder().fit_transform(dataset[['pet']])\n",
    "print(numi_pet)\n",
    "pet =  OneHotEncoder(sparse = False).fit_transform( numi_pet.reshape(-1,1))\n",
    "pet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### DataFrameMapper in pandas_sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "这个东西来自`sklearn_pandas`的三方库\n",
    "\n",
    "[参考](https://blog.csdn.net/hshuihui/article/details/53260922)\n",
    "pandas处理dataframe, sklearn很多是以narray为输入.\n",
    "\n",
    "DataFrameMapper来自sklearn_pandas，可以将sklearn 的 transformer灵活地运用在  DataFrame 当中\n",
    "\n",
    "DataFrameMapper内部机制是先将指定的 DataFrame 的列转换成 ndarray 类型，再输入到 sklearn 的相应 transformer中\n",
    "\n",
    "`DataFrameMapper就是提前定义好mapper,针对输入X的某些列，根据mapper做相应的数据变换`\n",
    "\n",
    "对列的变换比较灵活，可筛选出一个或多个列，并用一个或多个 sklearn 的 transformer 作用，组合起来极其强大；同时通过继承机制，它本身也可以看做是 sklearn 的 transformer 类，输入 sklearn 的相关类(如Pipeline, FeatureUnion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import random \n",
    "import sklearn \n",
    "import pandas as pd \n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "from sklearn_pandas import DataFrameMapper, cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pet</th>\n",
       "      <th>age</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>cat</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dog</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>dog</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fish</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    pet  age  salary\n",
       "0   cat    4       4\n",
       "1   dog    6       5\n",
       "2   dog    3       1\n",
       "3  fish    3       1"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.DataFrame({'pet': ['cat', 'dog', 'dog', 'fish'],                         \n",
    "'age': [4 , 6, 3, 3],                        \n",
    "'salary':[4, 5, 1, 1]});\n",
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/sklearn/utils/validation.py:475: DataConversionWarning: Data with input dtype int64 was converted to float64 by MinMaxScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-1.35973996e-16],\n",
       "       [ 1.63299316e+00],\n",
       "       [-8.16496581e-01],\n",
       "       [-8.16496581e-01]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapper = DataFrameMapper([        (['age'],[ MinMaxScaler(), StandardScaler()]),    ]) \n",
    "mapper.fit_transform(dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "组合模式，这个就很方便了"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/sklearn/utils/validation.py:475: DataConversionWarning: Data with input dtype int64 was converted to float64 by MinMaxScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4, 7)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapper = DataFrameMapper([ ('pet', LabelBinarizer()),  (['age'], [MinMaxScaler()]) , (['salary'], OneHotEncoder())    ])\n",
    "d = mapper.fit_transform(dataset)\n",
    "d.shape # 7  = 3+ 1+ 3 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "更厉害的,尺度归一化，PCA降维,生成二次项特征，都可以很简易的完成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/fastai-cpu/lib/python3.6/site-packages/sklearn/utils/validation.py:475: DataConversionWarning: Data with input dtype int64 was converted to float64 by MinMaxScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.23146041,  0.20995792,  1.        ,  0.75      ,  0.33333333,\n",
       "         0.5625    ,  0.25      ,  0.11111111],\n",
       "       [ 0.86453897, -0.11585794,  1.        ,  1.        ,  1.        ,\n",
       "         1.        ,  1.        ,  1.        ],\n",
       "       [-0.54799969, -0.04704999,  1.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ],\n",
       "       [-0.54799969, -0.04704999,  1.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "mapper = DataFrameMapper([        \n",
    "    (['salary','age'], [MinMaxScaler(), PCA(2)]),     \n",
    "      (['salary','age'],[MinMaxScaler(), PolynomialFeatures(2)]) \n",
    "           ]) \n",
    "mapper.fit_transform(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  }
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