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April 26, 2019 21:57
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Count Data Preprocessing
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Preprocessing on Count data\n", | |
| "- 「機械学習のための特徴量エンジニアリング」第2章\n", | |
| "\n", | |
| "カウントデータにおいてよく使われる前処理をまとめる。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 157, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import pandas as pd\n", | |
| "import numpy as np\n", | |
| "from matplotlib import pyplot as plt\n", | |
| "%matplotlib inline" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**二値化(Binarise)** \n", | |
| "カウントの絶対値ではなく、「0か1以上か」や「ある閾値より大きいか小さいか」といったような違いに興味がある場合。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 36, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 例えばあるユーザの、サイトの閲覧履歴\n", | |
| "cols = ['site_name','visit_count']\n", | |
| "data = [['abc.com',4],['xxx.com',2],['test.org',0],['apple.net',0],['yyy.com',1],\n", | |
| " ['zzz.org',2],['hello.io',13],['world.ie',0],['guitar.net',10],['yokohama.com',5]]\n", | |
| "df = pd.DataFrame(data,columns=cols)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 37, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def binarize(c,threshold):\n", | |
| " return 0 if c < threshold else 1" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 38, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "df['moreThan0'] = df['visit_count'].apply(lambda x: binarize(x,1))\n", | |
| "df['moreThan9'] = df['visit_count'].apply(lambda x: binarize(x,10))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 39, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<div>\n", | |
| "<table border=\"1\" class=\"dataframe\">\n", | |
| " <thead>\n", | |
| " <tr style=\"text-align: right;\">\n", | |
| " <th></th>\n", | |
| " <th>site_name</th>\n", | |
| " <th>visit_count</th>\n", | |
| " <th>moreThan0</th>\n", | |
| " <th>moreThan9</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>abc.com</td>\n", | |
| " <td>4</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>xxx.com</td>\n", | |
| " <td>2</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>test.org</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>apple.net</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>yyy.com</td>\n", | |
| " <td>1</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>5</th>\n", | |
| " <td>zzz.org</td>\n", | |
| " <td>2</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>6</th>\n", | |
| " <td>hello.io</td>\n", | |
| " <td>13</td>\n", | |
| " <td>1</td>\n", | |
| " <td>1</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>7</th>\n", | |
| " <td>world.ie</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>8</th>\n", | |
| " <td>guitar.net</td>\n", | |
| " <td>10</td>\n", | |
| " <td>1</td>\n", | |
| " <td>1</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>9</th>\n", | |
| " <td>yokohama.com</td>\n", | |
| " <td>5</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " site_name visit_count moreThan0 moreThan9\n", | |
| "0 abc.com 4 1 0\n", | |
| "1 xxx.com 2 1 0\n", | |
| "2 test.org 0 0 0\n", | |
| "3 apple.net 0 0 0\n", | |
| "4 yyy.com 1 1 0\n", | |
| "5 zzz.org 2 1 0\n", | |
| "6 hello.io 13 1 1\n", | |
| "7 world.ie 0 0 0\n", | |
| "8 guitar.net 10 1 1\n", | |
| "9 yokohama.com 5 1 0" | |
| ] | |
| }, | |
| "execution_count": 39, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**ビン分割(Binning)** \n", | |
| "カウントの絶対数よりも、「0~9,10~19,...」といったような階級幅ごとの分布に興味がある場合。\n", | |
| " \n", | |
| "##### 固定幅のビン分割" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 76, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 例えばあるSNSにおける30ユーザのフォロワー数データ(0フォロワー ~ 最大99フォロワーとする)\n", | |
| "df = pd.DataFrame(np.random.randint(0,100,30),columns=['follower_count'])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 77, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def bin_width(l,width):\n", | |
| " # l: list of original values\n", | |
| " # width: width of each bin\n", | |
| " return np.floor_divide(l,width)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 78, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "df['bin_10'] = bin_width(df['follower_count'],10)\n", | |
| "df['bin_20'] = bin_width(df['follower_count'],20)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 79, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<div>\n", | |
| "<table border=\"1\" class=\"dataframe\">\n", | |
| " <thead>\n", | |
| " <tr style=\"text-align: right;\">\n", | |
| " <th></th>\n", | |
| " <th>follower_count</th>\n", | |
| " <th>bin_10</th>\n", | |
| " <th>bin_20</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>17</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>26</td>\n", | |
| " <td>2</td>\n", | |
| " <td>1</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>89</td>\n", | |
| " <td>8</td>\n", | |
| " <td>4</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>18</td>\n", | |
| " <td>1</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>45</td>\n", | |
| " <td>4</td>\n", | |
| " <td>2</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " follower_count bin_10 bin_20\n", | |
| "0 17 1 0\n", | |
| "1 26 2 1\n", | |
| "2 89 8 4\n", | |
| "3 18 1 0\n", | |
| "4 45 4 2" | |
| ] | |
| }, | |
| "execution_count": 79, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df.head(5)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### 指定幅のビン分割" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 98, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 例えばあるSNSにおける30ユーザのフォロワー数データ(0フォロワー ~ 最大999フォロワーとする)\n", | |
| "df = pd.DataFrame(np.random.randint(0,1000,30),columns=['follower_count'])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 99, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def classify(x,bin_starts):\n", | |
| " # bin_starts: list of start value of each bin (must be ascending sorted list)\n", | |
| " for i in range(len(bin_starts)):\n", | |
| " if x < bin_starts[i]:\n", | |
| " return i\n", | |
| " return len(bin_starts)\n", | |
| "\n", | |
| "def bin_custom(l,bin_starts):\n", | |
| " return [classify(x,bin_starts) for x in l]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 100, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 指定ビン: 0~9, 10~49, 50~99, 100~499, 500~\n", | |
| "bins = [10,50,100,500]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 101, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "df['bin'] = bin_custom(df['follower_count'],bins)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 103, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<div>\n", | |
| "<table border=\"1\" class=\"dataframe\">\n", | |
| " <thead>\n", | |
| " <tr style=\"text-align: right;\">\n", | |
| " <th></th>\n", | |
| " <th>follower_count</th>\n", | |
| " <th>bin</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>589</td>\n", | |
| " <td>4</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>811</td>\n", | |
| " <td>4</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>419</td>\n", | |
| " <td>3</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>10</td>\n", | |
| " <td>1</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>169</td>\n", | |
| " <td>3</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " follower_count bin\n", | |
| "0 589 4\n", | |
| "1 811 4\n", | |
| "2 419 3\n", | |
| "3 10 1\n", | |
| "4 169 3" | |
| ] | |
| }, | |
| "execution_count": 103, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df.head(5)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### 固定対数幅のビン分割" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 104, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 例えばあるSNSにおける30ユーザのフォロワー数データ(0フォロワー ~ 最大999999フォロワーとする)\n", | |
| "df = pd.DataFrame([2,30,835225,450,982,321,6,3,1,45,67,90,81,956,674,8892,\n", | |
| " 6723,34534,3423462,9853,43,4346,343,6,5654,345,43,44,634,\n", | |
| " 645,4,12,5,34,43,68,235,2345,65,67566,765774,54737],columns=['follower_count'])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 105, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def bin_width_log10(l):\n", | |
| " # l: list of original values\n", | |
| " return np.floor(np.log10(l))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 106, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "df['bin'] = bin_width_log10(df['follower_count'])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 108, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<div>\n", | |
| "<table border=\"1\" class=\"dataframe\">\n", | |
| " <thead>\n", | |
| " <tr style=\"text-align: right;\">\n", | |
| " <th></th>\n", | |
| " <th>follower_count</th>\n", | |
| " <th>bin</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>2</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>30</td>\n", | |
| " <td>1</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>835225</td>\n", | |
| " <td>5</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>450</td>\n", | |
| " <td>2</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>982</td>\n", | |
| " <td>2</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " follower_count bin\n", | |
| "0 2 0\n", | |
| "1 30 1\n", | |
| "2 835225 5\n", | |
| "3 450 2\n", | |
| "4 982 2" | |
| ] | |
| }, | |
| "execution_count": 108, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df.head(5)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "##### 分位数によるビン分割" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 110, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 例えばあるSNSにおける30ユーザのフォロワー数データ(0フォロワー ~ 最大999999フォロワーとする)\n", | |
| "df = pd.DataFrame([2,30,835225,450,982,321,6,3,1,45,67,90,81,956,674,8892,\n", | |
| " 6723,34534,3423462,9853,43,4346,343,6,5654,345,43,44,634,\n", | |
| " 645,4,12,5,34,43,68,235,2345,65,67566,765774,54737],columns=['follower_count'])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 112, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.25 43.00\n", | |
| "0.50 278.00\n", | |
| "0.75 3845.75\n", | |
| "Name: follower_count, dtype: float64" | |
| ] | |
| }, | |
| "execution_count": 112, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "# 四分位を計算\n", | |
| "df.follower_count.quantile([0.25,0.5,0.75])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 116, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "df['bin'] = pd.qcut(df.follower_count,4,labels=False)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 118, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<div>\n", | |
| "<table border=\"1\" class=\"dataframe\">\n", | |
| " <thead>\n", | |
| " <tr style=\"text-align: right;\">\n", | |
| " <th></th>\n", | |
| " <th>follower_count</th>\n", | |
| " <th>bin</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>2</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>30</td>\n", | |
| " <td>0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>835225</td>\n", | |
| " <td>3</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>450</td>\n", | |
| " <td>2</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>982</td>\n", | |
| " <td>2</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " follower_count bin\n", | |
| "0 2 0\n", | |
| "1 30 0\n", | |
| "2 835225 3\n", | |
| "3 450 2\n", | |
| "4 982 2" | |
| ] | |
| }, | |
| "execution_count": 118, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df.head(5)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**ヒストグラムの対数変換** \n", | |
| "カウントデータでヒストグラムを作る時、非常に裾野の長い分布になるケースはよくある。例えばある動画サイトにおける、動画ごとの１時間あたり再生回数を考えてみる。 \n", | |
| "ある特定の人気動画が数千回再生される一方で、ほとんどの動画はせいぜい数回程度、多くても100回再生未満であるようなケース。こんな時、ヒストグラムは有効にデータを視覚化しない。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 201, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# 動画ごとの一時間あたり再生数\n", | |
| "x = np.arange(0,5000)\n", | |
| "y = np.floor(100000/(x+1)*np.random.rand(1))\n", | |
| "data = []\n", | |
| "for i in range(len(x)):\n", | |
| " data = data + [x[i]]*int(y[i])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 208, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x110eb1550>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# 通常のヒストグラム\n", | |
| "fig,ax = plt.subplots(1,1,figsize=(10,7))\n", | |
| "chart = ax.hist(data,100)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 215, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "data_x = [1 if e==0 else e for e in data]\n", | |
| "data_log = np.log10(data_x)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 218, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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S25Okqq5M8r4kVyS5PsnHq6qm3X0iya3dvSPJjqq6bqrfmuSF7n5bkruSfGy9DhAAYLOZ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\nAABJRU5ErkJggg==\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x1110e7ba8>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig,ax = plt.subplots(1,1,figsize=(10,7))\n", | |
| "chart = ax.hist(data_log,100)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.5.2" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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