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preprocessing.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## IRIS dataset \n",
"\n",
"https://archive.ics.uci.edu/ml/datasets/iris\n",
"\n",
"ヤマメの花のデータセット\n",
"\n",
"\n",
"> This is perhaps the best known database to be found in the pattern recognition literature. Fisher's paper is a classic in the field and is referenced frequently to this day. (See Duda & Hart, for example.) The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant. One class is linearly separable from the other 2; the latter are NOT linearly separable from each other.\n",
"> \n",
"> Predicted attribute: class of iris plant.\n",
"> \n",
"> This is an exceedingly simple domain.\n",
"> \n",
"> This data differs from the data presented in Fishers article (identified by Steve Chadwick, spchadwick '@' espeedaz.net ). The 35th sample should be: 4.9,3.1,1.5,0.2,\"Iris-setosa\" where the error is in the fourth feature. The 38th sample: 4.9,3.6,1.4,0.1,\"Iris-setosa\" where the errors are in the second and third features.\n",
"\n",
"翻訳： \n",
"これはおそらく、パターン認識の文献で最もよく知られたデータベースである。Fisherの論文はこの分野の古典であり、今日でも頻繁に参照されている（例えばDuda & Hartを参照）。(データセットには50インスタンスずつの3つのクラスがあり、各クラスはアヤメ科の植物の種類を表している。1つのクラスは、他の2つのクラスから線形分離可能で、後者は互いに線形分離不可能である。\n",
"\n",
"予測される属性：アヤメ科のクラス。\n",
"\n",
"これは非常に単純な領域である。\n",
"\n",
"このデータはFishersの記事で紹介されたデータ（Steve Chadwick, spchadwick '@' espeedaz.net ）と異なる。35番目のサンプルは、次のようになっているはずです。4.9,3.1,1.5,0.2, \"Iris-setosa\" のはずですが、4番目の特徴に誤りがあります。38番目のサンプル。4.9,3.6,1.4,0.1, \"Iris-setosa\" ここで、エラーは2番目と3番目の特徴にあります。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### データフレーム化の手順\n",
"\n",
"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/ からiris.dataをダウンロードしてください。このファイルが今回のターゲットです。このファイルは綺麗なCSV形式になっており、欠損値がありません。また、CSVファイルには最初の数行にheaderとして情報が書かれている場合がありますが、このファイルにはそのような記述もありません。更には、column（列）の名前も無いので、そのままダウンロードしてDataFrameで読み込んだ後に、必要ならばcolumn name（特徴量の名前）を追加することを考えます。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np \n",
"import pandas as pd \n",
"import plotly.express as px\n",
"import requests\n",
"from io import StringIO"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [
{
"data": {
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"<div>\n",
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"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
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"\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>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
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" <tr>\n",
" <th>145</th>\n",
" <td>6.7</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.3</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>146</th>\n",
" <td>6.3</td>\n",
" <td>2.5</td>\n",
" <td>5.0</td>\n",
" <td>1.9</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>147</th>\n",
" <td>6.5</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.0</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>148</th>\n",
" <td>6.2</td>\n",
" <td>3.4</td>\n",
" <td>5.4</td>\n",
" <td>2.3</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>149</th>\n",
" <td>5.9</td>\n",
" <td>3.0</td>\n",
" <td>5.1</td>\n",
" <td>1.8</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>150 rows × 5 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4\n",
"0 5.1 3.5 1.4 0.2 Iris-setosa\n",
"1 4.9 3.0 1.4 0.2 Iris-setosa\n",
"2 4.7 3.2 1.3 0.2 Iris-setosa\n",
"3 4.6 3.1 1.5 0.2 Iris-setosa\n",
"4 5.0 3.6 1.4 0.2 Iris-setosa\n",
".. ... ... ... ... ...\n",
"145 6.7 3.0 5.2 2.3 Iris-virginica\n",
"146 6.3 2.5 5.0 1.9 Iris-virginica\n",
"147 6.5 3.0 5.2 2.0 Iris-virginica\n",
"148 6.2 3.4 5.4 2.3 Iris-virginica\n",
"149 5.9 3.0 5.1 1.8 Iris-virginica\n",
"\n",
"[150 rows x 5 columns]"
]
},
"execution_count": 102,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"iris_url = \"http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n",
"\n",
"# データをurlから取得する\n",
"raw_data = requests.get(iris_url, stream=True)\n",
"# データをデータフレーム形式に保管\n",
"# 注意： headerをNoneとしないと、データの最初の1行目が、headerとなる\n",
"df = pd.read_csv(StringIO(raw_data.text),header =None)\n",
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"https://archive.ics.uci.edu/ml/datasets/iris に以下の記述があるので、特徴量はそれぞれ \n",
"[\"sepal length in cm\",\"sepal width in cm\",\"petal length in cm\",\"petal width in cm\"] \n",
"であることがわかります。\n",
"\n",
"> Attribute Information:\n",
"> \n",
"> 1. sepal length in cm\n",
"> 2. sepal width in cm\n",
"> 3. petal length in cm\n",
"> 4. petal width in cm\n",
"> 5. class: \n",
"> -- Iris Setosa \n",
"> -- Iris Versicolour \n",
"> -- Iris Virginica "
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\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>sepal length</th>\n",
" <th>sepal width</th>\n",
" <th>petal length</th>\n",
" <th>petal width</th>\n",
" <th>class</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
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" <th>145</th>\n",
" <td>6.7</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.3</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>146</th>\n",
" <td>6.3</td>\n",
" <td>2.5</td>\n",
" <td>5.0</td>\n",
" <td>1.9</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>147</th>\n",
" <td>6.5</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.0</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>148</th>\n",
" <td>6.2</td>\n",
" <td>3.4</td>\n",
" <td>5.4</td>\n",
" <td>2.3</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>149</th>\n",
" <td>5.9</td>\n",
" <td>3.0</td>\n",
" <td>5.1</td>\n",
" <td>1.8</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>150 rows × 5 columns</p>\n",
"</div>"
],
"text/plain": [
" sepal length sepal width petal length petal width class\n",
"0 5.1 3.5 1.4 0.2 Iris-setosa\n",
"1 4.9 3.0 1.4 0.2 Iris-setosa\n",
"2 4.7 3.2 1.3 0.2 Iris-setosa\n",
"3 4.6 3.1 1.5 0.2 Iris-setosa\n",
"4 5.0 3.6 1.4 0.2 Iris-setosa\n",
".. ... ... ... ... ...\n",
"145 6.7 3.0 5.2 2.3 Iris-virginica\n",
"146 6.3 2.5 5.0 1.9 Iris-virginica\n",
"147 6.5 3.0 5.2 2.0 Iris-virginica\n",
"148 6.2 3.4 5.4 2.3 Iris-virginica\n",
"149 5.9 3.0 5.1 1.8 Iris-virginica\n",
"\n",
"[150 rows x 5 columns]"
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.columns = [\"sepal length\",\"sepal width\",\"petal length\",\"petal width\",\"class\"]\n",
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"これでiris dataをDataFrameとして読み込むことができました。さて、DataFrameの情報を確認します。"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 150 entries, 0 to 149\n",
"Data columns (total 5 columns):\n",
" # Column Non-Null Count Dtype \n",
"--- ------ -------------- ----- \n",
" 0 sepal length 150 non-null float64\n",
" 1 sepal width 150 non-null float64\n",
" 2 petal length 150 non-null float64\n",
" 3 petal width 150 non-null float64\n",
" 4 class 150 non-null object \n",
"dtypes: float64(4), object(1)\n",
"memory usage: 6.0+ KB\n"
]
}
],
"source": [
"df.info()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"データは全て数値型（float64）であり、欠損値（null）が無いことがわかります。classについては特徴量というよりはラベルなので考えないことにします。また、データは全部で150個あるようです。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[コラム] \n",
"\n",
"浮動小数点数の型は複数あり、それぞれが対応する精度が異なります。numpyのそれぞれの浮動小数点型の表現できる最大値・最小値などの情報はnp.finfo関数で確認します。"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Machine parameters for float64\n",
"---------------------------------------------------------------\n",
"precision = 15 resolution = 1.0000000000000001e-15\n",
"machep = -52 eps = 2.2204460492503131e-16\n",
"negep = -53 epsneg = 1.1102230246251565e-16\n",
"minexp = -1022 tiny = 2.2250738585072014e-308\n",
"maxexp = 1024 max = 1.7976931348623157e+308\n",
"nexp = 11 min = -max\n",
"smallest_normal = 2.2250738585072014e-308 smallest_subnormal = 4.9406564584124654e-324\n",
"---------------------------------------------------------------\n",
"\n",
"Machine parameters for float32\n",
"---------------------------------------------------------------\n",
"precision = 6 resolution = 1.0000000e-06\n",
"machep = -23 eps = 1.1920929e-07\n",
"negep = -24 epsneg = 5.9604645e-08\n",
"minexp = -126 tiny = 1.1754944e-38\n",
"maxexp = 128 max = 3.4028235e+38\n",
"nexp = 8 min = -max\n",
"smallest_normal = 1.1754944e-38 smallest_subnormal = 1.4012985e-45\n",
"---------------------------------------------------------------\n",
"\n",
"Machine parameters for float16\n",
"---------------------------------------------------------------\n",
"precision = 3 resolution = 1.00040e-03\n",
"machep = -10 eps = 9.76562e-04\n",
"negep = -11 epsneg = 4.88281e-04\n",
"minexp = -14 tiny = 6.10352e-05\n",
"maxexp = 16 max = 6.55040e+04\n",
"nexp = 5 min = -max\n",
"smallest_normal = 6.10352e-05 smallest_subnormal = 5.96046e-08\n",
"---------------------------------------------------------------\n",
"\n"
]
}
],
"source": [
"print(np.finfo(np.float64))\n",
"print(np.finfo(np.float32))\n",
"print(np.finfo(np.float16))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"それぞれのfloat Nbitが何桁までの浮動小数点数を安全に表現できるのかについては注意が必要です。また、NumPyではCPUバックエンドのみが利用可能ですので、現代のモダンな計算機であればfloat64がデフォルトになるはずです。通常（データサイエンスや機械学習など）であれば、NumPyではfloat64を利用することになるでしょう。ただし、後述する（可能性のある）GPUをバックエンドにした計算をする場合はfloat32がデフォルトになります。GPUを利用する場合はNumPyを参考にして作られたTensorFlowやPyTorch、JAX、CuPyのようなライブラリを利用することになりますが、これらではより型を意識したプログラミングが必要になります。"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"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>sepal length</th>\n",
" <th>sepal width</th>\n",
" <th>petal length</th>\n",
" <th>petal width</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>150.000000</td>\n",
" <td>150.000000</td>\n",
" <td>150.000000</td>\n",
" <td>150.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>5.843333</td>\n",
" <td>3.054000</td>\n",
" <td>3.758667</td>\n",
" <td>1.198667</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>0.828066</td>\n",
" <td>0.433594</td>\n",
" <td>1.764420</td>\n",
" <td>0.763161</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>4.300000</td>\n",
" <td>2.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.100000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>5.100000</td>\n",
" <td>2.800000</td>\n",
" <td>1.600000</td>\n",
" <td>0.300000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>5.800000</td>\n",
" <td>3.000000</td>\n",
" <td>4.350000</td>\n",
" <td>1.300000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>6.400000</td>\n",
" <td>3.300000</td>\n",
" <td>5.100000</td>\n",
" <td>1.800000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>7.900000</td>\n",
" <td>4.400000</td>\n",
" <td>6.900000</td>\n",
" <td>2.500000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" sepal length sepal width petal length petal width\n",
"count 150.000000 150.000000 150.000000 150.000000\n",
"mean 5.843333 3.054000 3.758667 1.198667\n",
"std 0.828066 0.433594 1.764420 0.763161\n",
"min 4.300000 2.000000 1.000000 0.100000\n",
"25% 5.100000 2.800000 1.600000 0.300000\n",
"50% 5.800000 3.000000 4.350000 1.300000\n",
"75% 6.400000 3.300000 5.100000 1.800000\n",
"max 7.900000 4.400000 6.900000 2.500000"
]
},
"execution_count": 106,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 棒グラフ"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [],
"source": [
"from plotly.subplots import make_subplots"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
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},
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}
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"gridcolor": "white",
"linecolor": "white",
"ticks": "",
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"ticks": "",
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"xaxis": {
"anchor": "y",
"domain": [
0,
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"title": {
"text": "x"
}
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0,
1
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],
"source": [
"def barplot_for_iris(df, yrange=None):\n",
" if yrange is None:\n",
" max_val = df.iloc[:,:-1].max().max()\n",
" yrange = [0, max_val]\n",
" \n",
" for ix, feature_name in enumerate(df.columns[:-1]):\n",
" bar = px.bar(\n",
" df, \n",
" x=np.arange(len(df)), y=feature_name,\n",
" color=\"class\",\n",
" title=f\"bar chart of {feature_name}\",\n",
" height=300,\n",
" width=900,\n",
" )\n",
" bar.update_yaxes(range=yrange)\n",
" bar.show()\n",
"\n",
"barplot_for_iris(df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ヒストグラムと箱ひげ図"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
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},
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}
},
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],
"source": [
"pairplot = px.scatter_matrix(df,\n",
" dimensions=df.columns[:3],\n",
" color=\"class\",\n",
" height=800, \n",
" width=900,\n",
" title=\"Scatter matrix of iris data set\",\n",
" )\n",
"pairplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ここまでの可視化で分かったこと\n",
"\n",
"四つの特徴は、クラスごとに差分がありそうです。また特徴毎にスケールが違うようです。\n",
"クラス分類などを目的に機械学習モデルにこのままデータを入れた場合、特徴ごとに不要なスケールの違いを除去した方が良さそうですね。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## データの前処理"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Min Max Normalization (Min Max Scaling)\n",
"\n",
"ある特徴量$\\vec{x}$が与えられた時、値が0~1の範囲で収まるように変形した特徴量を作る。\n",
"\\begin{equation}\n",
"\\vec{x}_{n e w}=\\frac{\\vec{x}-\\min (\\vec{x})}{\\max (\\vec{x})-\\min (\\vec{x})}\n",
"\\end{equation}\n",
"\n",
"式の通りにpandasのメソッドを使って実装してみよう。"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
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" <tr>\n",
" <th>2</th>\n",
" <td>0.111111</td>\n",
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" <td>0.041667</td>\n",
" <td>Iris-setosa</td>\n",
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" <td>0.041667</td>\n",
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" <th>4</th>\n",
" <td>0.194444</td>\n",
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" <td>0.067797</td>\n",
" <td>0.041667</td>\n",
" <td>Iris-setosa</td>\n",
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" <th>...</th>\n",
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" <th>145</th>\n",
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" <td>0.916667</td>\n",
" <td>Iris-virginica</td>\n",
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" <tr>\n",
" <th>146</th>\n",
" <td>0.555556</td>\n",
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" <td>0.750000</td>\n",
" <td>Iris-virginica</td>\n",
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" <th>147</th>\n",
" <td>0.611111</td>\n",
" <td>0.416667</td>\n",
" <td>0.711864</td>\n",
" <td>0.791667</td>\n",
" <td>Iris-virginica</td>\n",
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" <tr>\n",
" <th>148</th>\n",
" <td>0.527778</td>\n",
" <td>0.583333</td>\n",
" <td>0.745763</td>\n",
" <td>0.916667</td>\n",
" <td>Iris-virginica</td>\n",
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" <th>149</th>\n",
" <td>0.444444</td>\n",
" <td>0.416667</td>\n",
" <td>0.694915</td>\n",
" <td>0.708333</td>\n",
" <td>Iris-virginica</td>\n",
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" </tbody>\n",
"</table>\n",
"<p>150 rows × 5 columns</p>\n",
"</div>"
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" sepal length sepal width petal length petal width class\n",
"0 0.222222 0.625000 0.067797 0.041667 Iris-setosa\n",
"1 0.166667 0.416667 0.067797 0.041667 Iris-setosa\n",
"2 0.111111 0.500000 0.050847 0.041667 Iris-setosa\n",
"3 0.083333 0.458333 0.084746 0.041667 Iris-setosa\n",
"4 0.194444 0.666667 0.067797 0.041667 Iris-setosa\n",
".. ... ... ... ... ...\n",
"145 0.666667 0.416667 0.711864 0.916667 Iris-virginica\n",
"146 0.555556 0.208333 0.677966 0.750000 Iris-virginica\n",
"147 0.611111 0.416667 0.711864 0.791667 Iris-virginica\n",
"148 0.527778 0.583333 0.745763 0.916667 Iris-virginica\n",
"149 0.444444 0.416667 0.694915 0.708333 Iris-virginica\n",
"\n",
"[150 rows x 5 columns]"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df2 = df.iloc[:,:-1]\n",
"\n",
"normalized_df = (df2 - df2.min()) / (df2.max() - df2.min())\n",
"normalized_df[\"class\"] = df[\"class\"]\n",
"normalized_df"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
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"source": [
"histgram = px.histogram(\n",
" normalized_df, \n",
" color=\"class\",\n",
" height=800, \n",
" width=900,\n",
" title=\"Histogram of iris data set\",\n",
" barmode='overlay',\n",
" marginal='box',\n",
" )\n",
"histgram.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"データ間の大小関係は変わらずに、それぞれの特徴の値域だけを変更できた。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Z-score Normalization (Standardization)\n",
"\n",
"\n",
"元のデータの平均を0、標準偏差が1のものへと変換する。\n",
"\\begin{equation}\n",
"\\vec{x}_{n e w}=\\frac{\\vec{x}-\\mu}{\\sigma}\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
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" <th>0</th>\n",
" <td>-0.897674</td>\n",
" <td>1.028611</td>\n",
" <td>-1.336794</td>\n",
" <td>-1.308593</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-1.139200</td>\n",
" <td>-0.124540</td>\n",
" <td>-1.336794</td>\n",
" <td>-1.308593</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-1.380727</td>\n",
" <td>0.336720</td>\n",
" <td>-1.393470</td>\n",
" <td>-1.308593</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-1.501490</td>\n",
" <td>0.106090</td>\n",
" <td>-1.280118</td>\n",
" <td>-1.308593</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-1.018437</td>\n",
" <td>1.259242</td>\n",
" <td>-1.336794</td>\n",
" <td>-1.308593</td>\n",
" <td>Iris-setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>145</th>\n",
" <td>1.034539</td>\n",
" <td>-0.124540</td>\n",
" <td>0.816888</td>\n",
" <td>1.443121</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>146</th>\n",
" <td>0.551486</td>\n",
" <td>-1.277692</td>\n",
" <td>0.703536</td>\n",
" <td>0.918985</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>147</th>\n",
" <td>0.793012</td>\n",
" <td>-0.124540</td>\n",
" <td>0.816888</td>\n",
" <td>1.050019</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>148</th>\n",
" <td>0.430722</td>\n",
" <td>0.797981</td>\n",
" <td>0.930239</td>\n",
" <td>1.443121</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>149</th>\n",
" <td>0.068433</td>\n",
" <td>-0.124540</td>\n",
" <td>0.760212</td>\n",
" <td>0.787951</td>\n",
" <td>Iris-virginica</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>150 rows × 5 columns</p>\n",
"</div>"
],
"text/plain": [
" sepal length sepal width petal length petal width class\n",
"0 -0.897674 1.028611 -1.336794 -1.308593 Iris-setosa\n",
"1 -1.139200 -0.124540 -1.336794 -1.308593 Iris-setosa\n",
"2 -1.380727 0.336720 -1.393470 -1.308593 Iris-setosa\n",
"3 -1.501490 0.106090 -1.280118 -1.308593 Iris-setosa\n",
"4 -1.018437 1.259242 -1.336794 -1.308593 Iris-setosa\n",
".. ... ... ... ... ...\n",
"145 1.034539 -0.124540 0.816888 1.443121 Iris-virginica\n",
"146 0.551486 -1.277692 0.703536 0.918985 Iris-virginica\n",
"147 0.793012 -0.124540 0.816888 1.050019 Iris-virginica\n",
"148 0.430722 0.797981 0.930239 1.443121 Iris-virginica\n",
"149 0.068433 -0.124540 0.760212 0.787951 Iris-virginica\n",
"\n",
"[150 rows x 5 columns]"
]
},
"execution_count": 114,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_df = ( df2 - df2.mean() ) / df2.std()\n",
"new_df[\"class\"] = df[\"class\"]\n",
"new_df"
]
},
{
"cell_type": "code",
"execution_count": 115,
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},
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},
"width": 900,
"xaxis": {
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"domain": [
0,
1
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"title": {
"text": "value"
}
},
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0,
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0,
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"text": "count"
}
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}
},
"metadata": {},
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],
"source": [
"histgram = px.histogram(\n",
" new_df, \n",
" color=\"class\",\n",
" height=800, \n",
" width=900,\n",
" title=\"Histogram of iris data set\",\n",
" barmode='overlay',\n",
" marginal='box',\n",
" )\n",
"histgram.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"各クラスのヒストグラムが単峰性になっていることがわかる。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"前処理についてはできるだけPandasの上でやってしまうのが簡単ですが、scikit-learnやscipyには前処理に便利な機能がたくさんあります。適宜numpy ndarrayに戻して処理を行い、その後に元のDataFrameに戻すような処理をすることを考えます。"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'numpy.ndarray'>\n"
]
}
],
"source": [
"from sklearn.preprocessing import StandardScaler, MinMaxScaler\n",
"\n",
"scaler = StandardScaler()\n",
"scaler.fit(df.iloc[:,:-1])\n",
"output = scaler.transform(df.iloc[:,:-1])\n",
"print(type(output))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
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