python - sklearn standardscaler 结果与手动结果不同

Question

我使用 sklearn standardscaler(均值去除和方差缩放)来缩放数据框，并将其与我“手动”减去均值并除以标准差的数据框进行比较。比较显示一致的小差异。谁能解释为什么？(我使用的数据集是这样的:http://archive.ics.uci.edu/ml/datasets/Wine

import pandas as pd
from sklearn.preprocessing import StandardScaler

df = pd.read_csv("~/DataSets/WineDataSetItaly/wine.data.txt", names=["Class", "Alcohol", "Malic acid", "Ash", "Alcalinity of ash", "Magnesium", "Total phenols", "Flavanoids", "Nonflavanoid phenols", "Proanthocyanins", "Color intensity", "Hue", "OD280/OD315 of diluted wines", "Proline"])

cols = list(df.columns)[1:]    # I didn't want to scale the "Class" column
std_scal = StandardScaler()
standardized = std_scal.fit_transform(df[cols])
df_standardized_fit = pd.DataFrame(standardized, index=df.index, columns=df.columns[1:])

df_standardized_manual = (df - df.mean()) / df.std()
df_standardized_manual.drop("Class", axis=1, inplace=True)

df_differences = df_standardized_fit - df_standardized_manual
df_differences.iloc[:,:5]


    Alcohol    Malic acid   Ash         Alcalinity  Magnesium
0   0.004272    -0.001582   0.000653    -0.003290   0.005384
1   0.000693    -0.001405   -0.002329   -0.007007   0.000051
2   0.000554    0.000060    0.003120    -0.000756   0.000249
3   0.004758    -0.000976   0.001373    -0.002276   0.002619
4   0.000832    0.000640    0.005177    0.001271    0.003606
5   0.004168    -0.001455   0.000858    -0.003628   0.002421

Answer 1

scikit-learn 使用 np.std默认情况下是总体标准差(偏差平方和除以观察数)，pandas 使用样本标准差(分母是观察数 - 1)(参见 Wikipedia's standard deviation article )。这是一个校正因子，用于对总体标准差进行无偏估计并由自由度 (ddof) 确定。所以默认情况下，numpy 和 scikit-learn 的计算使用 ddof=0 而 pandas 使用 ddof=1 ( docs )。

DataFrame.std(axis=None, skipna=None, level=None, ddof=1, numeric_only=None, **kwargs)

Return sample standard deviation over requested axis.

Normalized by N-1 by default. This can be changed using the ddof argument

如果您将 pandas 版本更改为:

df_standardized_manual = (df - df.mean()) / df.std(ddof=0)

差异几乎为零:

        Alcohol    Malic acid           Ash  Alcalinity of ash     Magnesium
0 -8.215650e-15 -5.551115e-16  3.191891e-15       0.000000e+00  2.220446e-16
1 -8.715251e-15 -4.996004e-16  3.441691e-15       0.000000e+00  0.000000e+00
2 -8.715251e-15 -3.955170e-16  2.886580e-15      -5.551115e-17  1.387779e-17
3 -8.437695e-15 -4.440892e-16  3.164136e-15      -1.110223e-16  1.110223e-16
4 -8.659740e-15 -3.330669e-16  2.886580e-15       5.551115e-17  2.220446e-16