（一）sklearn数据预处理

from sklearn import preprocessing
import numpy as np
X_train = np.array([[ 1., -1.,  2.],
                    [ 2.,  0.,  0.],
                    [ 0.,  1., -1.]])

1、使得均值0，方差1

X_scaled = preprocessing.scale(X_train)

X_scaled                                          

array([[ 0.        , -1.22474487,  1.33630621],
       [ 1.22474487,  0.        , -0.26726124],
       [-1.22474487,  1.22474487, -1.06904497]])

X_scaled.mean(axis=0),X_scaled.std(axis=0)

(array([ 0.,  0.,  0.]), array([ 1.,  1.,  1.]))

“axis=0”代表对arr[i][j]..等维度进行计算，假如arr[i][j]是$3*3$的数组，
计算后得到$1*3$的结果，即对每一列数据求平均值。

2、使得放缩在某个范围[0,1]

X_train = np.array([[ 1., -1.,  2.],
                    [ 2.,  0.,  0.],
                    [ 0.,  1., -1.]])

min_max_scaler = preprocessing.MinMaxScaler()

X_train_minmax = min_max_scaler.fit_transform(X_train)

X_train_minmax

array([[ 0.5       ,  0.        ,  1.        ],
       [ 1.        ,  0.5       ,  0.33333333],
       [ 0.        ,  1.        ,  0.        ]])

可以将相同的变换运用到test数据集

X_test = np.array([[ -3., -1.,  4.]])
X_test_minmax = min_max_scaler.transform(X_test)
X_test_minmax

array([[-1.5       ,  0.        ,  1.66666667]])

3、使得放缩在某个范围[-1,1]

X_train = np.array([[ 1., -1.,  2.],
                    [ 2.,  0.,  0.],
                    [ 0.,  1., -1.]])

max_abs_scaler = preprocessing.MaxAbsScaler()
X_train_maxabs = max_abs_scaler.fit_transform(X_train)
X_train_maxabs                # doctest +NORMALIZE_WHITESPACE^

array([[ 0.5, -1. ,  1. ],
       [ 1. ,  0. ,  0. ],
       [ 0. ,  1. , -0.5]])

类似scale， 对应有minmax_scale 和 maxabs_scale

4、缩放稀疏数据

MaxAbsScaler和maxabs_scale专门用于扩展稀疏数据

5、二进制归一化

X = [[ 1., -1.,  2.],
     [ 2.,  0.,  0.],
     [ 0.,  1., -1.]]

binarizer = preprocessing.Binarizer().fit(X)  # fit does nothing
binarizer

Binarizer(copy=True, threshold=0.0)

binarizer.transform(X)

array([[ 1.,  0.,  1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]])

#设定0,1划分值
binarizer = preprocessing.Binarizer(threshold=1.1)
binarizer.transform(X)

array([[ 0.,  0.,  1.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  0.]])

6.编码分类功能

特征不是连续值而是分类
属性可取的离散值：[“male”, “female”][“from Europe”, “from US”, “from Asia”][“uses Firefox”, “uses Chrome”, “uses Safari”, “uses Internet Explorer”]
[“male”, “from US”, “uses Internet Explorer”]可以表示：[0, 1, 3]
[“female”, “from Asia”, “uses Chrome”]可以表示：[1, 2, 1]

#给定数据，可以自动推断属性的类别数
enc = preprocessing.OneHotEncoder()
enc.fit([[0, 0, 3], [1, 1, 0], [0, 2, 1], [1, 0, 2]]) 

OneHotEncoder(categorical_features='all', dtype=<class 'numpy.float64'>,
       handle_unknown='error', n_values='auto', sparse=True)

#对一个数据进行重新编码
enc.transform([[0, 1, 3]]).toarray()

array([[ 1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  1.]])

#编码长度是9，即2+3+4，对应上面每个类别属性长度

#显示给出每个类别属性个数
enc = preprocessing.OneHotEncoder(n_values=[2, 3, 4])
# Note that there are missing categorical values for the 2nd and 3rd
# features
enc.fit([[1, 2, 3], [0, 2, 0]])  

OneHotEncoder(categorical_features='all', dtype=<class 'numpy.float64'>,
       handle_unknown='error', n_values=[2, 3, 4], sparse=True)

enc.transform([[1, 0, 0]]).toarray()

array([[ 0.,  1.,  1.,  0.,  0.,  1.,  0.,  0.,  0.]])

7.遗漏值的估算

from sklearn.preprocessing import Imputer
imp = Imputer(missing_values='NaN', strategy='mean', axis=0)

data=[[1, 2], [np.nan, 3], [7, 6]]

data

[[1, 2], [nan, 3], [7, 6]]

imp.fit(data)

Imputer(axis=0, copy=True, missing_values='NaN', strategy='mean', verbose=0)

X = [[np.nan, 2], [6, np.nan], [7, 6]]

#用平均值去填充nan
print(imp.transform(X))     

[[ 4.          2.        ]
 [ 6.          3.66666667]
 [ 7.          6.        ]]

8、生成多项式特征

import numpy as np
from sklearn.preprocessing import PolynomialFeatures
X = np.arange(6).reshape(3, 2)
X                                                 

array([[0, 1],
       [2, 3],
       [4, 5]])

特征从 $(X_1, X_2) 转化为 (1, X_1, X_2, X_1^2, X_1X_2, X_2^2).$

poly = PolynomialFeatures(2)
poly.fit_transform(X)  

array([[  1.,   0.,   1.,   0.,   0.,   1.],
       [  1.,   2.,   3.,   4.,   6.,   9.],
       [  1.,   4.,   5.,  16.,  20.,  25.]])

9、自定义转换器

#np.log()、np.log10()、np.log2()、np.log1p() 
#分别为自然对数（e）、底数为10、底数为2、log(1+x)

import numpy as np
from sklearn.preprocessing import FunctionTransformer
transformer = FunctionTransformer(np.log1p)
X = np.array([[0, 1], [2, 3]])
transformer.transform(X)

array([[ 0.        ,  0.69314718],
       [ 1.09861229,  1.38629436]])

def f(x):
    return x**2

transformer = FunctionTransformer(f)
X = np.array([[0, 1], [2, 3]])
transformer.transform(X)

array([[0, 1],
       [4, 9]])

参考http://scikit-learn.org/stable/modules/preprocessing.html#preprocessing