将数值化之后的特征值进行特征预处理，特征根和特征值

文章由Byrx.net分享于2019-09-27 09:09:41评论（171）

将数值化之后的特征值进行特征预处理，特征根和特征值

目标：

了解数值型数据、类别型数据特点

应用MinMaxScaler实现对特征数据归一化

应用StandarScaler实现对特征数据进行标准化

特征预处理：

通过一些转换函数将特征数据转化为更合适算法模型的特征数据过程

数值型数据的无量纲化（无量纲化，数学名词，不同规格的数据转换到统一规格）

归一化：根据最大最小值进行缩放，默认范围0-1，容易受到异常值的影响稳定性差，只适合小规模的数据场景

标准化：原始数据变化到0-1直接

特征预处理API：

sklearn.preprocession

为什么要进行归一化/标准化？

特征的单位或者大小相差较大，或者某特征的方差相比其他的特征要大出几个数量级，容易影响（支配）目标结果，使得一些算法无法学习到其他特征

1、归一化

定义：通过对原始数据进行变换把数据映射到（默认为[0,1]）之间

X' = (x - min)/(max - min) x'' = x' * (mx - mi) + mi

(max为一列的最大值，min为一列的最小值。mx，mi分别为指定区间值默认mx为1，mi为0）

sklearn.preprocessing.MinMaxScaler(feature_range = (0,1))

MinMaxScaler.fit_transform(X)

X:numpy array格式的数据[n_samples, n_features]

返回：转换后的形状相同的array

归一化总结：注意最大值最小值是变化的，另外，最大值与最小值非常容易受异常点影响，所以这种方法鲁棒性较差，知识和传统精确小数据场景。

from sklearn.datasets import load_iris
from sklearn.preprocessing import MinMaxScaler
import pandas as pd

#归一化
def minmax_demo():
    #使用sklearn的自带的数据集
    iris = load_iris()
    data = pd.DataFrame(iris.data, columns = iris.feature_names)
    data_new = data.iloc[:, :4].values
    print("data_new:\n", data_new)
    
    transfer = MinMaxScaler(feature_range = [1, 2]) #默认feature_range是[0, 1]
    
    data_minmax_value = transfer.fit_transform(data_new)
    print("data_minmax_value:\n", data_minmax_value)
    
    return None

if __name__ == '__main__':
    minmax_demo()



输出结果：
data_new:
 [[5.1 3.5 1.4 0.2]
 [4.9 3.  1.4 0.2]
 [4.7 3.2 1.3 0.2]
 [4.6 3.1 1.5 0.2]
 [5.  3.6 1.4 0.2]
 [5.4 3.9 1.7 0.4]
 [4.6 3.4 1.4 0.3]
 [5.  3.4 1.5 0.2]
 [4.4 2.9 1.4 0.2]
 [4.9 3.1 1.5 0.1]
 [5.4 3.7 1.5 0.2]
 [4.8 3.4 1.6 0.2]
 [4.8 3.  1.4 0.1]
 [4.3 3.  1.1 0.1]
 [5.8 4.  1.2 0.2]
 [5.7 4.4 1.5 0.4]
 [5.4 3.9 1.3 0.4]
 [5.1 3.5 1.4 0.3]
 [5.7 3.8 1.7 0.3]
 [5.1 3.8 1.5 0.3]
 [5.4 3.4 1.7 0.2]
 [5.1 3.7 1.5 0.4]
 [4.6 3.6 1.  0.2]
 [5.1 3.3 1.7 0.5]
 [4.8 3.4 1.9 0.2]
 [5.  3.  1.6 0.2]
 [5.  3.4 1.6 0.4]
 [5.2 3.5 1.5 0.2]
 [5.2 3.4 1.4 0.2]
 [4.7 3.2 1.6 0.2]
 [4.8 3.1 1.6 0.2]
 [5.4 3.4 1.5 0.4]
 [5.2 4.1 1.5 0.1]
 [5.5 4.2 1.4 0.2]
 [4.9 3.1 1.5 0.1]
 [5.  3.2 1.2 0.2]
 [5.5 3.5 1.3 0.2]
 [4.9 3.1 1.5 0.1]
 [4.4 3.  1.3 0.2]
 [5.1 3.4 1.5 0.2]
 [5.  3.5 1.3 0.3]
 [4.5 2.3 1.3 0.3]
 [4.4 3.2 1.3 0.2]
 [5.  3.5 1.6 0.6]
 [5.1 3.8 1.9 0.4]
 [4.8 3.  1.4 0.3]
 [5.1 3.8 1.6 0.2]
 [4.6 3.2 1.4 0.2]
 [5.3 3.7 1.5 0.2]
 [5.  3.3 1.4 0.2]
 [7.  3.2 4.7 1.4]
 [6.4 3.2 4.5 1.5]
 [6.9 3.1 4.9 1.5]
 [5.5 2.3 4.  1.3]
 [6.5 2.8 4.6 1.5]
 [5.7 2.8 4.5 1.3]
 [6.3 3.3 4.7 1.6]
 [4.9 2.4 3.3 1. ]
 [6.6 2.9 4.6 1.3]
 [5.2 2.7 3.9 1.4]
 [5.  2.  3.5 1. ]
 [5.9 3.  4.2 1.5]
 [6.  2.2 4.  1. ]
 [6.1 2.9 4.7 1.4]
 [5.6 2.9 3.6 1.3]
 [6.7 3.1 4.4 1.4]
 [5.6 3.  4.5 1.5]
 [5.8 2.7 4.1 1. ]
 [6.2 2.2 4.5 1.5]
 [5.6 2.5 3.9 1.1]
 [5.9 3.2 4.8 1.8]
 [6.1 2.8 4.  1.3]
 [6.3 2.5 4.9 1.5]
 [6.1 2.8 4.7 1.2]
 [6.4 2.9 4.3 1.3]
 [6.6 3.  4.4 1.4]
 [6.8 2.8 4.8 1.4]
 [6.7 3.  5.  1.7]
 [6.  2.9 4.5 1.5]
 [5.7 2.6 3.5 1. ]
 [5.5 2.4 3.8 1.1]
 [5.5 2.4 3.7 1. ]
 [5.8 2.7 3.9 1.2]
 [6.  2.7 5.1 1.6]
 [5.4 3.  4.5 1.5]
 [6.  3.4 4.5 1.6]
 [6.7 3.1 4.7 1.5]
 [6.3 2.3 4.4 1.3]
 [5.6 3.  4.1 1.3]
 [5.5 2.5 4.  1.3]
 [5.5 2.6 4.4 1.2]
 [6.1 3.  4.6 1.4]
 [5.8 2.6 4.  1.2]
 [5.  2.3 3.3 1. ]
 [5.6 2.7 4.2 1.3]
 [5.7 3.  4.2 1.2]
 [5.7 2.9 4.2 1.3]
 [6.2 2.9 4.3 1.3]
 [5.1 2.5 3.  1.1]
 [5.7 2.8 4.1 1.3]
 [6.3 3.3 6.  2.5]
 [5.8 2.7 5.1 1.9]
 [7.1 3.  5.9 2.1]
 [6.3 2.9 5.6 1.8]
 [6.5 3.  5.8 2.2]
 [7.6 3.  6.6 2.1]
 [4.9 2.5 4.5 1.7]
 [7.3 2.9 6.3 1.8]
 [6.7 2.5 5.8 1.8]
 [7.2 3.6 6.1 2.5]
 [6.5 3.2 5.1 2. ]
 [6.4 2.7 5.3 1.9]
 [6.8 3.  5.5 2.1]
 [5.7 2.5 5.  2. ]
 [5.8 2.8 5.1 2.4]
 [6.4 3.2 5.3 2.3]
 [6.5 3.  5.5 1.8]
 [7.7 3.8 6.7 2.2]
 [7.7 2.6 6.9 2.3]
 [6.  2.2 5.  1.5]
 [6.9 3.2 5.7 2.3]
 [5.6 2.8 4.9 2. ]
 [7.7 2.8 6.7 2. ]
 [6.3 2.7 4.9 1.8]
 [6.7 3.3 5.7 2.1]
 [7.2 3.2 6.  1.8]
 [6.2 2.8 4.8 1.8]
 [6.1 3.  4.9 1.8]
 [6.4 2.8 5.6 2.1]
 [7.2 3.  5.8 1.6]
 [7.4 2.8 6.1 1.9]
 [7.9 3.8 6.4 2. ]
 [6.4 2.8 5.6 2.2]
 [6.3 2.8 5.1 1.5]
 [6.1 2.6 5.6 1.4]
 [7.7 3.  6.1 2.3]
 [6.3 3.4 5.6 2.4]
 [6.4 3.1 5.5 1.8]
 [6.  3.  4.8 1.8]
 [6.9 3.1 5.4 2.1]
 [6.7 3.1 5.6 2.4]
 [6.9 3.1 5.1 2.3]
 [5.8 2.7 5.1 1.9]
 [6.8 3.2 5.9 2.3]
 [6.7 3.3 5.7 2.5]
 [6.7 3.  5.2 2.3]
 [6.3 2.5 5.  1.9]
 [6.5 3.  5.2 2. ]
 [6.2 3.4 5.4 2.3]
 [5.9 3.  5.1 1.8]]
data_minmax_value:
 [[1.22222222 1.625      1.06779661 1.04166667]
 [1.16666667 1.41666667 1.06779661 1.04166667]
 [1.11111111 1.5        1.05084746 1.04166667]
 [1.08333333 1.45833333 1.08474576 1.04166667]
 [1.19444444 1.66666667 1.06779661 1.04166667]
 [1.30555556 1.79166667 1.11864407 1.125     ]
 [1.08333333 1.58333333 1.06779661 1.08333333]
 [1.19444444 1.58333333 1.08474576 1.04166667]
 [1.02777778 1.375      1.06779661 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.30555556 1.70833333 1.08474576 1.04166667]
 [1.13888889 1.58333333 1.10169492 1.04166667]
 [1.13888889 1.41666667 1.06779661 1.        ]
 [1.         1.41666667 1.01694915 1.        ]
 [1.41666667 1.83333333 1.03389831 1.04166667]
 [1.38888889 2.         1.08474576 1.125     ]
 [1.30555556 1.79166667 1.05084746 1.125     ]
 [1.22222222 1.625      1.06779661 1.08333333]
 [1.38888889 1.75       1.11864407 1.08333333]
 [1.22222222 1.75       1.08474576 1.08333333]
 [1.30555556 1.58333333 1.11864407 1.04166667]
 [1.22222222 1.70833333 1.08474576 1.125     ]
 [1.08333333 1.66666667 1.         1.04166667]
 [1.22222222 1.54166667 1.11864407 1.16666667]
 [1.13888889 1.58333333 1.15254237 1.04166667]
 [1.19444444 1.41666667 1.10169492 1.04166667]
 [1.19444444 1.58333333 1.10169492 1.125     ]
 [1.25       1.625      1.08474576 1.04166667]
 [1.25       1.58333333 1.06779661 1.04166667]
 [1.11111111 1.5        1.10169492 1.04166667]
 [1.13888889 1.45833333 1.10169492 1.04166667]
 [1.30555556 1.58333333 1.08474576 1.125     ]
 [1.25       1.875      1.08474576 1.        ]
 [1.33333333 1.91666667 1.06779661 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.19444444 1.5        1.03389831 1.04166667]
 [1.33333333 1.625      1.05084746 1.04166667]
 [1.16666667 1.45833333 1.08474576 1.        ]
 [1.02777778 1.41666667 1.05084746 1.04166667]
 [1.22222222 1.58333333 1.08474576 1.04166667]
 [1.19444444 1.625      1.05084746 1.08333333]
 [1.05555556 1.125      1.05084746 1.08333333]
 [1.02777778 1.5        1.05084746 1.04166667]
 [1.19444444 1.625      1.10169492 1.20833333]
 [1.22222222 1.75       1.15254237 1.125     ]
 [1.13888889 1.41666667 1.06779661 1.08333333]
 [1.22222222 1.75       1.10169492 1.04166667]
 [1.08333333 1.5        1.06779661 1.04166667]
 [1.27777778 1.70833333 1.08474576 1.04166667]
 [1.19444444 1.54166667 1.06779661 1.04166667]
 [1.75       1.5        1.62711864 1.54166667]
 [1.58333333 1.5        1.59322034 1.58333333]
 [1.72222222 1.45833333 1.66101695 1.58333333]
 [1.33333333 1.125      1.50847458 1.5       ]
 [1.61111111 1.33333333 1.61016949 1.58333333]
 [1.38888889 1.33333333 1.59322034 1.5       ]
 [1.55555556 1.54166667 1.62711864 1.625     ]
 [1.16666667 1.16666667 1.38983051 1.375     ]
 [1.63888889 1.375      1.61016949 1.5       ]
 [1.25       1.29166667 1.49152542 1.54166667]
 [1.19444444 1.         1.42372881 1.375     ]
 [1.44444444 1.41666667 1.54237288 1.58333333]
 [1.47222222 1.08333333 1.50847458 1.375     ]
 [1.5        1.375      1.62711864 1.54166667]
 [1.36111111 1.375      1.44067797 1.5       ]
 [1.66666667 1.45833333 1.57627119 1.54166667]
 [1.36111111 1.41666667 1.59322034 1.58333333]
 [1.41666667 1.29166667 1.52542373 1.375     ]
 [1.52777778 1.08333333 1.59322034 1.58333333]
 [1.36111111 1.20833333 1.49152542 1.41666667]
 [1.44444444 1.5        1.6440678  1.70833333]
 [1.5        1.33333333 1.50847458 1.5       ]
 [1.55555556 1.20833333 1.66101695 1.58333333]
 [1.5        1.33333333 1.62711864 1.45833333]
 [1.58333333 1.375      1.55932203 1.5       ]
 [1.63888889 1.41666667 1.57627119 1.54166667]
 [1.69444444 1.33333333 1.6440678  1.54166667]
 [1.66666667 1.41666667 1.6779661  1.66666667]
 [1.47222222 1.375      1.59322034 1.58333333]
 [1.38888889 1.25       1.42372881 1.375     ]
 [1.33333333 1.16666667 1.47457627 1.41666667]
 [1.33333333 1.16666667 1.45762712 1.375     ]
 [1.41666667 1.29166667 1.49152542 1.45833333]
 [1.47222222 1.29166667 1.69491525 1.625     ]
 [1.30555556 1.41666667 1.59322034 1.58333333]
 [1.47222222 1.58333333 1.59322034 1.625     ]
 [1.66666667 1.45833333 1.62711864 1.58333333]
 [1.55555556 1.125      1.57627119 1.5       ]
 [1.36111111 1.41666667 1.52542373 1.5       ]
 [1.33333333 1.20833333 1.50847458 1.5       ]
 [1.33333333 1.25       1.57627119 1.45833333]
 [1.5        1.41666667 1.61016949 1.54166667]
 [1.41666667 1.25       1.50847458 1.45833333]
 [1.19444444 1.125      1.38983051 1.375     ]
 [1.36111111 1.29166667 1.54237288 1.5       ]
 [1.38888889 1.41666667 1.54237288 1.45833333]
 [1.38888889 1.375      1.54237288 1.5       ]
 [1.52777778 1.375      1.55932203 1.5       ]
 [1.22222222 1.20833333 1.33898305 1.41666667]
 [1.38888889 1.33333333 1.52542373 1.5       ]
 [1.55555556 1.54166667 1.84745763 2.        ]
 [1.41666667 1.29166667 1.69491525 1.75      ]
 [1.77777778 1.41666667 1.83050847 1.83333333]
 [1.55555556 1.375      1.77966102 1.70833333]
 [1.61111111 1.41666667 1.81355932 1.875     ]
 [1.91666667 1.41666667 1.94915254 1.83333333]
 [1.16666667 1.20833333 1.59322034 1.66666667]
 [1.83333333 1.375      1.89830508 1.70833333]
 [1.66666667 1.20833333 1.81355932 1.70833333]
 [1.80555556 1.66666667 1.86440678 2.        ]
 [1.61111111 1.5        1.69491525 1.79166667]
 [1.58333333 1.29166667 1.72881356 1.75      ]
 [1.69444444 1.41666667 1.76271186 1.83333333]
 [1.38888889 1.20833333 1.6779661  1.79166667]
 [1.41666667 1.33333333 1.69491525 1.95833333]
 [1.58333333 1.5        1.72881356 1.91666667]
 [1.61111111 1.41666667 1.76271186 1.70833333]
 [1.94444444 1.75       1.96610169 1.875     ]
 [1.94444444 1.25       2.         1.91666667]
 [1.47222222 1.08333333 1.6779661  1.58333333]
 [1.72222222 1.5        1.79661017 1.91666667]
 [1.36111111 1.33333333 1.66101695 1.79166667]
 [1.94444444 1.33333333 1.96610169 1.79166667]
 [1.55555556 1.29166667 1.66101695 1.70833333]
 [1.66666667 1.54166667 1.79661017 1.83333333]
 [1.80555556 1.5        1.84745763 1.70833333]
 [1.52777778 1.33333333 1.6440678  1.70833333]
 [1.5        1.41666667 1.66101695 1.70833333]
 [1.58333333 1.33333333 1.77966102 1.83333333]
 [1.80555556 1.41666667 1.81355932 1.625     ]
 [1.86111111 1.33333333 1.86440678 1.75      ]
 [2.         1.75       1.91525424 1.79166667]
 [1.58333333 1.33333333 1.77966102 1.875     ]
 [1.55555556 1.33333333 1.69491525 1.58333333]
 [1.5        1.25       1.77966102 1.54166667]
 [1.94444444 1.41666667 1.86440678 1.91666667]
 [1.55555556 1.58333333 1.77966102 1.95833333]
 [1.58333333 1.45833333 1.76271186 1.70833333]
 [1.47222222 1.41666667 1.6440678  1.70833333]
 [1.72222222 1.45833333 1.74576271 1.83333333]
 [1.66666667 1.45833333 1.77966102 1.95833333]
 [1.72222222 1.45833333 1.69491525 1.91666667]
 [1.41666667 1.29166667 1.69491525 1.75      ]
 [1.69444444 1.5        1.83050847 1.91666667]
 [1.66666667 1.54166667 1.79661017 2.        ]
 [1.66666667 1.41666667 1.71186441 1.91666667]
 [1.55555556 1.20833333 1.6779661  1.75      ]
 [1.61111111 1.41666667 1.71186441 1.79166667]
 [1.52777778 1.58333333 1.74576271 1.91666667]
 [1.44444444 1.41666667 1.69491525 1.70833333]]

2、标准化

定义：通过对原始数据进行变换把数据变换到均值为0，标准差为1范围内

公式：X' = (x - mean)/ ∝

mean是平均值，∝是标准差

对于归一化来说，如果出现异常点，影响了最大值和最小值，那么结果显然会发生改变

对于标准化来说：如果出现异常点，由于具有一定数据量，商量的异常点对于平均值的影响并不大，从而方差改变较小

总结：在已有样本足够多的情况下比较稳定，适合现代嘈杂大数据场景

from sklearn.datasets import load_iris
from sklearn.preprocessing import StandardScaler
import pandas as pd

def standard_demo():
    iris = load_iris()
    data = pd.DataFrame(iris.data, columns = iris.feature_names)
    data_new = data.iloc[:, :4].values
    
    print("data_new:\n", data_new)
    
    transfer = StandardScaler()
    
    data_standard_value = transfer.fit_transform(data_new)
    print("data_standard_value:\n", data_standard_value)
    
    return None

if __name__ == '__main__':
    standard_demo()



输出结果：
data_new:
 [[5.1 3.5 1.4 0.2]
 [4.9 3.  1.4 0.2]
 [4.7 3.2 1.3 0.2]
 [4.6 3.1 1.5 0.2]
 [5.  3.6 1.4 0.2]
 [5.4 3.9 1.7 0.4]
 [4.6 3.4 1.4 0.3]
 [5.  3.4 1.5 0.2]
 [4.4 2.9 1.4 0.2]
 [4.9 3.1 1.5 0.1]
 [5.4 3.7 1.5 0.2]
 [4.8 3.4 1.6 0.2]
 [4.8 3.  1.4 0.1]
 [4.3 3.  1.1 0.1]
 [5.8 4.  1.2 0.2]
 [5.7 4.4 1.5 0.4]
 [5.4 3.9 1.3 0.4]
 [5.1 3.5 1.4 0.3]
 [5.7 3.8 1.7 0.3]
 [5.1 3.8 1.5 0.3]
 [5.4 3.4 1.7 0.2]
 [5.1 3.7 1.5 0.4]
 [4.6 3.6 1.  0.2]
 [5.1 3.3 1.7 0.5]
 [4.8 3.4 1.9 0.2]
 [5.  3.  1.6 0.2]
 [5.  3.4 1.6 0.4]
 [5.2 3.5 1.5 0.2]
 [5.2 3.4 1.4 0.2]
 [4.7 3.2 1.6 0.2]
 [4.8 3.1 1.6 0.2]
 [5.4 3.4 1.5 0.4]
 [5.2 4.1 1.5 0.1]
 [5.5 4.2 1.4 0.2]
 [4.9 3.1 1.5 0.1]
 [5.  3.2 1.2 0.2]
 [5.5 3.5 1.3 0.2]
 [4.9 3.1 1.5 0.1]
 [4.4 3.  1.3 0.2]
 [5.1 3.4 1.5 0.2]
 [5.  3.5 1.3 0.3]
 [4.5 2.3 1.3 0.3]
 [4.4 3.2 1.3 0.2]
 [5.  3.5 1.6 0.6]
 [5.1 3.8 1.9 0.4]
 [4.8 3.  1.4 0.3]
 [5.1 3.8 1.6 0.2]
 [4.6 3.2 1.4 0.2]
 [5.3 3.7 1.5 0.2]
 [5.  3.3 1.4 0.2]
 [7.  3.2 4.7 1.4]
 [6.4 3.2 4.5 1.5]
 [6.9 3.1 4.9 1.5]
 [5.5 2.3 4.  1.3]
 [6.5 2.8 4.6 1.5]
 [5.7 2.8 4.5 1.3]
 [6.3 3.3 4.7 1.6]
 [4.9 2.4 3.3 1. ]
 [6.6 2.9 4.6 1.3]
 [5.2 2.7 3.9 1.4]
 [5.  2.  3.5 1. ]
 [5.9 3.  4.2 1.5]
 [6.  2.2 4.  1. ]
 [6.1 2.9 4.7 1.4]
 [5.6 2.9 3.6 1.3]
 [6.7 3.1 4.4 1.4]
 [5.6 3.  4.5 1.5]
 [5.8 2.7 4.1 1. ]
 [6.2 2.2 4.5 1.5]
 [5.6 2.5 3.9 1.1]
 [5.9 3.2 4.8 1.8]
 [6.1 2.8 4.  1.3]
 [6.3 2.5 4.9 1.5]
 [6.1 2.8 4.7 1.2]
 [6.4 2.9 4.3 1.3]
 [6.6 3.  4.4 1.4]
 [6.8 2.8 4.8 1.4]
 [6.7 3.  5.  1.7]
 [6.  2.9 4.5 1.5]
 [5.7 2.6 3.5 1. ]
 [5.5 2.4 3.8 1.1]
 [5.5 2.4 3.7 1. ]
 [5.8 2.7 3.9 1.2]
 [6.  2.7 5.1 1.6]
 [5.4 3.  4.5 1.5]
 [6.  3.4 4.5 1.6]
 [6.7 3.1 4.7 1.5]
 [6.3 2.3 4.4 1.3]
 [5.6 3.  4.1 1.3]
 [5.5 2.5 4.  1.3]
 [5.5 2.6 4.4 1.2]
 [6.1 3.  4.6 1.4]
 [5.8 2.6 4.  1.2]
 [5.  2.3 3.3 1. ]
 [5.6 2.7 4.2 1.3]
 [5.7 3.  4.2 1.2]
 [5.7 2.9 4.2 1.3]
 [6.2 2.9 4.3 1.3]
 [5.1 2.5 3.  1.1]
 [5.7 2.8 4.1 1.3]
 [6.3 3.3 6.  2.5]
 [5.8 2.7 5.1 1.9]
 [7.1 3.  5.9 2.1]
 [6.3 2.9 5.6 1.8]
 [6.5 3.  5.8 2.2]
 [7.6 3.  6.6 2.1]
 [4.9 2.5 4.5 1.7]
 [7.3 2.9 6.3 1.8]
 [6.7 2.5 5.8 1.8]
 [7.2 3.6 6.1 2.5]
 [6.5 3.2 5.1 2. ]
 [6.4 2.7 5.3 1.9]
 [6.8 3.  5.5 2.1]
 [5.7 2.5 5.  2. ]
 [5.8 2.8 5.1 2.4]
 [6.4 3.2 5.3 2.3]
 [6.5 3.  5.5 1.8]
 [7.7 3.8 6.7 2.2]
 [7.7 2.6 6.9 2.3]
 [6.  2.2 5.  1.5]
 [6.9 3.2 5.7 2.3]
 [5.6 2.8 4.9 2. ]
 [7.7 2.8 6.7 2. ]
 [6.3 2.7 4.9 1.8]
 [6.7 3.3 5.7 2.1]
 [7.2 3.2 6.  1.8]
 [6.2 2.8 4.8 1.8]
 [6.1 3.  4.9 1.8]
 [6.4 2.8 5.6 2.1]
 [7.2 3.  5.8 1.6]
 [7.4 2.8 6.1 1.9]
 [7.9 3.8 6.4 2. ]
 [6.4 2.8 5.6 2.2]
 [6.3 2.8 5.1 1.5]
 [6.1 2.6 5.6 1.4]
 [7.7 3.  6.1 2.3]
 [6.3 3.4 5.6 2.4]
 [6.4 3.1 5.5 1.8]
 [6.  3.  4.8 1.8]
 [6.9 3.1 5.4 2.1]
 [6.7 3.1 5.6 2.4]
 [6.9 3.1 5.1 2.3]
 [5.8 2.7 5.1 1.9]
 [6.8 3.2 5.9 2.3]
 [6.7 3.3 5.7 2.5]
 [6.7 3.  5.2 2.3]
 [6.3 2.5 5.  1.9]
 [6.5 3.  5.2 2. ]
 [6.2 3.4 5.4 2.3]
 [5.9 3.  5.1 1.8]]
data_standard_value:
 [[-9.00681170e-01  1.03205722e+00 -1.34127240e+00 -1.31297673e+00]
 [-1.14301691e+00 -1.24957601e-01 -1.34127240e+00 -1.31297673e+00]
 [-1.38535265e+00  3.37848329e-01 -1.39813811e+00 -1.31297673e+00]
 [-1.50652052e+00  1.06445364e-01 -1.28440670e+00 -1.31297673e+00]
 [-1.02184904e+00  1.26346019e+00 -1.34127240e+00 -1.31297673e+00]
 [-5.37177559e-01  1.95766909e+00 -1.17067529e+00 -1.05003079e+00]
 [-1.50652052e+00  8.00654259e-01 -1.34127240e+00 -1.18150376e+00]
 [-1.02184904e+00  8.00654259e-01 -1.28440670e+00 -1.31297673e+00]
 [-1.74885626e+00 -3.56360566e-01 -1.34127240e+00 -1.31297673e+00]
 [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]
 [-5.37177559e-01  1.49486315e+00 -1.28440670e+00 -1.31297673e+00]
 [-1.26418478e+00  8.00654259e-01 -1.22754100e+00 -1.31297673e+00]
 [-1.26418478e+00 -1.24957601e-01 -1.34127240e+00 -1.44444970e+00]
 [-1.87002413e+00 -1.24957601e-01 -1.51186952e+00 -1.44444970e+00]
 [-5.25060772e-02  2.18907205e+00 -1.45500381e+00 -1.31297673e+00]
 [-1.73673948e-01  3.11468391e+00 -1.28440670e+00 -1.05003079e+00]
 [-5.37177559e-01  1.95766909e+00 -1.39813811e+00 -1.05003079e+00]
 [-9.00681170e-01  1.03205722e+00 -1.34127240e+00 -1.18150376e+00]
 [-1.73673948e-01  1.72626612e+00 -1.17067529e+00 -1.18150376e+00]
 [-9.00681170e-01  1.72626612e+00 -1.28440670e+00 -1.18150376e+00]
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 [-9.00681170e-01  1.49486315e+00 -1.28440670e+00 -1.05003079e+00]
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 [-9.00681170e-01  5.69251294e-01 -1.17067529e+00 -9.18557817e-01]
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 [-1.02184904e+00 -1.24957601e-01 -1.22754100e+00 -1.31297673e+00]
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 [-1.38535265e+00  3.37848329e-01 -1.22754100e+00 -1.31297673e+00]
 [-1.26418478e+00  1.06445364e-01 -1.22754100e+00 -1.31297673e+00]
 [-5.37177559e-01  8.00654259e-01 -1.28440670e+00 -1.05003079e+00]
 [-7.79513300e-01  2.42047502e+00 -1.28440670e+00 -1.44444970e+00]
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 [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]
 [-1.02184904e+00  3.37848329e-01 -1.45500381e+00 -1.31297673e+00]
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 [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]
 [-1.74885626e+00 -1.24957601e-01 -1.39813811e+00 -1.31297673e+00]
 [-9.00681170e-01  8.00654259e-01 -1.28440670e+00 -1.31297673e+00]
 [-1.02184904e+00  1.03205722e+00 -1.39813811e+00 -1.18150376e+00]
 [-1.62768839e+00 -1.74477836e+00 -1.39813811e+00 -1.18150376e+00]
 [-1.74885626e+00  3.37848329e-01 -1.39813811e+00 -1.31297673e+00]
 [-1.02184904e+00  1.03205722e+00 -1.22754100e+00 -7.87084847e-01]
 [-9.00681170e-01  1.72626612e+00 -1.05694388e+00 -1.05003079e+00]
 [-1.26418478e+00 -1.24957601e-01 -1.34127240e+00 -1.18150376e+00]
 [-9.00681170e-01  1.72626612e+00 -1.22754100e+00 -1.31297673e+00]
 [-1.50652052e+00  3.37848329e-01 -1.34127240e+00 -1.31297673e+00]
 [-6.58345429e-01  1.49486315e+00 -1.28440670e+00 -1.31297673e+00]
 [-1.02184904e+00  5.69251294e-01 -1.34127240e+00 -1.31297673e+00]
 [ 1.40150837e+00  3.37848329e-01  5.35295827e-01  2.64698913e-01]
 [ 6.74501145e-01  3.37848329e-01  4.21564419e-01  3.96171883e-01]
 [ 1.28034050e+00  1.06445364e-01  6.49027235e-01  3.96171883e-01]
 [-4.16009689e-01 -1.74477836e+00  1.37235899e-01  1.33225943e-01]
 [ 7.95669016e-01 -5.87763531e-01  4.78430123e-01  3.96171883e-01]
 [-1.73673948e-01 -5.87763531e-01  4.21564419e-01  1.33225943e-01]
 [ 5.53333275e-01  5.69251294e-01  5.35295827e-01  5.27644853e-01]
 [-1.14301691e+00 -1.51337539e+00 -2.60824029e-01 -2.61192967e-01]
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 [-7.79513300e-01 -8.19166497e-01  8.03701950e-02  2.64698913e-01]
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 [ 6.86617933e-02 -1.24957601e-01  2.50967307e-01  3.96171883e-01]
 [ 1.89829664e-01 -1.97618132e+00  1.37235899e-01 -2.61192967e-01]
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 [ 1.03800476e+00  1.06445364e-01  3.64698715e-01  2.64698913e-01]
 [-2.94841818e-01 -1.24957601e-01  4.21564419e-01  3.96171883e-01]
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 [-2.94841818e-01 -1.28197243e+00  8.03701950e-02 -1.29719997e-01]
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 [ 6.74501145e-01 -5.87763531e-01  1.04708716e+00  1.31648267e+00]
 [ 5.53333275e-01 -5.87763531e-01  7.62758643e-01  3.96171883e-01]
 [ 3.10997534e-01 -1.05056946e+00  1.04708716e+00  2.64698913e-01]
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 [ 6.74501145e-01  1.06445364e-01  9.90221459e-01  7.90590793e-01]
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 [ 1.28034050e+00  1.06445364e-01  7.62758643e-01  1.44795564e+00]
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 [ 1.15917263e+00  3.37848329e-01  1.21768427e+00  1.44795564e+00]
 [ 1.03800476e+00  5.69251294e-01  1.10395287e+00  1.71090158e+00]
 [ 1.03800476e+00 -1.24957601e-01  8.19624347e-01  1.44795564e+00]
 [ 5.53333275e-01 -1.28197243e+00  7.05892939e-01  9.22063763e-01]
 [ 7.95669016e-01 -1.24957601e-01  8.19624347e-01  1.05353673e+00]
 [ 4.32165405e-01  8.00654259e-01  9.33355755e-01  1.44795564e+00]
 [ 6.86617933e-02 -1.24957601e-01  7.62758643e-01  7.90590793e-01]]

参考链接：https://www.cnblogs.com/ftl1012/p/10498480.html

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