Python3入门机器学习经典算法与应用——knn算法数据归一化 Feature Scaling

快来打我* 2022-12-20 12:48 117阅读 0赞

### 文章目录 ###

*  数据归一化 Feature Scaling
 *   *  最值归一化 normalization
 *  均值方差归一化 standardization
 *  对测试数据集如何归一化
 *  手写StandardScaler

# 数据归一化 Feature Scaling #

## 最值归一化 normalization ##

把所有数据映射到0-1之间  
![最值归一化][2020111216235857.png_pic_center]

适⽤用于分布有明显边界的情况；受outlier影响较⼤大

# 均值方差归一化 standardization #

均值方差归一化：把所有数据归⼀一到均值为0⽅方差为1的分布中  
![均值方差归一化][20201112162505855.png_pic_center]

# 对测试数据集如何归一化 #

测试数据是模拟真实环境  
• 真实环境很有可能⽆无法得到所有测试  
数据的均值和⽅方差  
• 对数据的归⼀一化也是算法的⼀一部分

(x_test - mean_train) / std_train

![在这里插入图片描述][20201112162654481.png_pic_center]  
模型

![在这里插入图片描述][20201112162725343.png_pic_center]

# 手写StandardScaler #

import numpy as np
    
    
    class StandardScaler:
    
        def __init__(self):
            self.mean_ = None
            self.scale_ = None
    
        def fit(self, X):
            """根据训练数据集X获得数据的均值和方差"""
            assert X.ndim == 2, "The dimension of X must be 2"
    
            self.mean_ = np.array([np.mean(X[:,i]) for i in range(X.shape[1])])
            self.scale_ = np.array([np.std(X[:,i]) for i in range(X.shape[1])])
    
            return self
    
        def transform(self, X):
            """将X根据这个StandardScaler进行均值方差归一化处理"""
            assert X.ndim == 2, "The dimension of X must be 2"
            assert self.mean_ is not None and self.scale_ is not None, \
                   "must fit before transform!"
            assert X.shape[1] == len(self.mean_), \
                   "the feature number of X must be equal to mean_ and std_"
    
            resX = np.empty(shape=X.shape, dtype=float)
            for col in range(X.shape[1]):
                resX[:,col] = (X[:,col] - self.mean_[col]) / self.scale_[col]
            return resX

[2020111216235857.png_pic_center]: /images/20221120/2a115c258703429689ef20d5aa9c3c74.png
[20201112162505855.png_pic_center]: /images/20221120/5150de39b38242bc89d205a4ce3e31fb.png
[20201112162654481.png_pic_center]: /images/20221120/f73fcc2c0d6046ee958f59a4b43dc2b4.png
[20201112162725343.png_pic_center]: /images/20221120/073c8de876e14a5c8f68bfe9991ce52d.png