k近邻算法-5.数据归一化

水深无声 2023-08-17 16:44 85阅读 0赞

# 数据归一化（Feature Scaling） #

多个特征值时，其中某个特征数量级比较大，其他特征较小时，分类结果会被特征值所主导，而弱化了其他特征的影响，这是各个特征值的量纲不同所致，需要将数据归一化处理  
![1465169-20190713170958837-193073319.png][]

如上图所示，样本间的距离，被发现时间所主导  
**解决办法：将所有的数据映射到同一尺度**

### 方法一：最值归一化 ###

把所有的数据映射到0-1之间，适用于有明显的边界，受outlier极值影响较大，比如收入的分布  
![1465169-20190713171011802-1191227838.png][]

import numpy 
    import matplotlib.pyplot as plt
    x = numpy.random.randint(0,100,(50,4))
    x = np.array(x,dtype=float)
    for i in range(x.shape[1]):
        x[:,i] = (x[:,i] - np.min(x[:,i])) / (np.max(x[:,i]) - np.min(x[:,i]))
    
    plt.scatter(x[:,0],x[:,1])
    plt.show()

![1465169-20190713171031906-1166625730.png][]

归一化后的平均值和方差：  
![1465169-20190713171045818-1890729884.png][]

### 方法二：均值方差归一化 ###

把所有数据归一化到均值为0，方差为1的分布中，适用于数据分布没有明显的边界，存在极端数据值的数据集  
![1465169-20190713171102772-1809843059.png][]

import numpy 
    import matplotlib.pyplot as plt
    x = numpy.random.randint(0,100,(50,4))
    x = numpy.array(x,dtype=float)
    for i in range(x.shape[1]):
        x[:,i] = (x[:,i] - numpy.mean(x[:,i])) / numpy.std(x[:,i])
    
    plt.scatter(x[:,0],x[:,1])
    plt.show()

![1465169-20190713171120414-264117617.png][]

归一化后的平均值和方差：  
![1465169-20190713171138477-1780404258.png][]

### scikit-learn 中的 StandardScaler ###

from sklearn.datasets import load_iris
    from sklearn.model_selection import train_test_split
    
    iris = load_iris()
    x = iris.data
    y = iris.target
    x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2)

从预处理模块导入标准 标量器

from sklearn.preprocessing import StandardScaler
    standardScaler = StandardScaler()
    standardScaler.fit(x_train)

![1465169-20190713171155635-959386897.png][]

x_train = standardScaler.transform(x_train)
    x_test = standardScaler.transform(x_test)
    
    from sklearn.neighbors import KNeighborsClassifier
    knn_clf = KNeighborsClassifier(n_neighbors=3)
    knn_clf.fit(x_train,y_train)
    knn_clf.score(x_test,y_test)

![1465169-20190713171210420-287128662.png][]

### 自己封装的StandardScaler ###

预处理文件

import numpy as np
    
    class StandardScaler:
        def __init__(self):
            self.mean_ = None
            self.scale_ = None
    
        #求出传入的x数据集的每一列的均值和标准差
        def fit(self, x):
            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
            
        #对x进行数据归一化
        def transform(self, x):
            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 os x must be equal to mean_ and std_"
    
            res_x = np.empty(shape=x.shape, dtype=float)
            for col in range(x.shape[1]):
                res_x[:,col] = (x[:,col] - self.mean_[col]) / self.scale_[col]
            return res_x

调用封装的预处理库

from mylib import preprocessing
    standScaler = preprocessing.StandardScaler() #创建一个均值方差归一化的类
    standScaler.fit(x_train)  #找出样本的均值和标准差
    
    x_train = standScaler.transform(x_train)  #根据均值，标准差，求出归一化的值
    x_test = standScaler.transform(x_test)    #针对测试数据，也是一样用训练集的均值，标准差
    knn = KNeighborsClassifier(n_neighbors=3)  #knn算法分类器
    knn.fit(x_train,y_train)    
    knn.score(x_test,y_test)

转载于:https://www.cnblogs.com/shuai-long/p/11183251.html

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[1465169-20190713171011802-1191227838.png]: /images/20230809/4d2eee65fd2a4e4981b1694d250aeaee.png
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[1465169-20190713171045818-1890729884.png]: /images/20230809/dfd95c2d22ea466b8bc917c585bb2f37.png
[1465169-20190713171102772-1809843059.png]: /images/20230809/52f14f457d504ee2a18d5ab4b6c77795.png
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[1465169-20190713171138477-1780404258.png]: /images/20230809/b53ec7b7848e499fba072d1c009092e4.png
[1465169-20190713171155635-959386897.png]: /images/20230809/a221d7e62bbc4a069680d1bb9cb6df7d.png
[1465169-20190713171210420-287128662.png]: /images/20230809/bda848f6b0d04852b0232e50f4ca7e90.png