前言：

     当alpha 值为0，求解过程和最小二乘法是一样的

优点：

   可以防止矩阵不可逆

   惩罚某个维度权重系数过高

一   岭回归原理

        输入：

                 m个样本,n个维度

               : 标签值

      模型

             其中w 为权重系数 [n,1]

        求解：

             w

        算法推导

               对w 求导，分母形式

二 CODE

# -*- coding: utf-8 -*-
"""
Created on Thu Jul  8 17:05:06 2021

@author: chengxf2
"""
import numpy as np
from sklearn.metrics import mean_squared_error , r2_score
import matplotlib.pyplot as plt
class RidgeRegression():
    
    '''
    加载数据集
    '''
    def LoadData(self):
        
        f = open(self.name)
        
        lines = f.readlines()
        self.n = len(lines[0].split())-1
        
        dataMat =[]
        labelMat =[]
        for line in lines:
            items = line.split('\t')
            lineData =[]
            for i in range(self.n):
                val = float(items[i])
                lineData.append(val)
            dataMat.append(lineData)
            y = float(items[-1])
            labelMat.append(y)
            
        return np.mat(dataMat),np.mat(labelMat).T
    
    def Train(self, dataMat, labelMat,alpha=0.01):
        
        #print("\n step1 ",dataMat)
        xx = np.dot(dataMat.T,dataMat)
        #print("\n step2 ")
        A = xx+alpha*np.eye(self.n)
        
        if np.linalg.det(A) ==0.0: #矩阵不可逆
           #print("\n ===========error=========")
           return
        B =dataMat.T*labelMat
         
        W = np.linalg.inv(A)*B
         
        return W
    
    '''
    预测
    '''
    def Predict(self, W,dataMat):
        y_predict = dataMat*W
        
        return y_predict
    
    def Test(self):
         dataMat, labelMat =rd.LoadData()
         
         alpha = np.arange(0.001,1.2,0.001)
         y_score =[]
         
         for a in alpha:
            w = rd.Train(dataMat, labelMat, a)
            y_predict = rd.Predict(w, dataMat)
            score = r2_score(labelMat, y_predict)
            y_score.append(score)
            #print("\n score ",score)
         fig = plt.figure()
         ax = fig.add_subplot(111)
         ax.plot(alpha,y_score,'go-',linewidth=1,label="alpha-score")
         ax.legend()
  
            
            
        
       
    def __init__(self):
        
        self.m = 0 #样本个数
        self.n = 0 #样本维度
        self.name ="ex0.txt"

if __name__ =="__main__":
    rd = RidgeRegression()
    rd.Test()
   

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