LinearRegressionWithRegularization

在线性回归的基础上加上正则项：

 # -*-coding:utf-8 -*-
 '''
 Created on 2016年12月15日

 @author: lpworkdstudy
 '''
 import numpy as np
 from numpy.core.multiarray import dtype
 import matplotlib.pyplot as plt

 filename = "ex1data1.txt"
 alpha = 0.01

 f = open(filename,"r")
 data = []
 y = []
 for item in f:
     item = item.rstrip().split(",")
     data.append(item[:-1])
     y.append(item[-1:])
 Data = np.array(data,dtype= "float64")
 Y = np.array(y,dtype = "float64")
 Y = (Y-Y.mean())/(Y.max()-Y.min())
 One = np.ones(Data.shape[0],dtype = "float64")
 Data = np.insert(Data, 0, values=One, axis=1)
 for i in range(1,Data.shape[1]):
     Data[:,i] = (Data[:,i]-Data[:,i].mean())/(Data[:,i].max()-Data[:,i].min())
 theta = np.zeros((1,Data.shape[1]),dtype= "float64")

 def CostFunction(Data,Y,theta):
     h = np.dot(Data,theta.T)
     cost = 1/float((2*Data.shape[0]))*(np.sum((h-Y)**2) + np.sum(theta[0,1:]**2) )
     return cost
 def GradientDescent(Data,Y,theta,alpha):
     costList = []
     for i in range(100000):
         temp = theta[0,0] - (alpha/Data.shape[0]*np.dot(Data[:,:1].T,(np.dot(Data,theta.T)-Y))).T
         theta[0,1:] =  (1-alpha/Data.shape[0])*theta[0,1:]- (alpha/Data.shape[0]*np.dot(Data[:,1:].T,(np.dot(Data,theta.T)-Y))).T
         theta[0,0] = temp
         cost = CostFunction(Data, Y, theta)
         costList.append(cost)
     plt.figure(1, figsize=(12,10), dpi=80, facecolor="green", edgecolor="black", frameon=True)
     plt.subplot(111)

     plt.plot(range(100000),costList)
     plt.xlabel("the no. of iterations")
     plt.ylabel("cost Error")
     plt.title("LinearRegression")  

     plt.savefig("LinearRegressionRegularized.png")
     return theta
 if __name__ == "__main__":
     weight = GradientDescent(Data,Y,theta,alpha)
     print weight
     cost = CostFunction(Data, Y, weight)
     print cost

运行得出损失函数随迭代次数的变化曲线如下图：

可以看出加入正则项并没有优化我们的模型，反而产生了不好的
影响，所以我们在解决问题时，不要盲目使用正则化项。