# -*-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。