LinearRegression

利用python实现简单的线性回归对房屋面积进行预测

 1 # -*-coding:utf-8 -*-
 2 ‘‘‘
 3 Created on 2016年12月15日
 4
 5 @author: lpworkdstudy
 6 ‘‘‘
 7 import numpy as np
 8 from numpy.core.multiarray import dtype
 9 import matplotlib.pyplot as plt
10
11 filename = "ex1data1.txt"
12 alpha = 0.01
13
14 f = open(filename,"r")
15 data = []
16 y = []
17 for item in f:
18     item = item.rstrip().split(",")
19     data.append(item[:-1])
20     y.append(item[-1:])
21 Data = np.array(data,dtype= "float64")
22 Y = np.array(y,dtype = "float64")
23 Y = (Y-Y.mean())/(Y.max()-Y.min())
24 One = np.ones(Data.shape[0],dtype = "float64")
25 Data = np.insert(Data, 0, values=One, axis=1)
26 for i in range(1,Data.shape[1]):
27     Data[:,i] = (Data[:,i]-Data[:,i].mean())/(Data[:,i].max()-Data[:,i].min())
28 theta = np.zeros((1,Data.shape[1]),dtype= "float64")
29
30 def CostFunction(Data,Y,theta):
31     h = np.dot(Data,theta.T)
32     cost = 1/float((2*Data.shape[0]))*np.sum((h-Y)**2)
33     return cost
34 def GradientDescent(Data,Y,theta,alpha):
35     costList = []
36     for i in range(10000):
37         theta =  theta- (alpha/Data.shape[0]*np.dot(Data.T,(np.dot(Data,theta.T)-Y))).T
38         cost = CostFunction(Data, Y, theta)
39         costList.append(cost)
40
41     plt.plot(range(10000),costList)
42     plt.xlabel("the no. of iterations")
43     plt.ylabel("cost Error")
44     plt.title("LinearRegression")
45     plt.show()
46     return theta
47 if __name__ == "__main__":
48     weight = GradientDescent(Data,Y,theta,alpha)
49     print weight
50     cost = CostFunction(Data, Y, weight)
51     print cost

上图是Loss Error 随 迭代次数变化的曲线，显然，在迭代4000次左右后随着迭代次数增加，loss下降缓慢。

注：在这里只是简单的利用LMS Loss Function 和 GD对Linear Regression进行了编写，并没有预测