LinearRegression

利用python实现简单的线性回归对房屋面积进行预测

 # -*-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)
     return cost
 def GradientDescent(Data,Y,theta,alpha):
     costList = []
     for i in range(10000):
         theta =  theta- (alpha/Data.shape[0]*np.dot(Data.T,(np.dot(Data,theta.T)-Y))).T
         cost = CostFunction(Data, Y, theta)
         costList.append(cost)

     plt.plot(range(10000),costList)
     plt.xlabel("the no. of iterations")
     plt.ylabel("cost Error")
     plt.title("LinearRegression")
     plt.show()
     return theta
 if __name__ == "__main__":
     weight = GradientDescent(Data,Y,theta,alpha)
     print weight
     cost = CostFunction(Data, Y, weight)
     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