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