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