#!/usr/bin/env python
# -*- encoding: utf-8 -*-
'''
@File : regression03.py
@Time : 2019/07/15 20:47:44
@Author : xiao ming
@Version : 1.0
@Contact : xiaoming3526@gmail.com
@Desc : 岭回归以及逐步线性回归
@github : https://github.com/aimi-cn/AILearners
'''
# here put the import lib
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
import numpy as np
'''
@description: 加载数据
@param: fileName - 文件名
@return: xArr - x数据集
yArr - y数据集
'''
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
xArr = []; yArr = []
fr = open(fileName)
for line in fr.readlines():
lineArr =[]
curLine = line.strip().split('\t')
for i in range(numFeat):
lineArr.append(float(curLine[i]))
xArr.append(lineArr)
yArr.append(float(curLine[-1]))
return xArr, yArr
'''
@description: 数据标准化
@param: xMat - x数据集
yMat - y数据集
@return: inxMat - 标准化后的x数据集
inyMat - 标准化后的y数据集
'''
def regularize(xMat, yMat):
inxMat = xMat.copy() #数据拷贝
inyMat = yMat.copy()
yMean = np.mean(yMat, 0) #行与行操作，求均值
inyMat = yMat - yMean #数据减去均值
inMeans = np.mean(inxMat, 0) #行与行操作，求均值
inVar = np.var(inxMat, 0) #行与行操作，求方差
inxMat = (inxMat - inMeans) / inVar #数据减去均值除以方差实现标准化
return inxMat, inyMat
'''
@description: 计算平方误差
@param：yArr - 预测值
yHatArr - 真实值
@return: 平方误差
'''
def rssError(yArr,yHatArr):
return ((yArr-yHatArr)**2).sum()
'''
@description: 前向逐步线性回归
@param： xArr - x输入数据
yArr - y预测数据
eps - 每次迭代需要调整的步长
numIt - 迭代次数
@return: returnMat - numIt次迭代的回归系数矩阵
'''
def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
xMat = np.mat(xArr); yMat = np.mat(yArr).T #数据集
xMat, yMat = regularize(xMat, yMat) #数据标准化
m, n = np.shape(xMat)
returnMat = np.zeros((numIt, n)) #初始化numIt次迭代的回归系数矩阵
ws = np.zeros((n, 1)) #初始化回归系数矩阵
wsTest = ws.copy()
wsMax = ws.copy()
for i in range(numIt): #迭代numIt次
# print(ws.T) #打印当前回归系数矩阵
lowestError = float('inf'); #正无穷
for j in range(n): #遍历每个特征的回归系数
for sign in [-1, 1]:
wsTest = ws.copy()
wsTest[j] += eps * sign #微调回归系数
yTest = xMat * wsTest #计算预测值
rssE = rssError(yMat.A, yTest.A) #计算平方误差
if rssE < lowestError: #如果误差更小，则更新当前的最佳回归系数
lowestError = rssE
wsMax = wsTest
ws = wsMax.copy()
returnMat[i,:] = ws.T #记录numIt次迭代的回归系数矩阵
return returnMat
'''
@description: 绘制岭回归系数矩阵
@param：None
@return: None
'''
def plotstageWiseMat():
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
xArr, yArr = loadDataSet('C:/Users/Administrator/Desktop/blog/github/AILearners/data/ml/jqxxsz/8.Regression/abalone.txt')
returnMat = stageWise(xArr, yArr, 0.005, 1000)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(returnMat)
ax_title_text = ax.set_title(u'前向逐步回归:迭代次数与回归系数的关系', FontProperties = font)
ax_xlabel_text = ax.set_xlabel(u'迭代次数', FontProperties = font)
ax_ylabel_text = ax.set_ylabel(u'回归系数', FontProperties = font)
plt.setp(ax_title_text, size = 15, weight = 'bold', color = 'red')
plt.setp(ax_xlabel_text, size = 10, weight = 'bold', color = 'black')
plt.setp(ax_ylabel_text, size = 10, weight = 'bold', color = 'black')
plt.show()
if __name__ == '__main__':
plotstageWiseMat()
