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regression.py
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regression.py
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# -*-coding:utf-8 -*-
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
import numpy as np
def loadDataSet(fileName):
"""
函数说明:加载数据
Parameters:
fileName - 文件名
Returns:
xArr - x数据集
yArr - y数据集
Website:
http://www.cuijiahua.com/
Modify:
2017-11-20
"""
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
def ridgeRegres(xMat, yMat, lam = 0.2):
"""
函数说明:岭回归
Parameters:
xMat - x数据集
yMat - y数据集
lam - 缩减系数
Returns:
ws - 回归系数
Website:
http://www.cuijiahua.com/
Modify:
2017-11-20
"""
xTx = xMat.T * xMat
denom = xTx + np.eye(np.shape(xMat)[1]) * lam
if np.linalg.det(denom) == 0.0:
print("矩阵为奇异矩阵,不能求逆")
return
ws = denom.I * (xMat.T * yMat)
return ws
def ridgeTest(xArr, yArr):
"""
函数说明:岭回归测试
Parameters:
xMat - x数据集
yMat - y数据集
Returns:
wMat - 回归系数矩阵
Website:
http://www.cuijiahua.com/
Modify:
2017-11-20
"""
xMat = np.mat(xArr); yMat = np.mat(yArr).T
#数据标准化
yMean = np.mean(yMat, axis = 0) #行与行操作，求均值
yMat = yMat - yMean #数据减去均值
xMeans = np.mean(xMat, axis = 0) #行与行操作，求均值
xVar = np.var(xMat, axis = 0) #行与行操作，求方差
xMat = (xMat - xMeans) / xVar #数据减去均值除以方差实现标准化
numTestPts = 30 #30个不同的lambda测试
wMat = np.zeros((numTestPts, np.shape(xMat)[1])) #初始回归系数矩阵
for i in range(numTestPts): #改变lambda计算回归系数
ws = ridgeRegres(xMat, yMat, np.exp(i - 10)) #lambda以e的指数变化，最初是一个非常小的数，
wMat[i, :] = ws.T #计算回归系数矩阵
return wMat
def plotwMat():
"""
函数说明:绘制岭回归系数矩阵
Website:
http://www.cuijiahua.com/
Modify:
2017-11-20
"""
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
abX, abY = loadDataSet('abalone.txt')
redgeWeights = ridgeTest(abX, abY)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(redgeWeights)
ax_title_text = ax.set_title(u'log(lambada)与回归系数的关系', FontProperties = font)
ax_xlabel_text = ax.set_xlabel(u'log(lambada)', FontProperties = font)
ax_ylabel_text = ax.set_ylabel(u'回归系数', FontProperties = font)
plt.setp(ax_title_text, size = 20, 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()
def regularize(xMat, yMat):
"""
函数说明:数据标准化
Parameters:
xMat - x数据集
yMat - y数据集
Returns:
inxMat - 标准化后的x数据集
inyMat - 标准化后的y数据集
Website:
http://www.cuijiahua.com/
Modify:
2017-12-03
"""
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
def rssError(yArr,yHatArr):
"""
函数说明:计算平方误差
Parameters:
yArr - 预测值
yHatArr - 真实值
Returns:
Website:
http://www.cuijiahua.com/
Modify:
2017-12-03
"""
return ((yArr-yHatArr)**2).sum()
def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
"""
函数说明:前向逐步线性回归
Parameters:
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
Returns:
returnMat - numIt次迭代的回归系数矩阵
Website:
http://www.cuijiahua.com/
Modify:
2017-12-03
"""
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
def plotstageWiseMat():
"""
函数说明:绘制岭回归系数矩阵
Website:
http://www.cuijiahua.com/
Modify:
2017-12-03
"""
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
xArr, yArr = loadDataSet('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()