205 lines
5.9 KiB
Python
Executable File
205 lines
5.9 KiB
Python
Executable File
#!/usr/bin/env python3
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# -*-coding:utf-8 -*-
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from matplotlib.font_manager import FontProperties
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import matplotlib.pyplot as plt
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import numpy as np
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def loadDataSet(fileName):
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"""
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函数说明:加载数据
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Parameters:
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fileName - 文件名
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Returns:
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xArr - x数据集
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yArr - y数据集
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-11-20
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"""
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numFeat = len(open(fileName).readline().split('\t')) - 1
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xArr = []; yArr = []
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fr = open(fileName)
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for line in fr.readlines():
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lineArr =[]
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curLine = line.strip().split('\t')
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for i in range(numFeat):
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lineArr.append(float(curLine[i]))
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xArr.append(lineArr)
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yArr.append(float(curLine[-1]))
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return xArr, yArr
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def ridgeRegres(xMat, yMat, lam = 0.2):
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"""
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函数说明:岭回归
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Parameters:
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xMat - x数据集
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yMat - y数据集
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lam - 缩减系数
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Returns:
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ws - 回归系数
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-11-20
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"""
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xTx = xMat.T * xMat
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denom = xTx + np.eye(np.shape(xMat)[1]) * lam
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if np.linalg.det(denom) == 0.0:
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print("矩阵为奇异矩阵,不能求逆")
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return
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ws = denom.I * (xMat.T * yMat)
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return ws
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def ridgeTest(xArr, yArr):
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"""
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函数说明:岭回归测试
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Parameters:
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xMat - x数据集
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yMat - y数据集
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Returns:
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wMat - 回归系数矩阵
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-11-20
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"""
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xMat = np.mat(xArr); yMat = np.mat(yArr).T
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#数据标准化
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yMean = np.mean(yMat, axis = 0) #行与行操作，求均值
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yMat = yMat - yMean #数据减去均值
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xMeans = np.mean(xMat, axis = 0) #行与行操作，求均值
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xVar = np.var(xMat, axis = 0) #行与行操作，求方差
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xMat = (xMat - xMeans) / xVar #数据减去均值除以方差实现标准化
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numTestPts = 30 #30个不同的lambda测试
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wMat = np.zeros((numTestPts, np.shape(xMat)[1])) #初始回归系数矩阵
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for i in range(numTestPts): #改变lambda计算回归系数
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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，
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wMat[i, :] = ws.T #计算回归系数矩阵
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return wMat
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def plotwMat():
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"""
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函数说明:绘制岭回归系数矩阵
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-11-20
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"""
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#font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
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abX, abY = loadDataSet('abalone.txt')
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redgeWeights = ridgeTest(abX, abY)
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fig = plt.figure()
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ax = fig.add_subplot(111)
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ax.plot(redgeWeights)
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ax_title_text = ax.set_title(u'log(lambada) and regession')
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ax_xlabel_text = ax.set_xlabel(u'log(lambada)')
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ax_ylabel_text = ax.set_ylabel(u'regression')
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plt.setp(ax_title_text, size = 20, weight = 'bold', color = 'red')
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plt.setp(ax_xlabel_text, size = 10, weight = 'bold', color = 'black')
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plt.setp(ax_ylabel_text, size = 10, weight = 'bold', color = 'black')
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plt.show()
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def regularize(xMat, yMat):
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"""
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函数说明:数据标准化
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Parameters:
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xMat - x数据集
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yMat - y数据集
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Returns:
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inxMat - 标准化后的x数据集
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inyMat - 标准化后的y数据集
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-12-03
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"""
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inxMat = xMat.copy() #数据拷贝
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inyMat = yMat.copy()
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yMean = np.mean(yMat, 0) #行与行操作，求均值
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inyMat = yMat - yMean #数据减去均值
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inMeans = np.mean(inxMat, 0) #行与行操作，求均值
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inVar = np.var(inxMat, 0) #行与行操作，求方差
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inxMat = (inxMat - inMeans) / inVar #数据减去均值除以方差实现标准化
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return inxMat, inyMat
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def rssError(yArr,yHatArr):
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"""
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函数说明:计算平方误差
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Parameters:
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yArr - 预测值
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yHatArr - 真实值
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Returns:
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-12-03
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"""
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return ((yArr-yHatArr)**2).sum()
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def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
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"""
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函数说明:前向逐步线性回归
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Parameters:
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xArr - x输入数据
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yArr - y预测数据
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eps - 每次迭代需要调整的步长
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numIt - 迭代次数
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Returns:
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returnMat - numIt次迭代的回归系数矩阵
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-12-03
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"""
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xMat = np.mat(xArr); yMat = np.mat(yArr).T #数据集
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xMat, yMat = regularize(xMat, yMat) #数据标准化
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m, n = np.shape(xMat)
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returnMat = np.zeros((numIt, n)) #初始化numIt次迭代的回归系数矩阵
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ws = np.zeros((n, 1)) #初始化回归系数矩阵
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wsTest = ws.copy()
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wsMax = ws.copy()
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for i in range(numIt): #迭代numIt次
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# print(ws.T) #打印当前回归系数矩阵
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lowestError = float('inf'); #正无穷
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for j in range(n): #遍历每个特征的回归系数
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for sign in [-1, 1]:
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wsTest = ws.copy()
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wsTest[j] += eps * sign #微调回归系数
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yTest = xMat * wsTest #计算预测值
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rssE = rssError(yMat.A, yTest.A) #计算平方误差
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if rssE < lowestError: #如果误差更小，则更新当前的最佳回归系数
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lowestError = rssE
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wsMax = wsTest
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ws = wsMax.copy()
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returnMat[i,:] = ws.T #记录numIt次迭代的回归系数矩阵
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return returnMat
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def plotstageWiseMat():
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"""
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函数说明:绘制岭回归系数矩阵
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Website:
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http://www.cuijiahua.com/
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Modify:
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2017-12-03
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"""
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#font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
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xArr, yArr = loadDataSet('abalone.txt')
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returnMat = stageWise(xArr, yArr, 0.005, 1000)
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fig = plt.figure()
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ax = fig.add_subplot(111)
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ax.plot(returnMat)
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ax_title_text = ax.set_title(u'front regression')
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ax_xlabel_text = ax.set_xlabel(u'regression')
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ax_ylabel_text = ax.set_ylabel(u'regression coefficient')
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plt.setp(ax_title_text, size = 15, weight = 'bold', color = 'red')
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plt.setp(ax_xlabel_text, size = 10, weight = 'bold', color = 'black')
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plt.setp(ax_ylabel_text, size = 10, weight = 'bold', color = 'black')
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plt.show()
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if __name__ == '__main__':
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plotstageWiseMat()
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