140 lines
4.0 KiB
Python
140 lines
4.0 KiB
Python
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#!/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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2017-11-19
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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 lwlr(testPoint, xArr, yArr, k = 1.0):
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"""
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函数说明:使用局部加权线性回归计算回归系数w
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Parameters:
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testPoint - 测试样本点
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xArr - x数据集
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yArr - y数据集
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k - 高斯核的k,自定义参数
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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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2017-11-19
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"""
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xMat = np.mat(xArr); yMat = np.mat(yArr).T
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m = np.shape(xMat)[0]
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weights = np.mat(np.eye((m))) #创建权重对角矩阵
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for j in range(m): #遍历数据集计算每个样本的权重
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diffMat = testPoint - xMat[j, :]
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weights[j, j] = np.exp(diffMat * diffMat.T/(-2.0 * k**2))
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xTx = xMat.T * (weights * xMat)
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if np.linalg.det(xTx) == 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 = xTx.I * (xMat.T * (weights * yMat)) #计算回归系数
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return testPoint * ws
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def lwlrTest(testArr, xArr, yArr, k=1.0):
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"""
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函数说明:局部加权线性回归测试
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Parameters:
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testArr - 测试数据集,测试集
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xArr - x数据集,训练集
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yArr - y数据集,训练集
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k - 高斯核的k,自定义参数
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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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2017-11-19
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"""
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m = np.shape(testArr)[0] #计算测试数据集大小
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yHat = np.zeros(m)
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for i in range(m): #对每个样本点进行预测
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yHat[i] = lwlr(testArr[i],xArr,yArr,k)
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return yHat
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def standRegres(xArr,yArr):
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"""
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函数说明:计算回归系数w
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Parameters:
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xArr - x数据集
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yArr - y数据集
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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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2017-11-19
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"""
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xMat = np.mat(xArr); yMat = np.mat(yArr).T
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xTx = xMat.T * xMat #根据文中推导的公示计算回归系数
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if np.linalg.det(xTx) == 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 = xTx.I * (xMat.T*yMat)
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return ws
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def rssError(yArr, yHatArr):
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"""
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误差大小评价函数
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Parameters:
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yArr - 真实数据
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yHatArr - 预测数据
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Returns:
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误差大小
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"""
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return ((yArr - yHatArr) **2).sum()
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if __name__ == '__main__':
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abX, abY = loadDataSet('abalone.txt')
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print('训练集与测试集相同:局部加权线性回归,核k的大小对预测的影响:')
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yHat01 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 0.1)
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yHat1 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 1)
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yHat10 = lwlrTest(abX[0:99], abX[0:99], abY[0:99], 10)
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print('k=0.1时,误差大小为:',rssError(abY[0:99], yHat01.T))
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print('k=1 时,误差大小为:',rssError(abY[0:99], yHat1.T))
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print('k=10 时,误差大小为:',rssError(abY[0:99], yHat10.T))
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print('')
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print('训练集与测试集不同:局部加权线性回归,核k的大小是越小越好吗？更换数据集,测试结果如下:')
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yHat01 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 0.1)
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yHat1 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 1)
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yHat10 = lwlrTest(abX[100:199], abX[0:99], abY[0:99], 10)
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print('k=0.1时,误差大小为:',rssError(abY[100:199], yHat01.T))
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print('k=1 时,误差大小为:',rssError(abY[100:199], yHat1.T))
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print('k=10 时,误差大小为:',rssError(abY[100:199], yHat10.T))
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print('')
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print('训练集与测试集不同:简单的线性归回与k=1时的局部加权线性回归对比:')
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print('k=1时,误差大小为:', rssError(abY[100:199], yHat1.T))
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ws = standRegres(abX[0:99], abY[0:99])
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yHat = np.mat(abX[100:199]) * ws
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print('简单的线性回归误差大小:', rssError(abY[100:199], yHat.T.A))
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