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ml/regression/regression_old.py

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2020-02-23 14:14:06 +00:00
#!/usr/bin/env python3
# -*- 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:
2017-11-12
"""
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 standRegres(xArr,yArr):
"""
函数说明:计算回归系数w
Parameters:
xArr - x数据集
yArr - y数据集
Returns:
ws - 回归系数
Website:
http://www.cuijiahua.com/
Modify:
2017-11-12
"""
xMat = np.mat(xArr); yMat = np.mat(yArr).T
xTx = xMat.T * xMat #根据文中推导的公示计算回归系数
if np.linalg.det(xTx) == 0.0:
print("矩阵为奇异矩阵,不能求逆")
return
ws = xTx.I * (xMat.T*yMat)
return ws
def plotDataSet():
"""
函数说明:绘制数据集
Parameters:
Returns:
Website:
http://www.cuijiahua.com/
Modify:
2017-11-12
"""
xArr, yArr = loadDataSet('ex0.txt') #加载数据集
n = len(xArr) #数据个数
xcord = []; ycord = [] #样本点
for i in range(n):
xcord.append(xArr[i][1]); ycord.append(yArr[i]) #样本点
fig = plt.figure()
ax = fig.add_subplot(111) #添加subplot
ax.scatter(xcord, ycord, s = 20, c = 'blue',alpha = .5) #绘制样本点
plt.title('DataSet') #绘制title
plt.xlabel('X')
plt.show()
def plotRegression():
"""
函数说明:绘制回归曲线和数据点
Parameters:
Returns:
Website:
http://www.cuijiahua.com/
Modify:
2017-11-12
"""
xArr, yArr = loadDataSet('ex0.txt') #加载数据集
ws = standRegres(xArr, yArr) #计算回归系数
xMat = np.mat(xArr) #创建xMat矩阵
yMat = np.mat(yArr) #创建yMat矩阵
xCopy = xMat.copy() #深拷贝xMat矩阵
xCopy.sort(0) #排序
yHat = xCopy * ws #计算对应的y值
fig = plt.figure()
ax = fig.add_subplot(111) #添加subplot
ax.plot(xCopy[:, 1], yHat, c = 'red') #绘制回归曲线
ax.scatter(xMat[:,1].flatten().A[0], yMat.flatten().A[0], s = 20, c = 'blue',alpha = .5) #绘制样本点
plt.title('DataSet') #绘制title
plt.xlabel('X')
plt.show()
def plotlwlrRegression():
"""
函数说明:绘制多条局部加权回归曲线
Parameters:
Returns:
Website:
http://www.cuijiahua.com/
Modify:
2017-11-15
"""
#font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
xArr, yArr = loadDataSet('ex0.txt') #加载数据集
yHat_1 = lwlrTest(xArr, xArr, yArr, 1.0) #根据局部加权线性回归计算yHat
yHat_2 = lwlrTest(xArr, xArr, yArr, 0.01) #根据局部加权线性回归计算yHat
yHat_3 = lwlrTest(xArr, xArr, yArr, 0.003) #根据局部加权线性回归计算yHat
xMat = np.mat(xArr) #创建xMat矩阵
yMat = np.mat(yArr) #创建yMat矩阵
srtInd = xMat[:, 1].argsort(0) #排序,返回索引值
xSort = xMat[srtInd][:,0,:]
fig, axs = plt.subplots(nrows=3, ncols=1,sharex=False, sharey=False, figsize=(10,8))
axs[0].plot(xSort[:, 1], yHat_1[srtInd], c = 'red') #绘制回归曲线
axs[1].plot(xSort[:, 1], yHat_2[srtInd], c = 'red') #绘制回归曲线
axs[2].plot(xSort[:, 1], yHat_3[srtInd], c = 'red') #绘制回归曲线
axs[0].scatter(xMat[:,1].flatten().A[0], yMat.flatten().A[0], s = 20, c = 'blue', alpha = .5) #绘制样本点
axs[1].scatter(xMat[:,1].flatten().A[0], yMat.flatten().A[0], s = 20, c = 'blue', alpha = .5) #绘制样本点
axs[2].scatter(xMat[:,1].flatten().A[0], yMat.flatten().A[0], s = 20, c = 'blue', alpha = .5) #绘制样本点
#设置标题,x轴label,y轴label
axs0_title_text = axs[0].set_title(u'Locally weighted regression curve,k=1.0')
axs1_title_text = axs[1].set_title(u'Locally weighted regression curve,k=0.01')
axs2_title_text = axs[2].set_title(u'Locally weighted regression curve,k=0.003')
plt.setp(axs0_title_text, size=8, weight='bold', color='red')
plt.setp(axs1_title_text, size=8, weight='bold', color='red')
plt.setp(axs2_title_text, size=8, weight='bold', color='red')
plt.xlabel('X')
plt.show()
def lwlr(testPoint, xArr, yArr, k = 1.0):
"""
函数说明:使用局部加权线性回归计算回归系数w
Parameters:
testPoint - 测试样本点
xArr - x数据集
yArr - y数据集
k - 高斯核的k,自定义参数
Returns:
ws - 回归系数
Website:
http://www.cuijiahua.com/
Modify:
2017-11-15
"""
xMat = np.mat(xArr); yMat = np.mat(yArr).T
m = np.shape(xMat)[0]
weights = np.mat(np.eye((m))) #创建权重对角矩阵
for j in range(m): #遍历数据集计算每个样本的权重
diffMat = testPoint - xMat[j, :]
weights[j, j] = np.exp(diffMat * diffMat.T/(-2.0 * k**2))
xTx = xMat.T * (weights * xMat)
if np.linalg.det(xTx) == 0.0:
print("矩阵为奇异矩阵,不能求逆")
return
ws = xTx.I * (xMat.T * (weights * yMat)) #计算回归系数
return testPoint * ws
def lwlrTest(testArr, xArr, yArr, k=1.0):
"""
函数说明:局部加权线性回归测试
Parameters:
testArr - 测试数据集
xArr - x数据集
yArr - y数据集
k - 高斯核的k,自定义参数
Returns:
ws - 回归系数
Website:
http://www.cuijiahua.com/
Modify:
2017-11-15
"""
m = np.shape(testArr)[0] #计算测试数据集大小
yHat = np.zeros(m)
for i in range(m): #对每个样本点进行预测
yHat[i] = lwlr(testArr[i],xArr,yArr,k)
return yHat
if __name__ == '__main__':
plotlwlrRegression()