10 ML locally weighted linear regression

from numpy import *
import matplotlib.pyplot as plt

def loadDataSet(fileName):      #general function to parse tab -delimited floats
    numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields 
    dataMat = []
    labelMat = []

    fr = open(fileName)
    for line in fr.readlines():
        lineArr =[]
        curLine = line.strip().split('\t')
        for i in range(numFeat):
            lineArr.append(float(curLine[i]))
        dataMat.append(lineArr)
        labelMat.append(float(curLine[-1])) # last is label
    return dataMat,labelMat

def lwlr(testPoint, xArr, yArr,k=1.0):
    xMat = mat(xArr)
    yMat = mat(yArr).T

    m = shape(xMat)[0]
    weights = mat(eye((m))) 

    for j in range(m):                      #next 2 lines create weights matrix
        diffMat = testPoint - xMat[j, :]     #
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))

    xTx = xMat.T * (weights * xMat)
    if linalg.det(xTx) == 0.0:
        print "This matrix is singular, cannot do inverse"
        return
    ws = xTx.I * (xMat.T * (weights * yMat))
    return testPoint * ws

def lwlrTest(testArr,xArr,yArr,k=1.0):  #loops over all the data points and applies lwlr to each one
    m = shape(testArr)[0] # row
    yHat = zeros(m)
    for i in range(m):
        yHat[i] = lwlr(testArr[i], xArr, yArr,k)
    return yHat


xArr, yArr = loadDataSet('ex0.txt')
#k = 0.003
#k = 0.01
k = 1.0
yHat = lwlrTest(xArr, xArr, yArr, k)

xMat = mat(xArr)
yMat = mat(yArr)

srtInd = xMat[:, 1].argsort(0) # first need sort
xSort  = xMat[srtInd][:, 0, :]

fig = plt.figure()
ax = fig.add_subplot(111)

ax.plot(xSort[:, 1], yHat[srtInd]) # draw y line
ax.scatter(xMat[:, 1].flatten().A[0], yMat.T.flatten().A[0], s=2, c='red') # scatter plot

plt.show()

1.0

1.0.png

0.01

0.01.png

0.003

3.png