机器学习线性回归实现
代码链接：
from numpy import *
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
dataMat = []
labelMat = []
fr = open(fileName)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split()
for i in range(numFeat):
lineArr.append(float(curLine[i]))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
def standRegres(xArr, yArr):
xMat = mat(xArr)
yMat = mat(yArr).T
xTx = xMat.T * xMat
if linalg.det(xTx) == 0.0:
print("This matrix is singular, cannot do inverse")
return
ws = xTx.I * (xMat.T * yMat)
return ws
def lwlr(testPoint, xArr, yArr, k=1.0):
xMat = mat(xArr)
yMat = mat(yArr).T
m = shape(xMat)[0]
weights = mat(eye((m))) # 单位矩阵, 对角线为1, 其他位置为0的矩阵
for j in range(m):
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):
m = shape(testArr)[0]
yHat = zeros(m)
for i in range(m):
yHat[i] = lwlr(testArr[i], xArr, yArr, k)
return yHat
def rssError(yArr, yHatArr):
return ((yArr - yHatArr) ** 2).sum()
# 计算回归系数
def ridgeRegres(xMat, yMat, lam=0.2):
xTx = xMat.T * xMat
denom = xTx + eye(shape(xMat)[1]) * lam
if linalg.det(denom) == 0.0:
print("This matrix is singular, cannot do inverse")
return
ws = denom.I * (xMat.T * yMat)
return ws
def ridgeTest(xArr, yArr):
xMat = mat(xArr)
yMat = mat(yArr).T
yMean = mean(yMat, 0) # 计算均值向量
yMat = yMat - yMean
xMeans = mean(xMat, 0)
xVar = var(xMat, 0) # 计算方差向量
xMat = (xMat - xMeans) / xVar
numTestPts = 30
wMat = zeros((numTestPts, shape(xMat)[1]))
for i in range(numTestPts):
ws = ridgeRegres(xMat, yMat, exp(i - 10))
wMat[i, :] = ws.T
return wMat
def regularize(xMat): # regularize by columns
inMat = xMat.copy()
inMeans = mean(inMat, 0) # calc mean then subtract it off
inVar = var(inMat, 0) # calc variance of Xi then divide by it
inMat = (inMat - inMeans) / inVar
return inMat
# xArr输入数据, yArr预测向量
# eps每次迭代需要调整的步长, numIt迭代次数
def stageWise(xArr, yArr, eps=0.01, numIt=100):
xMat = mat(xArr)
yMat = mat(yArr).T
yMean = mean(yMat, 0)
yMat = yMat - yMean
xMat = regularize(xMat)
m, n = shape(xMat)
returnMat = zeros((numIt, n))
ws = zeros((n, 1))
wsTest = ws.copy()
wsMax = ws.copy()
for i in range(numIt):
print(ws.T)
lowestError = inf
for j in range(n):
for sign in [-1, 1]:
wsTest = ws.copy()
wsTest[j] += eps * sign
yTest = xMat * wsTest
rssE = rssError(yMat.A, yTest.A)
if rssE < lowestError:
lowestError = rssE
wsMax = wsTest
ws = wsMax.copy() # 下一迭代从wsMax开始
returnMat[i, :] = ws.T
return returnMat
from time import sleep
import json
import urllib.request
def searchForSet(retX, retY, setNum, yr, numPce, origPrc):
sleep(10)
myAPIstr = 'get from code.google.com'
searchURL = 'https://www.googleapis.com/shopping/search/v1/' \
'public/products?key=%s&country=US&q=lego+%d&alt=json' % (myAPIstr, setNum)
pg = urllib.request.urlopen(searchURL)
retDict = json.loads(pg.read())
for i in range(len(retDict['items'])):
try:
curItem = retDict['items'][i]
if curItem['product']['condition'] == 'new':
newFlag = 1
else:
newFlag = 0
listOfInv = curItem['product']['inventories']
for item in listOfInv:
sellingPrice = item['price']
if sellingPrice > origPrc * 0.5:
print("%d\t%d\t%d\t%f\t%f" % (yr, numPce, newFlag, origPrc, sellingPrice))
retX.append([yr, numPce, newFlag, origPrc])
retY.append(sellingPrice)
except:
print('problem with item %d' % i)
# 数据收集
def setDataCollect(retX, retY):
searchForSet(retX, retY, 8288, 2006, 800, 49.99)
searchForSet(retX, retY, 10030, 2002, 3096, 269.99)
searchForSet(retX, retY, 10179, 2007, 5195, 499.99)
searchForSet(retX, retY, 10081, 2007, 3428, 199.99)
searchForSet(retX, retY, 10189, 2008, 5922, 299.99)
searchForSet(retX, retY, 10196, 2009, 3263, 249.99)
'''
shape(lgX)
lgX1= mat(ones((58,5)))
lgX1[:,1:5] = mat(lgX)
lgX[0]
lgX1[0]
ws = regression.standRegres(lgX1, lgY)
ws
lgX1[0]*ws
lgX1[-1]*ws
lgX1[43]*ws
'''
# xArr,yArr存放数据集x,y值
# numVal为交叉验证次数
def crossValidation(xArr, yArr, numVal=10):
m = len(yArr)
indexList = range(m)
errorMat = zeros((numVal, 30))
for i in range(numVal):
trainX = []
trainY = []
testX = []
testY = []
random.shuffle(indexList)
for j in range(m):
if j < m * 0.9:
trainX.append(xArr[indexList[j]])
trainY.append(yArr[indexList[j]])
else:
testX.append(xArr[indexList[j]])
testY.append(yArr[indexList[j]])
wMat = ridgeTest(trainX, trainY)
for k in range(30):
matTestX = mat(testX)
matTrainX = mat(trainX)
meanTrain = mean(matTrainX, 0)
varTrain = var(matTrainX, 0)
matTestX = (matTestX - meanTrain) / varTrain
yEst = matTestX * mat(wMat[k, :]).T + mean(trainY)
errorMat[i, k] = rssError(yEst.T.A, array(testY))
meanErrors = mean(errorMat, 0)
minMean = float(min(meanErrors))
bestWeights = wMat(nonzero(meanErrors == minMean))
xMat = mat(xArr)
yMat = mat(yArr).T
meanX = mean(xMat, 0)
varX = var(xMat, 0)
unReg = bestWeights / varX
print("the best model from Ridge Regression is:\n", unReg)
print("with constant term:", -1 * sum(multiply(meanX, unReg)) + mean(yMat))
'''
regression.crossValidation(lgX, lgY, 10)
regression.ridgeTest(lgX,lgY)
'''