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#-*-coding:utf8-*-
'''
Created on 2016年5月14日
@author: Gamer Think
'''
from numpy import *
#加载数据集
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("\t")
for i in range(numFeat):
lineArr.append(float(curLine[i]))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat,labelMat
#====================用线性回归找到最佳拟合曲线===========
#计算最佳拟合曲线
def standRegress(xArr,yArr):
xMat = mat(xArr); yMat = mat(yArr).T #.T代表转置矩阵
xTx = xMat.T * xMat
if linalg.det(xTx) ==0.0: #linalg.det(xTx) 计算行列式的值
print "This matrix is singular , cannot do inverse"
return
ws = xTx.I * (xMat.T * yMat)
return ws
#测试上边的函数
xArr,yArr = loadDataSet("ex0.txt")
ws = standRegress(xArr, yArr)
print "ws（相关系数）：",ws #ws 存放的就是回归系数
#画图展示
def show():
import matplotlib.pyplot as plt
xMat = mat(xArr); yMat = mat(yArr)
yHat = xMat*ws
fig = plt.figure() #创建绘图对象
ax = fig.add_subplot(111) #111表示将画布划分为1行2列选择使用从上到下第一块
#scatter绘制散点图
ax.scatter(xMat[:,1].flatten().A[0],yMat.T[:,0].flatten().A[0])
#复制，排序
xCopy =xMat.copy()
xCopy.sort(0)
yHat = xCopy * ws
#plot画线
ax.plot(xCopy[:,1],yHat)
plt.show()
# show()
#利用numpy库提供的corrcoef来计算预测值和真实值得相关性
yHat = mat(xArr) * ws #yHat = xMat * ws
print "相关性：",corrcoef(yHat.T,mat(yArr))
#====================用线性回归找到最佳拟合曲线===========
'''
#==================局部加权线性回归================
def lwlr(testPoint,xArr,yArr,k=1.0):
xMat = mat(xArr); yMat = mat(yArr).T
m = shape(xMat)[0]
weights = mat(eye((m))) #产生对角线矩阵
for j in range(m):
diffMat = testPoint - xMat[j,:]
#更新权重值，以指数级递减
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
xArr,yArr = loadDataSet('ex0.txt')
print "k=1.0：",lwlr(xArr[0],xArr,yArr,1.0)
print "k=0.001：",lwlr(xArr[0],xArr,yArr,0.001)
print "k=0.003：",lwlr(xArr[0],xArr,yArr,0.003)
#画图
def showlwlr():
yHat = lwlrTest(xArr, xArr, yArr, 0.01)
xMat = mat(xArr)
srtInd = xMat[:,1].argsort(0)
xSort = xMat[srtInd][:,0,:]
import matplotlib.pyplot as plt
fig = plt.figure() #创建绘图对象
ax = fig.add_subplot(111) #111表示将画布划分为1行2列选择使用从上到下第一块
ax.plot(xSort[:,1],yHat[srtInd])
#scatter绘制散点图
ax.scatter(xMat[:,1].flatten().A[0],mat(yArr).T[:,0].flatten().A[0],s=2,c='red')
plt.show()
showlwlr()
'''
'''
#=========================岭回归==================
#用于计算回归系数
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
#用于在一组lambda上做测试
def ridgeTest(xArr,yArr):
xMat = mat(xArr); yMat = mat(yArr).T
yMean = mean(yMat,0)
#数据标准化
yMat = yMat - yMean
xMeans = mean(xMat,0)
xVar = var(xMat,0)
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
abX,abY = loadDataSet('abalone.txt')
ridgeWeights = ridgeTest(abX,abY)
# print ridgeWeights
def showRidge():
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(ridgeWeights)
plt.show()
showRidge()
#===================岭回归=============
'''
#===================向前逐步回归============
#计算平方误差
def rssError(yArr,yHatArr): #yArr and yHatArr both need to be arrays
return ((yArr-yHatArr)**2).sum()
#数据标准化处理
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
def stageWise(xArr,yArr,eps=0.01,numIt=100):
xMat = mat(xArr); yMat=mat(yArr).T
yMean = mean(yMat,0)
yMat = yMat - yMean #can also regularize ys but will get smaller coef
xMat = regularize(xMat)
m,n=shape(xMat)
returnMat = zeros((numIt,n)) #testing code remove
ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()
for i in range(numIt):#could change this to while loop
#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()
returnMat[i,:]=ws.T
return returnMat
xArr,yArr = loadDataSet('abalone.txt')
print stageWise(xArr, yArr, 0.01, 200),"\n\n"
# print stageWise(xArr, yArr, 0.001, 200)
xMat = mat(xArr)
yMat = mat(yArr).T
xMat = regularize(xMat)
yM = mean(yMat,0)
yMat = yMat - yM
weights = standRegress(xMat, yMat.T)
print weights.T