机器学习实战 支持向量机

#!/usr/bin/env python# -*- coding: utf-8 -*-from numpy import *'''#######********************************Non-Kernel VErsions below#######********************************'''def loadDataSet(fileName):    dataMat = []; labelMat = []    fr = open(fileName)    for line in fr.readlines():        lineArr = line.strip().split('\t')        dataMat.append([float(lineArr[0]), float(lineArr[1])])        labelMat.append(float(lineArr[2]))    return dataMat,labelMatdef selectJrand(i,m):    j=i #we want to select any J not equal to i    while (j==i):        j = int(random.uniform(0,m))    return jdef clipAlpha(aj,H,L):    # 考虑无约束条件0<=a2<=C的解    # a2(new)= H, a2(new,unc) > H    #       = a2(new,unc), L <= a2(new,unc) <= H    #       = L, a2(new,unc) < L    if aj > H:         aj = H    if L > aj:        aj = L    return ajclass optStructK:    def __init__(self,dataMatIn, classLabels, C, toler):  # Initialize the structure with the parameters         self.X = dataMatIn        self.labelMat = classLabels        self.C = C        self.tol = toler        self.m = shape(dataMatIn)[0]        self.alphas = mat(zeros((self.m,1)))        self.b = 0        self.eCache = mat(zeros((self.m,2))) #误差缓存 #first column is valid flag#第一列为是否有效标志位        def calcEkK(oS, k):    # 分类函数    # F(X)= W.T * X + b    # W.T=∑(aj*yj)  X = ∑(Xj*Xi.T)    # F(Xi)= ∑((aj*yj)*(Xj*Xi.T)) + b    fXk = float(multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T)) + oS.b    Ek = fXk - float(oS.labelMat[k])#误差    return Ek        def selectJK(i, oS, Ei): #寻找满足条件max|E1-E2|的乘子a2   #this is the second choice -heurstic, and calcs Ej    maxK = -1; maxDeltaE = 0; Ej = 0    oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta E    validEcacheList = nonzero(oS.eCache[:,0].A)[0]    if (len(validEcacheList)) > 1:        for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta E            if k == i: continue #don't calc for i, waste of time            Ek = calcEkK(oS, k)            deltaE = abs(Ei - Ek)            if (deltaE > maxDeltaE):                maxK = k; maxDeltaE = deltaE; Ej = Ek        return maxK, Ej    else:#第一次循环 随机选择 #in this case (first time around) we don't have any valid eCache values        j = selectJrand(i, oS.m)        Ej = calcEkK(oS, j)    return j, Ejdef updateEkK(oS, k):#after any alpha has changed update the new value in the cache    Ek = calcEkK(oS, k)    oS.eCache[k] = [1,Ek]        def innerLK(i, oS):    Ei = calcEkK(oS, i)    # 第一个约束条件，存在不满足KKT条件的ai,需要更新这些ai    # 不满足KKT条件的情况:yi*ui<=1且ai<C, yi*ui>=1且ai>0, yi*ui=1且ai=C    if ((oS.labelMat[i]*Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or ((oS.labelMat[i]*Ei > oS.tol) and (oS.alphas[i] > 0)):        j,Ej = selectJK(i, oS, Ei) #this has been changed from selectJrand        alphaIold = oS.alphas[i].copy(); alphaJold = oS.alphas[j].copy();        # 由第二个约束条件 ∑ai*yi = 0 得 a1(new)*y1+a2(new)*y2 = a1(old)*y1+a2(odl)*y2 = ζ        if (oS.labelMat[i] != oS.labelMat[j]):               #当y1 != y2 ,则alphas[j] - alphas[i] = ζ            L = max(0, oS.alphas[j] - oS.alphas[i])          #L = max(0,-ζ)            H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])#H = min(C,C-ζ)        else:                                                #当y1 = y2,则alphas[j] + alphas[i] = ζ            L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)   #L = max(0,ζ-C)            H = min(oS.C, oS.alphas[j] + oS.alphas[i])       #H = min(C,ζ)        if L==H: print "L==H"; return 0        # eta是alpha[j]的最优修改量        # eta = η = 2*k(x1,x2)-k(x1,x1)-k(x2,x2)        eta = 2.0 * oS.X[i,:]*oS.X[j,:].T - oS.X[i,:]*oS.X[i,:].T - oS.X[j,:]*oS.X[j,:].T        if eta >= 0: print "eta>=0"; return 0        #更新a2        #a2(new,unc)=a2(old)-y2*(E1-E2)/η #无约束条件0<=a2<=C的解，即未经剪辑时的解        oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/eta        # 考虑有约束条件0<=a2<=C的解        # a2(new)= H, a2(new,unc) > H        #       = a2(new,unc), L <= a2(new,unc) <= H        #       = L, a2(new,unc) < L        oS.alphas[j] = clipAlpha(oS.alphas[j],H,L)        updateEkK(oS, j) #added this for the Ecache        if (abs(oS.alphas[j] - alphaJold) < 0.00001): print "j not moving enough"; return 0        # 更新a1        # a1(new) = a1(old)+y1*y2*(a2(old)-a2(new))        oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j        updateEkK(oS, i) #added this for the Ecache                    #the update is in the oppostie direction        # 更新b        # b1=b(old) - E1 - y1*(a1(new)-a1(old))k(x1,x1) - y2(a2(new)-a2(old))k(x1,x2)        # b2=b(old) - E2 - y1*(a1(new)-a1(old))k(x1,x2) - y2(a2(new)-a2(old))k(x2,x2)        b1 = oS.b - Ei- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.X[i,:]*oS.X[i,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[i,:]*oS.X[j,:].T        b2 = oS.b - Ej- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.X[i,:]*oS.X[j,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[j,:]*oS.X[j,:].T        # b = b1, 0<a1(new)<C        #  = b2, 0<a2(new)<C        #  = (b1+b2)/2,其他        if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]): oS.b = b1        elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2        else: oS.b = (b1 + b2)/2.0        return 1    else: return 0def smoPK(dataMatIn, classLabels, C, toler, maxIter): #数据集 类别标签 常数C 容错律 最大循环数   #full Platt SMO    oS = optStructK(mat(dataMatIn),mat(classLabels).transpose(),C,toler)    iter = 0    entireSet = True; alphaPairsChanged = 0    while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):        alphaPairsChanged = 0        if entireSet:   #go over all            for i in range(oS.m):#self.m = shape(dataMatIn)[0]=100                alphaPairsChanged += innerLK(i,oS)                print "fullSet, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged)            iter += 1        else:#go over non-bound (railed) alphas            nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]            for i in nonBoundIs:                alphaPairsChanged += innerLK(i,oS)                print "non-bound, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged)            iter += 1        if entireSet: entireSet = False #toggle entire set loop        elif (alphaPairsChanged == 0): entireSet = True          print "iteration number: %d" % iter    return oS.b,oS.alphasdef calcWs(alphas,dataArr,classLabels):    X = mat(dataArr); labelMat = mat(classLabels).transpose()    m,n = shape(X)    w = zeros((n,1))    for i in range(m):        w += multiply(alphas[i]*labelMat[i],X[i,:].T)    return wif __name__ == '__main__':    dataArr, labelArr = loadDataSet('testSet.txt')    b, alphas = smoPK(dataArr, labelArr, 0.6, 0.001, 40)#数据集 类别标签 常数C 容错律 最大循环数    print 'b:',b    print 'alphas[alphas>0]:',alphas[alphas>0]    for i in range(100):        if alphas[i]>0.0: print '支持向量:', dataArr[i], labelArr[i]    ws = calcWs(alphas, dataArr, labelArr)    print ws    datMat = mat(dataArr)    print datMat[0]*mat(ws)+b, labelArr[0]

testSet.txt:

3.542485    1.977398    -1
3.018896    2.556416    -1
7.551510    -1.580030    1
2.114999    -0.004466    -1
8.127113    1.274372    1
7.108772    -0.986906    1
8.610639    2.046708    1
2.326297    0.265213    -1
3.634009    1.730537    -1
0.341367    -0.894998    -1
3.125951    0.293251    -1