机器学习实战Chp6： SVM-支持向量机--径向基函数---手写数字识别

• 机器学习实战Chp6： SVM-支持向量机–径向基函数—手写数字识别

# -*- coding: utf-8 -*-
"""
Created on Tue Jul 24 20:01:44 2018

@author: muli
"""

# 参考李航《统计学习方法》
# 监督学习一般使用两种类型的目标变量：标称型和数值型
# 标称型：标称型目标变量的结果只在有限目标集中取值，如真与假(标称型目标变量主要用于分类)
# 数值型：数值型目标变量则可以从无限的数值集合中取值，如0.100，42.001等 (数值型目标变量主要用于回归分析)

# 如果所有样本点都可以正确被分类，则我们假设所有点到超平面的距离均大于等于1
#（可以通过将w和b缩放的形式达到该目标），
# 并且称距离唯一的点为支持向量，两个异类支持向量到划分超平面的距离之和为间隔。

from numpy import *
from time import sleep
from os import listdir


# 将图像转换为向量
def img2vector(filename):
    returnVect = zeros((1,1024))
    fr = open(filename)
    for i in range(32):
        lineStr = fr.readline()
        for j in range(32):
            returnVect[0,32*i+j] = int(lineStr[j])
    return returnVect


# 读取数据
def loadImages(dirName):
    hwLabels = []
    trainingFileList = listdir(dirName)           #load the training set
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     #take off .txt
        classNumStr = int(fileStr.split('_')[0])
        # 此处的定义，如果是数字是9为-1，如果数字是1则为1
        if classNumStr == 9: 
            hwLabels.append(-1)
        else: 
            hwLabels.append(1)
        trainingMat[i,:] = img2vector('%s/%s' % (dirName, fileNameStr))
    return trainingMat, hwLabels   


# 用于在区间内选择一个整数，i为alpha的下标，m为alpha的个数
def selectJrand(i,m):
    j=i 
    # 只要函数值不等于输入值i就会随机
    # 因为要满足 ∑alpha(i)*label(i)=0,同时改变两个alpha
    while (j==i):
        j = int(random.uniform(0,m))
    return j


# 用来调整大于H或小于L的alpha值
def clipAlpha(aj,H,L):
    if aj > H: 
        aj = H
    if L > aj:
        aj = L
    return aj


###################################################################
## 完整版的 Platt SMO 算法
###################################################################
# 数据结构的对象
class optStruct:
#    def __init__(self,dataMatIn, classLabels, C, toler):
    def __init__(self,dataMatIn, classLabels, C, toler, kTup):  # 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))) #first column is valid flag
        self.K = mat(zeros((self.m,self.m)))
        for i in range(self.m):
            self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)


# 核转换函数
def kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional space
    m,n = shape(X)
    K = mat(zeros((m,1)))
    if kTup[0]=='lin': 
        K = X * A.T   #linear kernel
    elif kTup[0]=='rbf':
        for j in range(m):
            # 李航《统计学习方法》P122 式 7.90
            # ∆=x-z
            deltaRow = X[j,:] - A
            # K[j] =∆*∆.T=||x-z||²
            K[j] = deltaRow*deltaRow.T
            # kTup[1]=σ
            # 个人认为，下式少一个2,应该为-2*kTup[1]**2
        K = exp(K/(-1*kTup[1]**2)) #divide in NumPy is element-wise not matrix like Matlab
    else: 
        raise NameError('Houston We Have a Problem --That Kernel is not recognized')
    return K


# 模块化 计算fXk的值 
def calcEk(oS, k):
#    fXk = float(multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T)) + oS.b
#    Ek = fXk - float(oS.labelMat[k])
    fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)
    Ek = fXk - float(oS.labelMat[k])
    return Ek

def selectJ(i, oS, Ei):         #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 = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k; maxDeltaE = deltaE; Ej = Ek
        return maxK, Ej
    else:   #in this case (first time around) we don't have any valid eCache values
        j = selectJrand(i, oS.m)
#        j = selectJ(i, oS.m)
        Ej = calcEk(oS, j)
    return j, Ej


def updateEk(oS, k):#after any alpha has changed update the new value in the cache
    Ek = calcEk(oS, k)
    oS.eCache[k] = [1,Ek]


def innerL(i, oS):
    Ei = calcEk(oS, i)
    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 = selectJ(i, oS, Ei) #this has been changed from selectJrand
        alphaIold = oS.alphas[i].copy(); alphaJold = oS.alphas[j].copy();
        if (oS.labelMat[i] != oS.labelMat[j]):
            L = max(0, oS.alphas[j] - oS.alphas[i])
            H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
        else:
            L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
            H = min(oS.C, oS.alphas[j] + oS.alphas[i])
        if L==H: 
            print "L==H"; return 0
        eta = 2.0 * oS.K[i,j] - oS.K[i,i] - oS.K[j,j] #changed for kernel
#        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
        oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/eta
        oS.alphas[j] = clipAlpha(oS.alphas[j],H,L)
        updateEk(oS, j) #added this for the Ecache
        if (abs(oS.alphas[j] - alphaJold) < 0.00001): print "j not moving enough"; return 0
        oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j
        updateEk(oS, i) #added this for the Ecache                    #the update is in the oppostie direction
        b1 = oS.b - Ei- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,i] - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[i,j]
        b2 = oS.b - Ej- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,j]- oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[j,j]
#        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 - Ei- 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
        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 0


# 相当于是 启动函数    
def smoP(dataMatIn, classLabels, C, toler, maxIter,kTup=('lin', 0)):    #full Platt SMO
    oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler,kTup)
    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):        
                alphaPairsChanged += innerL(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 += innerL(i,oS)
                print "non-bound, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged)
            iter += 1
        # 1: 在所有数据集上单遍扫描
        # 2：在非边界 alpha 中 实现单遍扫描
        # 两种交替执行
        if entireSet: 
            entireSet = False #toggle entire set loop
        elif (alphaPairsChanged == 0): 
            entireSet = True  
        print "iteration number: %d" % iter
    return oS.b,oS.alphas


# 计算w值，参考周志华《机器学习》P124 式6.12
def 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 w


# 手写字体识别
def testDigits(kTup=('rbf', 10)):
    dataArr,labelArr = loadImages('digits/trainingDigits')
#    b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1))
    b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)
    datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
    svInd=nonzero(alphas.A>0)[0]
    sVs=datMat[svInd] 
    labelSV = labelMat[svInd];
    print "there are %d Support Vectors" % shape(sVs)[0]
    m,n = shape(datMat)
    # 训练
    errorCount = 0
    for i in range(m):
        kernelEval = kernelTrans(sVs,datMat[i,:],kTup)
        predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b
        if sign(predict)!=sign(labelArr[i]): 
            errorCount += 1
    print "the training error rate is: %f" % (float(errorCount)/m)
    # 测试
    dataArr,labelArr = loadImages('digits/testDigits')
    errorCount = 0
    datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
    m,n = shape(datMat)
    for i in range(m):
        kernelEval = kernelTrans(sVs,datMat[i,:],kTup)
        predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b
        if sign(predict)!=sign(labelArr[i]): 
            errorCount += 1    
    print "the test error rate is: %f" % (float(errorCount)/m) 


# 测试模块
if __name__ == "__main__" :
    # 高斯核函数
#    testDigits(('rbf',10))
    # 线性核函数
    testDigits(('lin',))