<转>SVM实现之SMO算法

#################################################
# SVM: support vector machine
# Author : zouxy
# Date   : 2013-12-12
# HomePage : http://blog.csdn.net/zouxy09
# Email  : zouxy09@qq.com
#################################################

from numpy import *
import time
import matplotlib.pyplot as plt 


# calulate kernel value
def calcKernelValue(matrix_x, sample_x, kernelOption):
    kernelType = kernelOption[0]
    numSamples = matrix_x.shape[0]
    kernelValue = mat(zeros((numSamples, 1)))
    
    if kernelType == ‘linear‘:
        kernelValue = matrix_x * sample_x.T
    elif kernelType == ‘rbf‘:
        sigma = kernelOption[1]
        if sigma == 0:
            sigma = 1.0
        for i in xrange(numSamples):
            diff = matrix_x[i, :] - sample_x
            kernelValue[i] = exp(diff * diff.T / (-2.0 * sigma**2))
    else:
        raise NameError(‘Not support kernel type! You can use linear or rbf!‘)
    return kernelValue


# calculate kernel matrix given train set and kernel type
def calcKernelMatrix(train_x, kernelOption):
    numSamples = train_x.shape[0]
    kernelMatrix = mat(zeros((numSamples, numSamples)))
    for i in xrange(numSamples):
        kernelMatrix[:, i] = calcKernelValue(train_x, train_x[i, :], kernelOption)
    return kernelMatrix


# define a struct just for storing variables and data
class SVMStruct:
    def __init__(self, dataSet, labels, C, toler, kernelOption):
        self.train_x = dataSet # each row stands for a sample
        self.train_y = labels  # corresponding label
        self.C = C             # slack variable
        self.toler = toler     # termination condition for iteration
        self.numSamples = dataSet.shape[0] # number of samples
        self.alphas = mat(zeros((self.numSamples, 1))) # Lagrange factors for all samples
        self.b = 0
        self.errorCache = mat(zeros((self.numSamples, 2)))
        self.kernelOpt = kernelOption
        self.kernelMat = calcKernelMatrix(self.train_x, self.kernelOpt)

        
# calculate the error for alpha k
def calcError(svm, alpha_k):
    output_k = float(multiply(svm.alphas, svm.train_y).T * svm.kernelMat[:, alpha_k] + svm.b)
    error_k = output_k - float(svm.train_y[alpha_k])
    return error_k


# update the error cache for alpha k after optimize alpha k
def updateError(svm, alpha_k):
    error = calcError(svm, alpha_k)
    svm.errorCache[alpha_k] = [1, error]


# select alpha j which has the biggest step
def selectAlpha_j(svm, alpha_i, error_i):
    svm.errorCache[alpha_i] = [1, error_i] # mark as valid(has been optimized)
    candidateAlphaList = nonzero(svm.errorCache[:, 0].A)[0] # mat.A return array
    maxStep = 0; alpha_j = 0; error_j = 0

    # find the alpha with max iterative step
    if len(candidateAlphaList) > 1:
        for alpha_k in candidateAlphaList:
            if alpha_k == alpha_i: 
                continue
            error_k = calcError(svm, alpha_k)
            if abs(error_k - error_i) > maxStep:
                maxStep = abs(error_k - error_i)
                alpha_j = alpha_k
                error_j = error_k
    # if came in this loop first time, we select alpha j randomly
    else:           
        alpha_j = alpha_i
        while alpha_j == alpha_i:
            alpha_j = int(random.uniform(0, svm.numSamples))
        error_j = calcError(svm, alpha_j)
    
    return alpha_j, error_j


# the inner loop for optimizing alpha i and alpha j
def innerLoop(svm, alpha_i):
    error_i = calcError(svm, alpha_i)

    ### check and pick up the alpha who violates the KKT condition
    ## satisfy KKT condition
    # 1) yi*f(i) >= 1 and alpha == 0 (outside the boundary)
    # 2) yi*f(i) == 1 and 0<alpha< C (on the boundary)
    # 3) yi*f(i) <= 1 and alpha == C (between the boundary)
    ## violate KKT condition
    # because y[i]*E_i = y[i]*f(i) - y[i]^2 = y[i]*f(i) - 1, so
    # 1) if y[i]*E_i < 0, so yi*f(i) < 1, if alpha < C, violate!(alpha = C will be correct) 
    # 2) if y[i]*E_i > 0, so yi*f(i) > 1, if alpha > 0, violate!(alpha = 0 will be correct)
    # 3) if y[i]*E_i = 0, so yi*f(i) = 1, it is on the boundary, needless optimized
    if (svm.train_y[alpha_i] * error_i < -svm.toler) and (svm.alphas[alpha_i] < svm.C) or        (svm.train_y[alpha_i] * error_i > svm.toler) and (svm.alphas[alpha_i] > 0):

        # step 1: select alpha j
        alpha_j, error_j = selectAlpha_j(svm, alpha_i, error_i)
        alpha_i_old = svm.alphas[alpha_i].copy()
        alpha_j_old = svm.alphas[alpha_j].copy()

        # step 2: calculate the boundary L and H for alpha j
        if svm.train_y[alpha_i] != svm.train_y[alpha_j]:
            L = max(0, svm.alphas[alpha_j] - svm.alphas[alpha_i])
            H = min(svm.C, svm.C + svm.alphas[alpha_j] - svm.alphas[alpha_i])
        else:
            L = max(0, svm.alphas[alpha_j] + svm.alphas[alpha_i] - svm.C)
            H = min(svm.C, svm.alphas[alpha_j] + svm.alphas[alpha_i])
        if L == H:
            return 0

        # step 3: calculate eta (the similarity of sample i and j)
        eta = 2.0 * svm.kernelMat[alpha_i, alpha_j] - svm.kernelMat[alpha_i, alpha_i]                   - svm.kernelMat[alpha_j, alpha_j]
        if eta >= 0:
            return 0

        # step 4: update alpha j
        svm.alphas[alpha_j] -= svm.train_y[alpha_j] * (error_i - error_j) / eta

        # step 5: clip alpha j
        if svm.alphas[alpha_j] > H:
            svm.alphas[alpha_j] = H
        if svm.alphas[alpha_j] < L:
            svm.alphas[alpha_j] = L

        # step 6: if alpha j not moving enough, just return        
        if abs(alpha_j_old - svm.alphas[alpha_j]) < 0.00001:
            updateError(svm, alpha_j)
            return 0

        # step 7: update alpha i after optimizing aipha j
        svm.alphas[alpha_i] += svm.train_y[alpha_i] * svm.train_y[alpha_j]                                 * (alpha_j_old - svm.alphas[alpha_j])

        # step 8: update threshold b
        b1 = svm.b - error_i - svm.train_y[alpha_i] * (svm.alphas[alpha_i] - alpha_i_old)                                                     * svm.kernelMat[alpha_i, alpha_i]                              - svm.train_y[alpha_j] * (svm.alphas[alpha_j] - alpha_j_old)                                                     * svm.kernelMat[alpha_i, alpha_j]
        b2 = svm.b - error_j - svm.train_y[alpha_i] * (svm.alphas[alpha_i] - alpha_i_old)                                                     * svm.kernelMat[alpha_i, alpha_j]                              - svm.train_y[alpha_j] * (svm.alphas[alpha_j] - alpha_j_old)                                                     * svm.kernelMat[alpha_j, alpha_j]
        if (0 < svm.alphas[alpha_i]) and (svm.alphas[alpha_i] < svm.C):
            svm.b = b1
        elif (0 < svm.alphas[alpha_j]) and (svm.alphas[alpha_j] < svm.C):
            svm.b = b2
        else:
            svm.b = (b1 + b2) / 2.0

        # step 9: update error cache for alpha i, j after optimize alpha i, j and b
        updateError(svm, alpha_j)
        updateError(svm, alpha_i)

        return 1
    else:
        return 0


# the main training procedure
def trainSVM(train_x, train_y, C, toler, maxIter, kernelOption = (‘rbf‘, 1.0)):
    # calculate training time
    startTime = time.time()

    # init data struct for svm
    svm = SVMStruct(mat(train_x), mat(train_y), C, toler, kernelOption)
    
    # start training
    entireSet = True
    alphaPairsChanged = 0
    iterCount = 0
    # Iteration termination condition:
    #     Condition 1: reach max iteration
    #     Condition 2: no alpha changed after going through all samples,
    #                  in other words, all alpha (samples) fit KKT condition
    while (iterCount < maxIter) and ((alphaPairsChanged > 0) or entireSet):
        alphaPairsChanged = 0

        # update alphas over all training examples
        if entireSet:
            for i in xrange(svm.numSamples):
                alphaPairsChanged += innerLoop(svm, i)
            print ‘---iter:%d entire set, alpha pairs changed:%d‘ % (iterCount, alphaPairsChanged)
            iterCount += 1
        # update alphas over examples where alpha is not 0 & not C (not on boundary)
        else:
            nonBoundAlphasList = nonzero((svm.alphas.A > 0) * (svm.alphas.A < svm.C))[0]
            for i in nonBoundAlphasList:
                alphaPairsChanged += innerLoop(svm, i)
            print ‘---iter:%d non boundary, alpha pairs changed:%d‘ % (iterCount, alphaPairsChanged)
            iterCount += 1

        # alternate loop over all examples and non-boundary examples
        if entireSet:
            entireSet = False
        elif alphaPairsChanged == 0:
            entireSet = True

    print ‘Congratulations, training complete! Took %fs!‘ % (time.time() - startTime)
    return svm


# testing your trained svm model given test set
def testSVM(svm, test_x, test_y):
    test_x = mat(test_x)
    test_y = mat(test_y)
    numTestSamples = test_x.shape[0]
    supportVectorsIndex = nonzero(svm.alphas.A > 0)[0]
    supportVectors         = svm.train_x[supportVectorsIndex]
    supportVectorLabels = svm.train_y[supportVectorsIndex]
    supportVectorAlphas = svm.alphas[supportVectorsIndex]
    matchCount = 0
    for i in xrange(numTestSamples):
        kernelValue = calcKernelValue(supportVectors, test_x[i, :], svm.kernelOpt)
        predict = kernelValue.T * multiply(supportVectorLabels, supportVectorAlphas) + svm.b
        if sign(predict) == sign(test_y[i]):
            matchCount += 1
    accuracy = float(matchCount) / numTestSamples
    return accuracy


# show your trained svm model only available with 2-D data
def showSVM(svm):
    if svm.train_x.shape[1] != 2:
        print "Sorry! I can not draw because the dimension of your data is not 2!"
        return 1

    # draw all samples
    for i in xrange(svm.numSamples):
        if svm.train_y[i] == -1:
            plt.plot(svm.train_x[i, 0], svm.train_x[i, 1], ‘or‘)
        elif svm.train_y[i] == 1:
            plt.plot(svm.train_x[i, 0], svm.train_x[i, 1], ‘ob‘)

    # mark support vectors
    supportVectorsIndex = nonzero(svm.alphas.A > 0)[0]
    for i in supportVectorsIndex:
        plt.plot(svm.train_x[i, 0], svm.train_x[i, 1], ‘oy‘)
    
    # draw the classify line
    w = zeros((2, 1))
    for i in supportVectorsIndex:
        w += multiply(svm.alphas[i] * svm.train_y[i], svm.train_x[i, :].T) 
    min_x = min(svm.train_x[:, 0])[0, 0]
    max_x = max(svm.train_x[:, 0])[0, 0]
    y_min_x = float(-svm.b - w[0] * min_x) / w[1]
    y_max_x = float(-svm.b - w[0] * max_x) / w[1]
    plt.plot([min_x, max_x], [y_min_x, y_max_x], ‘-g‘)
    plt.show()

#################################################
# SVM: support vector machine
# Author : zouxy
# Date   : 2013-12-12
# HomePage : http://blog.csdn.net/zouxy09
# Email  : zouxy09@qq.com
#################################################

from numpy import *
import SVM

################## test svm #####################
## step 1: load data
print "step 1: load data..."
dataSet = []
labels = []
fileIn = open(‘E:/Python/Machine Learning in Action/testSet.txt‘)
for line in fileIn.readlines():
    lineArr = line.strip().split(‘\t‘)
    dataSet.append([float(lineArr[0]), float(lineArr[1])])
    labels.append(float(lineArr[2]))

dataSet = mat(dataSet)
labels = mat(labels).T
train_x = dataSet[0:81, :]
train_y = labels[0:81, :]
test_x = dataSet[80:101, :]
test_y = labels[80:101, :]

## step 2: training...
print "step 2: training..."
C = 0.6
toler = 0.001
maxIter = 50
svmClassifier = SVM.trainSVM(train_x, train_y, C, toler, maxIter, kernelOption = (‘linear‘, 0))

## step 3: testing
print "step 3: testing..."
accuracy = SVM.testSVM(svmClassifier, test_x, test_y)

## step 4: show the result
print "step 4: show the result..."    
print ‘The classify accuracy is: %.3f%%‘ % (accuracy * 100)
SVM.showSVM(svmClassifier)