SVM.py

import numpy as np


def selectJrand(i, m):
    j = i  # 随机找一个不等于i的j
    while (j == i):
        j = int(np.random.uniform(0, m))
    return j


def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
    dataMatrix = np.mat(dataMatIn);
    labelMat = np.mat(classLabels).transpose()
    b = 0;
    m, n = np.shape(dataMatrix)
    alphas = np.mat(np.zeros((m, 1)))
    iter = 0
    while (iter < maxIter):
        alphaPairsChanged = 0
        for i in range(m):
            fXi = float(np.multiply(alphas, labelMat).T * (dataMatrix * dataMatrix[i, :].T)) + b
            Ei = fXi - float(labelMat[i])  # if checks if an example violates KKT conditions
            if ((labelMat[i] * Ei < -toler) and (alphas[i] < C)) or ((labelMat[i] * Ei > toler) and (alphas[i] > 0)):
                j = selectJrand(i, m)
                fXj = float(np.multiply(alphas, labelMat).T * (dataMatrix * dataMatrix[j, :].T)) + b
                Ej = fXj - float(labelMat[j])
                alphaIold = alphas[i].copy();
                alphaJold = alphas[j].copy();
                if (labelMat[i] != labelMat[j]):
                    L = max(0, alphas[j] - alphas[i])
                    H = min(C, C + alphas[j] - alphas[i])
                else:
                    L = max(0, alphas[j] + alphas[i] - C)
                    H = min(C, alphas[j] + alphas[i])
                if L == H:
                    print("L==H")
                    continue
                eta = 2.0 * dataMatrix[i, :] * dataMatrix[j, :].T - dataMatrix[i, :] * dataMatrix[i, :].T - dataMatrix[
                                                                                                            j,
                                                                                                            :] * dataMatrix[
                                                                                                                 j, :].T
                if eta >= 0:
                    print("eta>=0")
                    continue
                alphas[j] -= labelMat[j] * (Ei - Ej) / eta
                alphas[j] = clipAlpha(alphas[j], H, L)
                if (abs(alphas[j] - alphaJold) < 0.00001):
                    print("j not moving enough")
                    continue
                alphas[i] += labelMat[j] * labelMat[i] * (alphaJold - alphas[j])  # update i by the same amount as j
                # the update is in the oppostie direction
                b1 = b - Ei - labelMat[i] * (alphas[i] - alphaIold) * dataMatrix[i, :] * dataMatrix[i, :].T - labelMat[
                    j] * (alphas[j] - alphaJold) * dataMatrix[i, :] * dataMatrix[j, :].T
                b2 = b - Ej - labelMat[i] * (alphas[i] - alphaIold) * dataMatrix[i, :] * dataMatrix[j, :].T - labelMat[
                    j] * (alphas[j] - alphaJold) * dataMatrix[j, :] * dataMatrix[j, :].T
                if (0 < alphas[i]) and (C > alphas[i]):
                    b = b1
                elif (0 < alphas[j]) and (C > alphas[j]):
                    b = b2
                else:
                    b = (b1 + b2) / 2.0
                alphaPairsChanged += 1
                print("iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
        if (alphaPairsChanged == 0):
            iter += 1
        else:
            iter = 0
        print("iteration number: %d" % iter)
    return b, alphas


def kernelTrans(X, A, kTup):  # 计算核函数值，将样本映射到高维空间
    m, n = np.shape(X)
    K = np.mat(np.zeros((m, 1)))
    if kTup[0] == 'lin':
        K = X * A.T  # linear kernel 线性核
    elif kTup[0] == 'rbf':  # 高斯核函数
        for j in range(m):
            deltaRow = X[j, :] - A
            K[j] = deltaRow * deltaRow.T
        K = np.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


class optStruct:
    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 = np.shape(dataMatIn)[0]
        self.alphas = np.mat(np.zeros((self.m, 1)))
        self.b = 0
        self.eCache = np.mat(np.zeros((self.m, 2)))  # first column is valid flag
        self.K = np.mat(np.zeros((self.m, self.m)))
        for i in range(self.m):  # 暴力n^2算出所有xTx对的核函数值
            self.K[:, i] = kernelTrans(self.X, self.X[i, :], kTup)


def calcEk(oS, k):
    fXk = float(np.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 = np.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)
        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 clipAlpha(aj, H, L):
    if aj > H:
        aj = H
    if L > aj:
        aj = L
    return aj


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
        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]
        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


def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):  # full Platt SMO
    oS = optStruct(np.mat(dataMatIn), np.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 = np.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
        if entireSet:
            entireSet = False  # toggle entire set loop
        elif (alphaPairsChanged == 0):
            entireSet = True
        print("iteration number: %d" % iter)
    return oS.b, oS.alphas


def calcWs(alphas, dataArr, classLabels):
    X = np.mat(dataArr)
    labelMat = np.mat(classLabels).transpose()
    m, n = np.shape(X)
    w = np.zeros((1, n))  # 横向
    for i in range(m):
        w += np.multiply(alphas[i] * labelMat[i], X[i, :])
    return np.mat(w)


def SMO(dataSetIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
    # b, alphas = smoSimple(dataSetIn, classLabels, C, toler, maxIter)
    b, alphas = smoP(dataSetIn, classLabels, C, toler, maxIter, kTup)  # SVM 训练
    w = calcWs(alphas, dataSetIn, classLabels)  # 计算w
    return w, b, alphas  # 返回类型均为np.matrix   w(1,n),b(1,1),alpha(m,1)


# 以下是SVM测试：
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, labelMat


def plot_vector(dataSet, label, b, alphlas):
    import matplotlib.pyplot as plt

    xcord1 = []
    ycord1 = []
    xcord2 = []
    ycord2 = []
    for i in range(len(dataSet)):
        if alphlas[i] == 0.0:
            xcord1.append(dataSet[i][0])
            ycord1.append(dataSet[i][1])
        else:
            xcord2.append(dataSet[i][0])  # 支持向量
            ycord2.append(dataSet[i][1])

    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xcord1, ycord1, s=30, c='black', marker='s')
    ax.scatter(xcord2, ycord2, s=30, c='red')

    plt.xlabel('X1')
    plt.ylabel('X2')
    plt.show()


if __name__ == '__main__':
    dataSet, label = loadDataSet('svm_testSet.txt')
    b, alphas = smoP(dataSet, label, 0.6, 0.001, 40)
    plot_vector(dataSet, label, b, alphas)