python中svm方法實現

資料如下：

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
2.123252    ,-0.783563  , -1
0.887835    ,-2.797792  , -1
7.139979    ,-2.329896  , 1
1.696414    ,-1.212496  , -1
8.117032    ,0.623493   , 1
8.497162    ,-0.266649  , 1
4.658191    ,3.507396   ,-1
8.197181    ,1.545132    ,1
1.208047    ,0.213100    ,-1
1.928486    ,-0.321870   ,-1
2.175808    ,-0.014527   ,-1
7.886608    ,0.461755    ,1
3.223038    ,-0.552392   ,-1
3.628502    ,2.190585    ,-1
7.407860    ,-0.121961   ,1
7.286357    ,0.251077    ,1
2.301095    ,-0.533988   ,-1
-0.232542   ,-0.547690   ,-1
3.457096    ,-0.082216   ,-1
3.023938    ,-0.057392   ,-1
8.015003    ,0.885325    ,1
8.991748    ,0.923154    ,1
7.916831    ,-1.781735   ,1
7.616862    ,-0.217958   ,1
2.450939    ,0.744967    ,-1
7.270337    ,-2.507834   ,1
1.749721    ,-0.961902   ,-1
1.803111    ,-0.176349   ,-1
8.804461    ,3.044301    ,1
1.231257    ,-0.568573   ,-1
2.074915    ,1.410550    ,-1
-0.743036   ,-1.736103   ,-1
3.536555    ,3.964960    ,-1
8.410143    ,0.025606    ,1
7.382988    ,-0.478764   ,1
6.960661    ,-0.245353   ,1
8.234460    ,0.701868    ,1
8.168618    ,-0.903835   ,1
1.534187    ,-0.622492   ,-1
9.229518    ,2.066088    ,1
7.886242    ,0.191813    ,1
2.893743    ,-1.643468   ,-1
1.870457    ,-1.040420   ,-1
5.286862    ,-2.358286   ,1
6.080573    ,0.418886    ,1
2.544314    ,1.714165    ,-1
6.016004    ,-3.753712   ,1
0.926310    ,-0.564359   ,-1
0.870296    ,-0.109952   ,-1
2.369345    ,1.375695    ,-1
1.363782    ,-0.254082   ,-1
7.279460    ,-0.189572   ,1
1.896005    ,0.515080    ,-1
8.102154    ,-0.603875   ,1
2.529893    ,0.662657    ,-1
1.963874    ,-0.365233   ,-1
8.132048    ,0.785914    ,1
8.245938    ,0.372366    ,1
6.543888    ,0.433164    ,1
-0.236713   ,-5.766721   ,-1
8.112593    ,0.295839    ,1
9.803425    ,1.495167    ,1
1.497407    ,-0.552916   ,-1
1.336267    ,-1.632889   ,-1
9.205805    ,-0.586480   ,1
1.966279    ,-1.840439   ,-1
8.398012    ,1.584918    ,1
7.239953    ,-1.764292   ,1
7.556201    ,0.241185    ,1
9.015509    ,0.345019    ,1
8.266085    ,-0.230977   ,1
8.545620    ,2.788799    ,1
9.295969    ,1.346332    ,1
2.404234    ,0.570278    ,-1
2.037772    ,0.021919    ,-1
1.727631    ,-0.453143   ,-1
1.979395    ,-0.050773   ,-1
8.092288    ,-1.372433   ,1
1.667645    ,0.239204    ,-1
9.854303    ,1.365116    ,1
7.921057    ,-1.327587   ,1
8.500757    ,1.492372    ,1
1.339746    ,-0.291183   ,-1
3.107511    ,0.758367    ,-1
2.609525    ,0.902979    ,-1
3.263585    ,1.367898    ,-1
2.912122    ,-0.202359   ,-1
1.731786    ,0.589096    ,-1
2.387003    ,1.573131    ,-1

python程式碼如下：

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

def loadDataSet(fileName):
    dataMat = []
    labelMat = []
    with open(fileName) as fr:
        for line in fr:
            lineArr = line.split(',')
            print(line)
            dataMat.append([float(lineArr[0]), float(lineArr[1])])
            labelMat.append(float(lineArr[2]))
    return dataMat, labelMat

def selectJrand(i, m):
    j = i
    while (j == i):
        j = int(random.uniform(0, m))
    return j

def clipAlpha(aj, H, L):
    if aj > H:
        aj = H
    if L > aj:
        aj = L
    return aj

class optStruct:
    def __init__(self, dataMatIn, classLabels, C, toler):
        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)))

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])
    return Ek

def selectJ(i, oS, Ei):
    maxK = -1
    maxDeltaE = 0
    Ej = 0
    oS.eCache[i] = [1, Ei]
    validEcacheList = nonzero(oS.eCache[:, 0].A)[0]
    if (len(validEcacheList)) > 1:
        for k in validEcacheList:
            if k == i:
                continue
            Ek = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k
                maxDeltaE = deltaE
                Ej = Ek
        return maxK, Ej
    else:
        j = selectJrand(i, oS.m)
        Ej = calcEk(oS, j)
    return j, Ej

def updateEk(oS, k):
    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)
        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.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)
        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])
        updateEk(oS, i)
        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

def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
    """
    輸入：資料集, 類別標籤, 常數C, 容錯率, 最大迴圈次數
    輸出：目標b, 引數alphas
    """
    oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler)
    iterr = 0
    entireSet = True
    alphaPairsChanged = 0
    while (iterr < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
        alphaPairsChanged = 0
        if entireSet:
            for i in range(oS.m):
                alphaPairsChanged += innerL(i, oS)
            # print("fullSet, iter: %d i:%d, pairs changed %d" % (iterr, i, alphaPairsChanged))
            iterr += 1
        else:
            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" % (iterr, i, alphaPairsChanged))
            iterr += 1
        if entireSet:
            entireSet = False
        elif (alphaPairsChanged == 0):
            entireSet = True
        # print("iteration number: %d" % iterr)
    return oS.b, oS.alphas

def calcWs(alphas, dataArr, classLabels):
    """
    輸入：alphas, 資料集, 類別標籤
    輸出：目標w
    """
    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

def plotFeature(dataMat, labelMat, weights, b):
    dataArr = array(dataMat)
    n = shape(dataArr)[0]
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(n):
        if int(labelMat[i]) == 1:
            xcord1.append(dataArr[i, 0])
            ycord1.append(dataArr[i, 1])
        else:
            xcord2.append(dataArr[i, 0])
            ycord2.append(dataArr[i, 1])
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
    ax.scatter(xcord2, ycord2, s=30, c='green')
    x = arange(2, 7.0, 0.1)
    y = (-b[0, 0] * x) - 10 / linalg.norm(weights)
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2')
    plt.show()

def main():
    trainDataSet, trainLabel = loadDataSet('testSet.txt')
    b, alphas = smoP(trainDataSet, trainLabel, 0.6, 0.0001, 40)
    ws = calcWs(alphas, trainDataSet, trainLabel)
    print("ws = \n", ws)
    print("b = \n", b)
    plotFeature(trainDataSet, trainLabel, ws, b)

if __name__ == '__main__':
    start = time.clock()
    main()
    end = time.clock()
    print('finish all in %s' % str(end - start))

實驗結果：

ws = 
 [[ 0.65307162]
 [-0.17196128]]
b = 
 [[-2.89901748]]

圖片