simpleSmo

该代码是在理解了svm方法及smo的原理的基础上写的，不过因为编程水平有限加上对svm和smo的理解还不够透彻，原版代码只有该版代码的50％左右，最终还是改成了书上的版本。

import random
from numpy import *

def loadDataSet(filename):                                        #读取数据文件并进行处理。得到数据点数组和分类数组
    dataMat = [];labelMat = []
    fr = open(filename)
    for read in fr.readlines():
        lineArr = read.strip().split('\t')
        dataMat.append([float(lineArr[0]),float(lineArr[1])])
        labelMat.append(float(lineArr[2]))
    return dataMat,labelMat

def selectJRand(i,m):                                             #随机选取一个与i不同的点
    j = i
    while (j == i):
        j = int(random.uniform(0,m))
    return j

def clipAlpha(aj,H,L):                                            #当alpha在范围外时，将其变换到边界上
    if aj > H :
        aj = H
    if aj < L :
        aj = L
    return aj

def smoSimple(dataMatIn,classLabels,C,toler,maxIter):             #输入参数为数据数组、分类数组、惩罚系数C(决定在多大\
    dataMatrix = mat(dataMatIn);labelMat = \                      #程度上容忍过界点)、toler(对误差容忍度的绝对值)\
    mat(classLabels).transpose()                                  #及maxIter(最大迭代次数)
    b=0;m,n = shape(dataMatrix)                                   
    alphas = mat(zeros((m,1)))                                   
    iteration = 0
    while(iteration<maxIter):
        alphaPairsChanged = 0
        for i in range(m):
            fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T))+b
            Ei = fXi - float(labelMat[i])                         #计算误差
            if((labelMat[i]*Ei<-toler)and(alphas[i]<C) \          #若误差过大，则随机选择另一个点对alpha进行更新
            or ((labelMat[i]*Ei>toler) and (alphas[i] > 0)):
               j = selectJrand(i,m)                         
               fXj = float(multiply(alphas,labelMat).T*(dataMatrix * dataMatrix[j,:].T))+b
               Ej = fXj - float(labelMat[j])
               alphaIold = alphas[i].copy()                       #为了不改变原值，使用copy()
               alphaJold = alphas[j].copy()
               if(labelMat[i] != labelMat[j]):                    #因为ai与aj类别不同时，计算公式不同
                   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\   #eta为aj的最优修改量，若≥0，则不需修改
                - 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)<0.0001):print \      #若aj改变过小，则认为该点无效果，另选它点计算
               "j not moving enough";continue
               alphas[i] += labelMat[j] * labelMat[i] * (alphaJold - alphas[j])
               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-Ei-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            #实际上，只要aiNew或ajNew在(0,C)上，b1=b2，\
           else:b=(b1+b2)/2.0                                     #否则，取其中值
           alphaPairsChanged += 1
           print "iter:%d i:%d,paris changed %d" % (iteration,i,alphaPairsChanged)
        if alphaPairsChanged == 0 : iteration += 1
        else:iteration = 0
        print "iteration number:%d"%iteration
    return b,alphas

运行结果如下:

…

结果为：