【机器学习实战】6.支持向量机——简化SMO算法

主体是书上的程序，添加了一个画图函数，查看分类结果。实际上，按照书上的程序，分类结果并不一定好。书上图6-4只是理想结果。程序后附上结果。

# -*- coding: utf-8 -*-
"""
Created on Thu Mar 15 10:26:20 2018

@author: ###
"""

import numpy as np
import matplotlib.pyplot as plt

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

def clipAlpha(aj,H,L):
    '''
    限制函数
    '''
    if aj>H:
        aj=H
    if L>aj:
        aj=L
    return aj


def smoSimple(dataMatIn,classLabels,C,toler,maxIter):
    '''
    简化版SMO函数
    输入：数据集、标签集、惩罚常数C、容错率、最大迭代次数
    numpy.multiply(),数组点乘
    
    '''
    #将列表转为矩阵，labelMat进行转置，使数据集每行与标签集每行相对应
    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   #存储没有任何alpha改变情况下遍历数据集的次数
    while(iter w 利用拉格朗日乘子法得到

            fXi=float(np.multiply(alphas,labelMat).T*\
                      (dataMatrix*dataMatrix[i,:].T))+b
            Ei=fXi-float(labelMat[i])
            if((labelMat[i]*Ei<-toler)and(alphas[i]toler) and (alphas[i]>0)):   #不满足KTT条件
                    j=selectJrand(i,m)                    #随机选择第二个alpha
                    fXj=float(np.multiply(alphas,labelMat).T* \
                              (dataMatrix*dataMatrix[j,:].T))+b
                    Ej=fXj-float(labelMat[j])
                    alphaIold=alphas[i].copy()   #保留原先的alpha值
                    alphaJold=alphas[j].copy()
                    '''
                    计算第二个变量的取值范围
                    根据 a1*y1+a2*y2=k 约束条件：
                     1)y1!=y2 : a1-a2=k' -> a2=a1-k' 
                     2)y1==y2 : a1+a2=k' -> a2=-a1+k'
                    
                    '''
                    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;
                    #计算新的第二个变量值    #计算eta
                    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])#更新第一个变量
                    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(0alphas[i]):
                        b=b1
                    elif (0alphas[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 plotF(dataIn,classLabel,b,alphas):   
    '''
    画出数据集及决策边界
    '''
    xcord1=[]
    ycord1=[]
    xcord2=[]
    ycord2=[]
    dataArr=np.array(dataIn)    
    m=np.shape(dataArr)[0]    
    markx=[]
    marky=[]
    for i in range(m):
        if(classLabel[i]==1):
            xcord1.append(dataArr[i][0])
            ycord1.append(dataArr[i][1])
        else:
            xcord2.append(dataArr[i][0])
            ycord2.append(dataArr[i][1])
        if(alphas[i]>0):
            markx.append(dataArr[i][0])
            marky.append(dataArr[i][1])
    
    fig=plt.figure()
    ax=fig.add_subplot(111)
    ax.scatter(xcord1,ycord1,s=30,c='red',marker='s',label=1)
    ax.scatter(xcord2,ycord2,s=30,c='green',marker='*',label=-1)
    ax.scatter(markx,marky,s=80,c='',edgecolors='blue')
    #画决策边界
    x=np.arange(1,6,0.1)    
    datamatrix=np.mat(dataIn)
    labelMat=np.mat(classLabel)
    beta=np.multiply(alphas,labelMat.T).T*datamatrix
    y=(-b[0,0]-beta[0,0]*x)/beta[0,1]
    ax.legend(loc='upper left')
    ax.plot(x,y)
    plt.show()

      
if __name__=='__main__':
    dataArr,labelArr=loadDataSet("testSet.txt")
   
    b,alphas=smoSimple(dataArr,labelArr,0.6,0.001,40)
    print(alphas[alphas>0])
    for i in range(100):
        if(alphas[i]>0):
            print(alphas[i], dataArr[i],labelArr[i])
            
    plotF(dataArr,labelArr,b,alphas)  

运行结果：