使用smo算法编写svm对CIFAR-10数据分类

公式太难打了，弄成图片，可能不太美观，但知识没变味

3：实验内容

3.1 提取hog特征

本实验的核心在于设计svm算法，因此提取特征使用库函数实现，最主要代码如下

from skimage import feature as ft
ft.hog(data[i],feature_vector=True,block_norm='L2-Hys',transform_sqrt=True)

3.2 使用SVM库验证特征提取后的分类效果

使用库的核心代码如下

trainmatrix=data2image(trainImg['Data'])
hogtrain=meanlie(feature_hog(trainmatrix))
testmatrix=data2image(testImg['Data'])
hogtest=meanlie(feature_hog(testmatrix))
from sklearn import svm
from skimage import feature as ft
clf=svm.SVC()
clf.fit(hogtrain,trainImg['Label'])
pre=clf.predict(hogtest)

分类结果如下
其中，count为正确分类的样本数，为4075，总的测试集样本数为5000。可以看到，分类准确性很高，达到0.815。这还是没有仔细调参的结果，这样的结果是很理想的，证明了hog特征+svm的思路切实可行，下面将其运用到自己编写的svm算法上。

3.3 验证自编二分类算法的正确性

本实验是个多分类问题，因此自己编写svm算法分两步，第一步编写二分类算法，第二步结合前面所选定的多分类策略基于此二分类算法实现多分类。
因此先来第一步：验证自编二分类算法
这里我分别抽取训练集和测试集中的6和9两类，训练集中每类分别选500个样本（只是为了运行快一些），二分类的类命名为PlattSMO，单独保存成自定义模块plattSMO，方便导入
完整smo代码太长，在附录给出，调用部分主要代码如下

trainmatrix=data2image(trainImg['Data'])
hogtrain=meanlie(feature_hog(trainmatrix))
testmatrix=data2image(testImg['Data'])
hogtest=meanlie(feature_hog(testmatrix))
hogtraindata,hogtrainlabel=extractClass(hogtrain,trainImg['Label'],6,9)
hogtraindata,hogtrainlabel=extractPart(hogtraindata,hogtrainlabel,500)
hogtestdata,hogtestlabel=extractClass(hogtest,testImg['Label'],6,9)
smo = plattSMO.PlattSMO(hogtraindata, hogtrainlabel, 0.05, 0.0001, 200, name='rbf', theta=20)
smo.smoP()
testResult = smo.predict(hogtestdata)
count=0
for i in range(len(testResult)):if testResult[i]==hogtestlabel[i]:count+=1
print('right rate:%f'%(float(count)/len(hogtestlabel)))

smoP函数就是完整的线性SMO算法
结果如下
其中，count是正确分类的样本数，1724个，而测试集中这两类样本一共2000个，二分类准确率0.862。验证了自编二分类代码是正确的。

3.4 验证自编多分类算法的正确性

多分类算法中，我们需要构建n(n-1)/2个二分类模型，只需调用PlattSMO类，实例化即可。构建好10个模型后，对于每个测试样本，使用模型进行分类，调整权重，最后投票表决得出结果即可。多分类的类命名为LibSVM，保存成模块libsvm，在主函数中调用即可。多分类代码主要有训练和预测函数，train和predict，train函数训练模型，保存到self.classfy变量，predict函数多分类策略，值得一提的是，10个模型的分类结果可能会使得某几个类别的权重相同，这种情况下我将这几个权重最大（相同权重）的类别取出来，再对该样本继续分类，调整权重，投票。相当于实行两次多分类策略，只是第二次的类别数较少一些（因为剔除了第一次权重小的类别）
完整代码在附件给出，主要代码如下

def __init__(self,data=[],label=[],C=0,toler=0,maxIter=0,**kernelargs):self.classlabel = unique(label)self.classNum = len(self.classlabel)self.classfyNum = (self.classNum * (self.classNum-1))/2self.classfy = []self.dataSet={}self.kernelargs = kernelargsself.C = Cself.toler = tolerself.maxIter = maxIterm = shape(data)[0]for i in range(m):label[i]=int(label[i])if label[i] not in self.dataSet.keys():self.dataSet[int(label[i])] = []self.dataSet[int(label[i])].append(data[i][:])else:self.dataSet[int(label[i])].append(data[i][:])def train(self):num = self.classNumfor i in range(num):for j in range(i+1,num):data = []label = [1.0]*shape(self.dataSet[self.classlabel[i]])[0]label.extend([-1.0]*shape(self.dataSet[self.classlabel[j]])[0])data.extend(self.dataSet[self.classlabel[i]])data.extend(self.dataSet[self.classlabel[j]])svm = PlattSMO(array(data),array(label),self.C,self.toler,self.maxIter,**self.kernelargs)svm.smoP()self.classfy.append(svm)self.dataSet = Nonedef predict(self,data,label):m = shape(data)[0]num = self.classNumclasslabel = []count = 0.0for n in range(m):result = [0] * numindex = -1for i in range(num):for j in range(i + 1, num):index += 1s = self.classfy[index]t = s.predict([data[n]])[0]if t > 0.0:result[i] +=1else:result[j] +=1#classlabel.append(self.classlabel[result.index(max(result))])resultmax=max(result)maxindex=result.index(resultmax)index1=[maxindex]for i in range(maxindex+1,5):if result[i]==resultmax:index1.append(i)index2 = [0 for _ in range(len(index1))]if len(index1) > 1:for i in range(len(index1)):for j in range(i+1,len(index1)):if index1[i]==0:s = self.classfy[index1[j-1]]elif index1[i]==3:s=self.classfy[9]else:s=self.classfy[2*index1[i]+index1[j]]t = s.predict([data[n]])[0]if t > 0.0:index2[i]+=1else:index2[j]+=1classlabel.append(self.classlabel[index1[index2.index(max(index2))]])if classlabel[-1] != label[n]:count +=1print label[n],classlabel[n]#print classlabelcountright=m-countprint "right rate:",countright / mreturn classlabel

主函数调用核心代码，libSVM.LibSVM参数很重要，这里选择的松弛变量C为10，容错率toler为0.0001，最大迭代次数maxIter为200，核函数为高斯核’rbf’，对应的带宽theta为20。可调优

 trainImg = loadData(file)testImg=loadData(file1)traindata,trainlabel=extractData(trainImg['Data'],trainImg['Label'],400)trainmatrix=data2image(traindata)hogtrain=meanlie(feature_hog(trainmatrix))testmatrix=data2image(testImg['Data'])hogtest=meanlie(feature_hog(testmatrix))#C选10最好，0.678svm = libSVM.LibSVM(hogtrain, trainlabel, 10, 0.0001, 200, name='rbf', theta=20)svm.train()svm.predict(hogtest,testImg['Label'])

训练模型时，只取训练集中一部分样本，每个类别取200或者400个样本，总共1000或者2000个样本进行训练，运行时间约5min以内，是很快的。但是若取全部样本训练，则时间难以忍受，当然只选择这样少的样本训练模型，一定会使得分类准确度下降，但是即便只选择400个样本，准确率已经可以达到0.678了，这是很不错的结果，可以想见，当使用全样本训练时，结果应该可以达到前面使用svm库的0.815的准确率。
实验结果如下
每类抽取200个样本
其中countright为正确分类的样本数，3282个，分类正确率为0.6564
每类抽取400个样本
正确分类的样本数countright为3473，分类正确率为0.6946。比用每类200个样本时高了约4%，而全部训练样本为14968个，如果用上全部样本数据，准确率还会有不小的提升

附录：

代码中各函数功能说明

trialsvm.py
def meanlie(data):
data中每个元素除以对应列的均值，这一步骤替代归一化，在提取hog特征后因为要进行1后续的分类，所以需要归一化数据。而实验发现归一化后分类准确性不是很高，发现是由于每个特征对应的data中的列总是有个别的数极大，其他很小，因此采用每个元素除以所在列的均值的方式代替归一化
def loadData(file):
导入数据集，很简单
def data2image(data):
将每个样本对应的行向量转化成图片并灰度化，因为hog特征是在图片上提取，而数据集中图片是以一个1x3072的行向量表示的
def feature_hog(data):
对传进来的data提取hog特征，返回提取特征后的数据
def extractData(data,label,num):
从大的数据集data中抽取部分样本，num是每类需要抽取的样本数，返回抽取后的样本数据和对应的标签
plattSMO.py
class PlattSMO：
二分类的类
def init(self,dataMat,classlabels,C,toler,maxIter,**kernelargs):
初始化函数，初始化一些变量dataMat-数据矩阵，C - 松弛变量，classLabels - 数据标签，toler - 容错率，maxIter-最大迭代次数，**kernelargs-核函数有关的参数
def kernelTrans(self,x,z):
通过核函数将数据转换更高维的空间
def calcEK(self,k):
计算误差
def updateEK(self,k):
计算Ek,并更新误差缓存
def selectJ(self,i,Ei):
内循环启发方式2
def innerL(self,i):
优化的SMO算法
def smoP(self):
完整的线性SMO算法
def calcw(self):
计算权重W
def predict(self,testData):
预测函数，预测样本类别
libsvm.py
class LibSVM:
多分类类
def train(self):
训练函数，训练10个分类模型
def predict(self,data,label):
预测函数，实现多分类策略，使用训练模型对测试数据data进行预测，给出分类结果

trialsvm.py

# -*- coding: utf-8 -*-
"""
Created on Fri Dec 14 19:15:13 2018@author: Administrator
"""
from mysvm import plattSMO,libSVM
import matplotlib.pyplot as plt
import numpy as np
import random
from numpy import *
import scipy.io as sio
from sklearn.decomposition import PCA
from sklearn import preprocessing
from skimage import feature as ft
def meanlie(data):#每个元素除以对应列的均值，这一步骤替代归一化，因归一化效果不好m,n=data.shapemeandata=np.mean(data,axis=0)# axis=0，计算每一列的均值for i in range(n):data[:,i]/=meandata[i]return datadef loadData(file):#file='G:/lecture of grade one/pattern recognition/data/train_data.mat'trainImg=sio.loadmat(file)return trainImg
def data2image(data):newdata=[]m,n=data.shapefor i in range(m):img=data[i,:].reshape((3,32,32))#gray=img.convert('L')gray = img[0,:, :]*0.2990+img[1,:, :]*0.5870+img[2,:, :]*0.1140newdata.append(gray)#np.array(newdata)return newdata
def feature_hog(data):#提取hog特征fea=[]for i in range(len(data)):#data[i]=Image.fromarray(data[i][0])fea.append(ft.hog(data[i],feature_vector=True,block_norm='L2-Hys',transform_sqrt=True))fea=np.array(fea)return fea
'''
def extractClass(data,label,class1,class2):#抽取两类，并将类别标签改为1或-1，方便做svmm,n=data.shapeindex=[]for i in range(m):if label[i][0]!=class1 and label[i][0]!=class2:index.append(i)data=np.delete(data,index,0)label=np.delete(label,index,0)min_max_scaler=preprocessing.MinMaxScaler()data=min_max_scaler.fit_transform(data)Y=[]        for i in label:if i[0]==class1:#class1对应1Y.append(1)else:Y.append(-1)#class2对应-1Y=np.array(Y)return data,Y
def extractPart(data,label,nums):m,n=data.shapeindex=[]a=0;b=0for i in range(m):if label[i]==1 and a<nums:index.append(i)a+=1if label[i]==-1 and b<nums:index.append(i)b+=1if a>nums and b>nums:breakdata=data[index]label=label[index]    return data,label
'''
def extractData(data,label,num):m,n=data.shapecount=[0,0,0,0,0]cla=[0,6,7,8,9]index=[]for i in range(m):for j in range(5):if label[i]==cla[j] and count[j]<num:count[j]+=1index.append(i)data=data[index]label=label[index]return data,labelif __name__ == '__main__':file='G:/lecture of grade one/pattern recognition/trial three/data3/train_data3.mat'file1='G:/lecture of grade one/pattern recognition/trial three/data3/test_data3.mat'trainImg = loadData(file)testImg=loadData(file1)traindata,trainlabel=extractData(trainImg['Data'],trainImg['Label'],400)#testdata,testlabel=extractData(testImg['Data'],testImg['Label'],1000)trainmatrix=data2image(traindata)hogtrain=meanlie(feature_hog(trainmatrix))testmatrix=data2image(testImg['Data'])hogtest=meanlie(feature_hog(testmatrix))#C选10最好，0.678svm = libSVM.LibSVM(hogtrain, trainlabel, 10, 0.0001, 200, name='rbf', theta=20)svm.train()svm.predict(hogtest,testImg['Label'])'''trainmatrix=data2image(trainImg['Data'])hogtrain=meanlie(feature_hog(trainmatrix))testmatrix=data2image(testImg['Data'])hogtest=meanlie(feature_hog(testmatrix))hogtraindata,hogtrainlabel=extractClass(hogtrain,trainImg['Label'],6,9)hogtraindata,hogtrainlabel=extractPart(hogtraindata,hogtrainlabel,500)hogtestdata,hogtestlabel=extractClass(hogtest,testImg['Label'],6,9)smo = plattSMO.PlattSMO(hogtraindata, hogtrainlabel, 0.05, 0.0001, 200, name='rbf', theta=20)smo.smoP()testResult = smo.predict(hogtestdata)count=0for i in range(len(testResult)):if testResult[i]==hogtestlabel[i]:count+=1print('right rate:%f'%(float(count)/len(hogtestlabel)))'''

plattSMO.py

import sys
from numpy import *
from svm import *
from os import listdir
class PlattSMO:def __init__(self,dataMat,classlabels,C,toler,maxIter,**kernelargs):self.x = array(dataMat)self.label = array(classlabels).transpose()self.C = Cself.toler = tolerself.maxIter = maxIterself.m = shape(dataMat)[0]self.n = shape(dataMat)[1]self.alpha = array(zeros(self.m),dtype='float64')self.b = 0.0self.eCache = array(zeros((self.m,2)))self.K = zeros((self.m,self.m),dtype='float64')self.kwargs = kernelargsself.SV = ()self.SVIndex = Nonefor i in range(self.m):for j in range(self.m):self.K[i,j] = self.kernelTrans(self.x[i,:],self.x[j,:])def calcEK(self,k):fxk = dot(self.alpha*self.label,self.K[:,k])+self.bEk = fxk - float(self.label[k])return Ekdef updateEK(self,k):Ek = self.calcEK(k)self.eCache[k] = [1 ,Ek]def selectJ(self,i,Ei):maxE = 0.0selectJ = 0Ej = 0.0validECacheList = nonzero(self.eCache[:,0])[0]if len(validECacheList) > 1:for k in validECacheList:if k == i:continueEk = self.calcEK(k)deltaE = abs(Ei-Ek)if deltaE > maxE:selectJ = kmaxE = deltaEEj = Ekreturn selectJ,Ejelse:selectJ = selectJrand(i,self.m)Ej = self.calcEK(selectJ)return selectJ,Ejdef innerL(self,i):Ei = self.calcEK(i)if (self.label[i] * Ei < -self.toler and self.alpha[i] < self.C) or \(self.label[i] * Ei > self.toler and self.alpha[i] > 0):self.updateEK(i)j,Ej = self.selectJ(i,Ei)alphaIOld = self.alpha[i].copy()alphaJOld = self.alpha[j].copy()if self.label[i] != self.label[j]:L = max(0,self.alpha[j]-self.alpha[i])H = min(self.C,self.C + self.alpha[j]-self.alpha[i])else:L = max(0,self.alpha[j]+self.alpha[i] - self.C)H = min(self.C,self.alpha[i]+self.alpha[j])if L == H:return 0eta = 2*self.K[i,j] - self.K[i,i] - self.K[j,j]if eta >= 0:return 0self.alpha[j] -= self.label[j]*(Ei-Ej)/etaself.alpha[j] = clipAlpha(self.alpha[j],H,L)self.updateEK(j)if abs(alphaJOld-self.alpha[j]) < 0.00001:return 0self.alpha[i] +=  self.label[i]*self.label[j]*(alphaJOld-self.alpha[j])self.updateEK(i)b1 = self.b - Ei - self.label[i] * self.K[i, i] * (self.alpha[i] - alphaIOld) - \self.label[j] * self.K[i, j] * (self.alpha[j] - alphaJOld)b2 = self.b - Ej - self.label[i] * self.K[i, j] * (self.alpha[i] - alphaIOld) - \self.label[j] * self.K[j, j] * (self.alpha[j] - alphaJOld)if 0<self.alpha[i] and self.alpha[i] < self.C:self.b = b1elif 0 < self.alpha[j] and self.alpha[j] < self.C:self.b = b2else:self.b = (b1 + b2) /2.0return 1else:return 0def smoP(self):iter = 0entrySet = TruealphaPairChanged = 0while iter < self.maxIter and ((alphaPairChanged > 0) or (entrySet)):alphaPairChanged = 0if entrySet:for i in range(self.m):alphaPairChanged+=self.innerL(i)iter += 1else:nonBounds = nonzero((self.alpha > 0)*(self.alpha < self.C))[0]for i in nonBounds:alphaPairChanged+=self.innerL(i)iter+=1if entrySet:entrySet = Falseelif alphaPairChanged == 0:entrySet = Trueself.SVIndex = nonzero(self.alpha)[0]self.SV = self.x[self.SVIndex]self.SVAlpha = self.alpha[self.SVIndex]self.SVLabel = self.label[self.SVIndex]self.x = Noneself.K = Noneself.label = Noneself.alpha = Noneself.eCache = None
#   def K(self,i,j):
#       return self.x[i,:]*self.x[j,:].Tdef kernelTrans(self,x,z):if array(x).ndim != 1 or array(x).ndim != 1:raise Exception("input vector is not 1 dim")if self.kwargs['name'] == 'linear':return sum(x*z)elif self.kwargs['name'] == 'rbf':theta = self.kwargs['theta']return exp(sum((x-z)*(x-z))/(-1*theta**2))def calcw(self):for i in range(self.m):self.w += dot(self.alpha[i]*self.label[i],self.x[i,:])def predict(self,testData):test = array(testData)#return (test * self.w + self.b).getA()result = []m = shape(test)[0]for i in range(m):tmp = self.bfor j in range(len(self.SVIndex)):tmp += self.SVAlpha[j] * self.SVLabel[j] * self.kernelTrans(self.SV[j],test[i,:])while tmp == 0:tmp = random.uniform(-1,1)if tmp > 0:tmp = 1else:tmp = -1result.append(tmp)return result
def plotBestfit(data,label,w,b):import matplotlib.pyplot as pltn = shape(data)[0]fig = plt.figure()ax = fig.add_subplot(111)x1 = []x2 = []y1 = []y2 = []for i in range(n):if int(label[i]) == 1:x1.append(data[i][0])y1.append(data[i][1])else:x2.append(data[i][0])y2.append(data[i][1])ax.scatter(x1,y1,s=10,c='red',marker='s')ax.scatter(x2,y2, s=10, c='green', marker='s')x = arange(-2,10,0.1)y = ((-b-w[0]*x)/w[1])plt.plot(x,y)plt.xlabel('X')plt.ylabel('y')plt.show()
def loadImage(dir,maps = None):dirList = listdir(dir)data = []label = []for file in dirList:label.append(file.split('_')[0])lines = open(dir +'/'+file).readlines()row = len(lines)col = len(lines[0].strip())line = []for i in range(row):for j in range(col):line.append(float(lines[i][j]))data.append(line)if maps != None:label[-1] = float(maps[label[-1]])else:label[-1] = float(label[-1])return array(data),array(label)def main():'''data,label = loadDataSet('testSetRBF.txt')smo = PlattSMO(data,label,200,0.0001,10000,name = 'rbf',theta = 1.3)smo.smoP()smo.calcw()print smo.predict(data)'''maps = {'1':1.0,'9':-1.0}data,label = loadImage("digits/trainingDigits",maps)smo = PlattSMO(data, label, 200, 0.0001, 10000, name='rbf', theta=20)smo.smoP()print len(smo.SVIndex)test,testLabel = loadImage("digits/testDigits",maps)testResult = smo.predict(test)m = shape(test)[0]count  = 0.0for i in range(m):if testLabel[i] != testResult[i]:count += 1print "classfied error rate is:",count / m#smo.kernelTrans(data,smo.SV[0])if __name__ == "__main__":sys.exit(main())

libsvm.py

import sys
from numpy import *
from svm import *
from os import listdir
from plattSMO import PlattSMO
import pickle
class LibSVM:def __init__(self,data=[],label=[],C=0,toler=0,maxIter=0,**kernelargs):self.classlabel = unique(label)self.classNum = len(self.classlabel)self.classfyNum = (self.classNum * (self.classNum-1))/2self.classfy = []self.dataSet={}self.kernelargs = kernelargsself.C = Cself.toler = tolerself.maxIter = maxIterm = shape(data)[0]for i in range(m):label[i]=int(label[i])if label[i] not in self.dataSet.keys():self.dataSet[int(label[i])] = []self.dataSet[int(label[i])].append(data[i][:])else:self.dataSet[int(label[i])].append(data[i][:])def train(self):num = self.classNumfor i in range(num):for j in range(i+1,num):data = []label = [1.0]*shape(self.dataSet[self.classlabel[i]])[0]label.extend([-1.0]*shape(self.dataSet[self.classlabel[j]])[0])data.extend(self.dataSet[self.classlabel[i]])data.extend(self.dataSet[self.classlabel[j]])svm = PlattSMO(array(data),array(label),self.C,self.toler,self.maxIter,**self.kernelargs)svm.smoP()self.classfy.append(svm)self.dataSet = Nonedef predict(self,data,label):m = shape(data)[0]num = self.classNumclasslabel = []count = 0.0for n in range(m):result = [0] * numindex = -1for i in range(num):for j in range(i + 1, num):index += 1s = self.classfy[index]t = s.predict([data[n]])[0]if t > 0.0:result[i] +=1else:result[j] +=1#classlabel.append(self.classlabel[result.index(max(result))])resultmax=max(result)maxindex=result.index(resultmax)index1=[maxindex]for i in range(maxindex+1,5):if result[i]==resultmax:index1.append(i)index2 = [0 for _ in range(len(index1))]if len(index1) > 1:for i in range(len(index1)):for j in range(i+1,len(index1)):if index1[i]==0:s = self.classfy[index1[j-1]]elif index1[i]==3:s=self.classfy[9]else:s=self.classfy[2*index1[i]+index1[j]]t = s.predict([data[n]])[0]if t > 0.0:index2[i]+=1else:index2[j]+=1classlabel.append(self.classlabel[index1[index2.index(max(index2))]])if classlabel[-1] != label[n]:count +=1#print label[n],classlabel[n]#print classlabelcountright=m-countprint "right rate:",countright / mreturn classlabeldef save(self,filename):fw = open(filename,'wb')pickle.dump(self,fw,2)fw.close()@staticmethoddef load(filename):fr = open(filename,'rb')svm = pickle.load(fr)fr.close()return svmdef loadImage(dir,maps = None):dirList = listdir(dir)data = []label = []for file in dirList:label.append(file.split('_')[0])lines = open(dir +'/'+file).readlines()row = len(lines)col = len(lines[0].strip())line = []for i in range(row):for j in range(col):line.append(float(lines[i][j]))data.append(line)if maps != None:label[-1] = float(maps[label[-1]])else:label[-1] = float(label[-1])return data,label
def main():'''data,label = loadImage('trainingDigits')svm = LibSVM(data, label, 200, 0.0001, 10000, name='rbf', theta=20)svm.train()svm.save("svm.txt")'''svm = LibSVM.load("svm.txt")test,testlabel = loadImage('testDigits')svm.predict(test,testlabel)if __name__ == "__main__":sys.exit(main())