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))/2

self.classfy = []

self.dataSet={}

self.kernelargs = kernelargs

self.C = C

self.toler = toler

self.maxIter = maxIter

m = 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.classNum

for 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 = None

def predict(self,data,label):

m = shape(data)[0]

num = self.classNum

classlabel = []

count = 0.0

for n in range(m):

result = [0] * num

index = -1

for i in range(num):

for j in range(i + 1, num):

index += 1

s = self.classfy[index]

t = s.predict([data[n]])[0]

if t > 0.0:

result[i] +=1

else:

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]+=1

else:

index2[j]+=1

classlabel.append(self.classlabel[index1[index2.index(max(index2))]])

if classlabel[-1] != label[n]:

count +=1

print label[n],classlabel[n]

#print classlabel

countright=m-count

print "right rate:",countright / m

return 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，0.678

svm = 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.shape

meandata=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 data

def 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.shape

for 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,:, :]*0.1140

newdata.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svm

m,n=data.shape

index=[]

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1

Y.append(1)

else:

Y.append(-1)#class2对应-1

Y=np.array(Y)

return data,Y

def extractPart(data,label,nums):

m,n=data.shape

index=[]

a=0;b=0

for i in range(m):

if label[i]==1 and anums and b>nums:

break

data=data[index]

label=label[index]

return data,label

'''

def extractData(data,label,num):

m,n=data.shape

count=[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]

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 = C

self.toler = toler

self.maxIter = maxIter

self.m = shape(dataMat)[0]

self.n = shape(dataMat)[1]

self.alpha = array(zeros(self.m),dtype='float64')

self.b = 0.0

self.eCache = array(zeros((self.m,2)))

self.K = zeros((self.m,self.m),dtype='float64')

self.kwargs = kernelargs

self.SV = ()

self.SVIndex = None

for 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.b

Ek = fxk - float(self.label[k])

return Ek

def updateEK(self,k):

Ek = self.calcEK(k)

self.eCache[k] = [1 ,Ek]

def selectJ(self,i,Ei):

maxE = 0.0

selectJ = 0

Ej = 0.0

validECacheList = nonzero(self.eCache[:,0])[0]

if len(validECacheList) > 1:

for k in validECacheList:

if k == i:continue

Ek = self.calcEK(k)

deltaE = abs(Ei-Ek)

if deltaE > maxE:

selectJ = k

maxE = deltaE

Ej = Ek

return selectJ,Ej

else:

selectJ = selectJrand(i,self.m)

Ej = self.calcEK(selectJ)

return selectJ,Ej

def 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 0

eta = 2*self.K[i,j] - self.K[i,i] - self.K[j,j]

if eta >= 0:

return 0

self.alpha[j] -= self.label[j]*(Ei-Ej)/eta

self.alpha[j] = clipAlpha(self.alpha[j],H,L)

self.updateEK(j)

if abs(alphaJOld-self.alpha[j]) < 0.00001:

return 0

self.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 00) or (entrySet)):

alphaPairChanged = 0

if entrySet:

for i in range(self.m):

alphaPairChanged+=self.innerL(i)

iter += 1

else:

nonBounds = nonzero((self.alpha > 0)*(self.alpha < self.C))[0]

for i in nonBounds:

alphaPairChanged+=self.innerL(i)

iter+=1

if entrySet:

entrySet = False

elif alphaPairChanged == 0:

entrySet = True

self.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 = None

self.K = None

self.label = None

self.alpha = None

self.eCache = None

# def K(self,i,j):

# return self.x[i,:]*self.x[j,:].T

def 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.b

for 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 = 1

else:

tmp = -1

result.append(tmp)

return result

def plotBestfit(data,label,w,b):

import matplotlib.pyplot as plt

n = 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 = 0.0

for i in range(m):

if testLabel[i] != testResult[i]:

count += 1

print "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))/2

self.classfy = []

self.dataSet={}

self.kernelargs = kernelargs

self.C = C

self.toler = toler

self.maxIter = maxIter

m = 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.classNum

for 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 = None

def predict(self,data,label):

m = shape(data)[0]

num = self.classNum

classlabel = []

count = 0.0

for n in range(m):

result = [0] * num

index = -1

for i in range(num):

for j in range(i + 1, num):

index += 1

s = self.classfy[index]

t = s.predict([data[n]])[0]

if t > 0.0:

result[i] +=1

else:

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]+=1

else:

index2[j]+=1

classlabel.append(self.classlabel[index1[index2.index(max(index2))]])

if classlabel[-1] != label[n]:

count +=1

#print label[n],classlabel[n]

#print classlabel

countright=m-count

print "right rate:",countright / m

return classlabel

def save(self,filename):

fw = open(filename,'wb')

pickle.dump(self,fw,2)

fw.close()

@staticmethod

def load(filename):

fr = open(filename,'rb')

svm = pickle.load(fr)

fr.close()

return svm

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 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())