模式识别与智能计算第6章

例6.1

>>load

mydata;high=mydata(1:3,:);mid=mydata(4:6,:);low=mydata(7:9,:);test=mydata(10:11,:);

>>num=nchoosek(1:3,2); %1,2,3三个数字两两配对，1代表高，2代表中，3代表低

>>Training={high,mid,low};SVM=cell(size(num,1),1);%元胞形式的训练集及SVM >>for k=1:size(num,1)

t1=Training{num(k,1)}; t2=Training{num(k,2)};%配对组成训练集

SVM{k}=svmtrain([t1;t2],[ones(size(t1,1),1);zeros(size(t2,1),1)],'Kernel_function',…

'polynomial','polyorder',1);%训练函数

end

>>for kk=1:size(test,1)

for k=1:length(SVM)

result(k)=svmclassify(SVM{k},test(kk,:)); %分类函数

temp(k)=num(k,1).*result(k)+num(k,2).*~result(k);%每个分类器的分类结果end

results(kk)=mode(temp,2); %依据每个数字出现的次数，决定总的分类结果

end

>> results

例6.3

picformat={'*.jpg','JPEG image(*,jpg)';'*.bmp','bitmap image(*,bmp)';'*.*','All files(*,*)'};

%可以处理图片的各种格式

[filename, filepath]=uigetfile(picformat,'导入图片','*.jpg','multiselect','on');

%可以一次性选择多张图片输入

filename=cellstr(filename);%图片名字，如01，代表数字0的第一幅图片

n=length(filename);totalpicture=zeros(n,256);group=zeros(n,1);%亮度255代表白色

for i=1:n

I=imread([filepath,filename{i}]);I=255-I;I=im2bw(I,0.5);%反色处理并转化为二值图像[y,x]=find(I==1);bw=I(min(y):max(y),min(x):max(x));%含完整数字的最小区域bw=imresize(bw,[16,16]);%20×20像素大小

totalpicture(i,:)=double(bw(:)');%将图像转化数字矩阵

group(i)=str2double(filename{i}(1));%图片对应的真实数字

end

train_pic=arrayfun(@(k)totalpicture(group==k,:),0:9,'uniformoutput',false);

%循环函数，即将指定的函数应用到给定数组的所有元素

nchk=nchoosek(0:9,2);%将0~9两两配对

svm=cell(size(nchk,1),1);%将0~9数字分类总共需要的向量机

for k=1:size(nchk,1)

t1=train_pic{nchk(k,1)+1};t2=train_pic{nchk(k,2)+1};%构成训练样本

s vm{k}=svmtrain([t1;t2],[ones(size(t1,1),1);zeros(size(t2,1),1)],'kernel_function',…

'polynomial','polyorder',1); %支持向量机训练函数，核函数可以选用其他end

for i=1:n

true_num(i)=str2double(filename{i}(2));%每幅图片代表的真实数字，文件名为001等I=imread([filepath,filename{i}]);I=255-I;I=im2bw(I,0.5);[y,x]=find(I==1);

bw=I(min(y):max(y),min(x):max(x));bw=imresize(bw,[16,16]);test=double(bw(:)');

for k=1:length(svm)

svmresult(k)=svmclassify(svm{k},test);%支持向量机分类函数

temp(k)=nchk(k,1).*svmresult(k)+nchk(k,2).*~svmresult(k);

end

result(i)=mode(temp);%两两比较，以出现次数多的为最终类别

end

例6.4

a=0;totalpicture=zeros(80,256);group=zeros(80,1);

for i=0:9

for j=1:8

a=a+1;%图片序列号

I=imread(['F:\手写体图片\',strcat(num2str(i),num2str(j)),'.jpg']);

I=255-I;I=im2bw(I,0.5);[y,x]=find(I==1);bw=I(min(y):max(y),min(x):max(x));

bw=imresize(bw,[16,16]);totalpicture(a,:)=double(bw(:)');group(a)=i;

end

end

train_pic=arrayfun(@(k)totalpicture(group==k,:),0:9,'uniformoutput',false);

nchk=nchoosek(0:9,2);svm=cell(size(nchk,1),1);

for k=1:size(nchk,1)

t1=train_pic{nchk(k,1)+1};t2=train_pic{nchk(k,2)+1};

svm{k}=svmtrain([t1;t2],[ones(size(t1,1),1);zeros(size(t2,1),1)],'kernel_function','rbf','RBF_ SIGMA',x(1),'boxconstraint',x(2));

end

a=0;true_num=zeros(1,30);result=zeros(30,1);svmresult=zeros(length(svm),1);

for i=0:9

for j=1:3

a=a+1;I=imread(['F:\手写体图片\',strcat(num2str(0),num2str(i),num2str(j)),'.jpg']);

true_num(a)=i;I=255-I;I=im2bw(I,0.5);[y,x]=find(I==1);

bw=I(min(y):max(y),min(x):max(x));bw=imresize(bw,[16,16]);test=double(bw(:)');

for k=1:length(svm);svmresult(k)=svmclassify(svm{k},test);end

temp=nchk(:,1).*svmresult+nchk(:,2).*~svmresult;result(a)=mode(temp);

end

end

result=result';y=-sum(result==true_num)/30;

例6.5

h=mean(x);n=length(x);a1=0;a2=0;

for i=1:n;a2=a2+(x(i)-h)^2;end

for k=1:7;for i=k+1:n;a1=a1+(x(i)-h)*(x(i-k)-h);end;r(k)=a1/a2;end

可以从r值确定自相关系数的大小，从而确定m值。在此例中选择m=4。这样就可确定输入数据矩阵：

m=4;n=length(xx);

for i=m+1:n

for j=1:m;x1(i,j)=xx(i-(m-j+1));end

end

x1=x1(m+1:end,:);y=xx(m+1:end);

然后就可以用下列支持向量机回归函数进行预测：

function svm=mysvmRegression(varargin) %支持向量机训练函数

options = optimset;https://www.360docs.net/doc/bd6909599.html,rgeScale = 'off';options.Display = 'off';

svmType=varargin{1};X=varargin{2};Y=varargin{3};ker=varargin{4};

switch svmType

case 'svr_epsilon',

C = varargin{5};e = varargin{6};n = length(Y);Q = kernel(ker,X,X); %核函数

H = [Q,-Q;-Q,Q];f = [e*ones(n,1)-Y';e*ones(n,1)+Y'];

A = [];b = [];Aeq = [ones(1,n),-ones(1,n)];beq = 0;%约束条件

lb = zeros(2*n,1);ub = C*ones(2*n,1);a0 = zeros(2*n,1); %边界条件

a=quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options); %二次规划函数求支持向量机

a=a(1:n)-a(n+1:end);svm.type = svmType;svm.ker = ker;svm.x = X;svm.y = Y;svm.a = a'; case 'svr_nu',

C =varargin{5};nu =varargin{6};n = length(Y);Q = kernel(ker,X,X);

H = [Q,-Q;-Q,Q];f = [-Y';+Y'];A = [];b = [];

Aeq = [ones(1,n),-ones(1,n);ones(1,2*n)];beq = [0;C*n*nu];

lb = zeros(2*n,1);ub = C*ones(2*n,1);a0 = zeros(2*n,1);

a=quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);

a = a(1:n)-a(n+1:end);svm.type = svmType;svm.ker = ker;svm.x = X;svm.y = Y;svm.a = a'; end

function y_out = mysvmSim(svm,Xt) %支持向量机仿真函数

cathe = 10e+6; nx = size(svm.x,2);nt = size(Xt,2);block = ceil(nx*nt/cathe);

num = ceil(nt/block);

for i = 1:block

if (i==block);index = [(i-1)*num+1:nt];else;index = (i-1)*num+[1:num];end

y_out(index) = svmSim_block(svm,Xt(:,index));

end

function Yd = svmSim_block(svm,Xt)

ker = svm.ker;X = svm.x;Y = svm.y;a = svm.a;epsilon = 1e-8;

mysupport_v = find(abs(a)>epsilon); % 支持向量

temp = a*kernel(ker,X,X(:,mysupport_v));b = Y(mysupport_v)-temp;b = mean(b);

temp =a*kernel(ker,X,Xt);y_out= (temp+b);

为了更好地得到预测结果，首先用遗传算法对支持向量机中的相关参数进行优化。编写下列的适应度函数：

xx=[5.3425 10.5679 14.6753 15.3289 14.287 13.6541 12.2313 9.653 11.2345 9.3578 8.3456

7.8563 6.9682 6.3421 5.8432 6.5437 9.7685 14.3256];

m=4;[x1,y]=timeinput(xx,m);

ker = struct('type','gauss','width',x(1));C=x(2);nu=x(3); %高斯核函数及相应的参数

svm=mysvmRegression('svr_nu',x1',y,ker,C,nu);%训练函数

y1=mysvmSim(svm,[5.8432 6.5437 9.7685 14.3256;6.5437 9.7685 14.3256 16.8645]'); % 仿真

y=(y1(1)-15.8645)^2+(y1(2)-14.8976)^2;

例6.6

>>type = 'function estimation';

>>[alpha,b] = trainlssvm({xx(1:13,1:end-1),xx(1:13,end),type,165,63.85,'RBF_kernel'}); >> Yt = simlssvm({xx(1:13,1:end-1),xx(1:13,end),type,x(1),x(2),'RBF_kernel','preprocess'},…

{alpha,b},xx(14:18,1:end-1))

Yt =8.2881 8.1531 3.9540 4.8864 8.1795