lda.m

站长！这是使用LDA和PCA模式识别方法对人脸特征进行提取计算的Matlab程序框架

load('ORLFace.mat');
% basic information
dim=size(Iv,1);
tal=size(Iv,2);
class=size(Iv,3);

ell=5; % ell training sample;
ellsample=5; % ellsample test sample;
t=1e7; % Similarity matrix 的参数

order=1;  
dita=1e7; 
NumTotal=ell*class;
lpp=NumTotal-class;
lda=class-1;
lda=35
polynomial=1

%------------------- step 1     KPCA       ------------------------------%
Itr=zeros(dim,ell,class);  % Training sample feature vector
for classnum=1:class
    for e=1:ell
        Itr(:,e,classnum)=Iv(:,e,classnum);  %
    end    
end
It=zeros(dim,ellsample,class);% Testing sample feature vector
for classnum=1:class
    for e=1:ellsample
        It(:,e,classnum)=Iv(:,e+ell,classnum);  %
    end    
end
%----------------------------------------------------------------%
%   倒入向量 Iv(dim,ell)
%   样本类数  class
Imean=zeros(dim,1);
for classnum=1:class
    for i=1:ell
        Imean=Imean+Itr(:,i,classnum); 
    end
end
Imean=(1/(ell*class))*Imean;                       %求平均向量
Q=zeros(dim,ell*class);
for classnum=1:class
    for num=1:ell
        Q(:,num+(classnum-1)*ell)=Itr(:,num,classnum)-Imean(:,1);
    end
end
R=zeros(ell*class,ell*class);
R=Q'*Q;    % R's size is ell * ell
d=rank(R);
d=40
[U,L]=eigs(R,d,'LM');  % 求出 R 的eigenvector and eigenvalue
Wpca=zeros(dim,d);
for p=1:d
    Wpca(:,p)=(1/(sqrt(L(p,p))))*Q*U(:,p);
end
%% 程序至此得到了线形变换的矩阵  W  .
%----------------------------------------------------------------%
Iy=zeros(d,ell,class); % training feature vector  %   
for classnum=1:class
    for num=1:ell
        Y=zeros(d,1);
        Iy(:,num,classnum)=Wpca'*Itr(:,num,classnum);
    end
end
% -------------------------------------------------------------------------
Tpca=zeros(d,ellsample,class);
for classnum=1:class
    for num=1:ellsample
        Tpca(:,num,classnum)=Wpca'*It(:,num,classnum);
    end
end
% ----------------                       step 3      LDA                           -----------------%
Minclass=zeros(d,class);
for classnum=1:class      % 得到 每一个类内的样本的平均值
    for i=1:ell
        Minclass(:,classnum)=Minclass(:,classnum)+Iy(:,i,classnum); 
    end
    Minclass(:,classnum)=(1/ell)*Minclass(:,classnum);  
end
Sw=zeros(d,d);    % 计算wihin-class matrix Sw
for classnum=1:class      
    for i=1:ell
        
        Sw=Sw+(Iy(:,i,classnum)-Minclass(:,classnum))*(Iy(:,i,classnum)-Minclass(:,classnum))';
        
    end
end
Msample=zeros(d,1); % 得到 所有样本的平均值
for classnum=1:class
    for i=1:ell
        Msample=Msample+Iy(:,i,classnum); 
    end
end
Msample=(1/(ell*class))*Msample;                       %求平均向量
Sb=zeros(d,d);    % 计算between-class matrix Sb
for classnum=1:class      
    Sb=Sb+ell*(Minclass(:,classnum)-Msample)*(Minclass(:,classnum)-Msample)';
end
% d=dim;                                 % 选择 d =dim 个最大的特征值
[Fi,Ci]=eigs(Sw,d,'LM');  % 求出 R 的eigenvector and eigenvalue
Diag=zeros(1,d)
for p=1:d
    Diag(1,p)=1/(sqrt(Ci(p,p)));
end
Cmodify=diag(Diag);
Klda=Cmodify*Fi'*Sb*Fi*Cmodify;
m=lda;
[Ulda,Llda]=eigs(Klda,m,'LM');  % 求出 R 的eigenvector and eigenvalue
Wfld=Fi*Cmodify*Ulda;
Ilda=zeros(m,ell,class); 
for classnum=1:class
    for num=1:ell
        Ilda(:,num,classnum)=Wfld'*Iy(:,num,classnum);
    end
end

% -------------------------------------------------------------------------
Tlda=zeros(m,ellsample,class);
for classnum=1:class
    for num=1:ellsample
        Tlda(:,num,classnum)=Wfld'*Tpca(:,num,classnum);
    end
end
%%%%%-----------------------------------------------%%%%%


% --------------------------------------算法性能测试----------------------------------------%
r=zeros(ellsample,ellsample); 
CorrectMatrix=zeros(1,class*ellsample);
Glda=zeros(class,ellsample, class);


for cl=1:class
    for img=1:ellsample        %从此处到程序结束都为循环体
        
        
        %---------------------------循环体开始-------------------------------%
        
        X=Tlda(:,img,cl);                     % X   input sample vector            %
        %以下为改进算法, 求每个类的 Z1 的平均值
        Iymean=zeros(m,class); 
        for classnum=1:class              % Z1 :  the mean of Z1
            for i=1:ell
                Iymean(:,classnum)=Iymean(:,classnum)+Ilda(:,i,classnum); 
            end
            Iymean(:,classnum)=(1/ell)*Iymean(:,classnum);
        end
        %-------------------------进行匹配－－－－－－－－－－－－－－－－－－－%
        %----------------此处可以进行修改，利用其他simlarity measure------------%
        
        G2=zeros(1,class); 
        
        for classnum=1:class   
            G2(1,classnum)=(X'*Iymean(:,classnum))/(norm(X)*norm(Iymean(:,classnum)));      
        end
        Glda(:,img,cl)=G2';
        Sclass=max(G2);
        
        %---------------得出最后的结果－－－－－－－－－－－－－－－－－－－－－%
        for classnum=1:class   
            if Sclass==G2(1,classnum)
                lastresult=classnum;
            end   
        end
        lastresult
        %---------------进行最后结果的评估  -----------------%
        
        if lastresult==cl
            CorrectMatrix(1,img+(cl-1)*ellsample)=1;% 如果正确，则置为 1；否则，保持不变为0；
        end
        
        rate=sum(CorrectMatrix)/(class*ellsample);
        
    end
end