fisher鉴别分析（FLDA）Matlab代码实现

% Fisherface for Recognition function [ ProjectedTrainSamples,ProjectedTestSamples ]=LDA_zq(TrainSamples ,TestSamples,ClassNum) c = ClassNum; % 类别数 ni = 2*size(TrainSamples,2)/c; % 每类样本数 smalle = 10.^(-5); % 一个小数字阈值 nitr = ni/2; % 每类一半样本作为训练样本 nite = ni - nitr; % 其余一般作为测试样本 trsize = nitr*c; % 训练样本总数 N tesize = size(TestSamples,2); % 测试样本总数 x = TrainSamples; xm = mean(x,2); x = x - repmat(xm,1,trsize); % 训练样本及中心化 %%PCA [w e explain] = pcacov(x'*x); r = length(find(e>smalle)); w = w(:,1:r); e = e(1:r); w = x*w*diag(1./sqrt(e)); % SVD方法求解PCA x0 = w'*x; % 将训练样本投影到PCA子空间, 这里,w 即为W_pca xt0 = w'*(TestSamples - repmat(xm,1,tesize)); % 同样地，将测试样本投影到PCA子空间 clear xm; clear w; clear x; dim = trsize-c; % Fisherface方法要求将PCA子空间的维数取为N-c x = x0(1:dim,:); xm = mean(x,2); Hw = []; mi = []; %LDA for i = 1:c xi = x(:,(i-1)*nitr+1:i*nitr); mi(:,i) = mean(xi,2); Hw = [Hw,xi-repmat(mi(:,i),1,nitr)]; clear xi; end Sw = Hw*Hw'; % 计算类内散布矩阵Sw clear Hw; Hb = mi - repmat(xm,1,c); Sb = nitr*Hb*Hb'; clear Hb; % 计算类间散布矩阵Sb [w e] = eig(inv(Sw)*Sb); % 求解 Sb * w = lamda * Sw * w e = diag(e); re = find(imag(e)==0 & real(e)>smalle); e = e(re); w = w(:,re); [e2 id] = sort(e); w2 = w(:,id); e = flipud(e2); w = fliplr(w2); clear e2; clear w2; r = length(e); % r 是最终LDA子空间的维数，一般情况下等于c-1 xproj0 = w'*x; % 将训练样本进一步降维到LDA子空间，这里,w 即为W_lda xtproj0 = w'*xt0(1:dim,:); % 同样地，将测试样本进一步降维到同样的LDA子空间 prj = r; % Dimensionality of the final subspace xproj = xproj0(1:prj,:); % 最终被降维后的训练样本 xtproj = xtproj0(1:prj,:); % 最终被降维后的测试样本 ProjectedTrainSamples=xproj; ProjectedTestSamples=xtproj;