流形学习算法实现（LE\LLE\Isomap）.zip

function Z = Isomap(X,K,d) X = X'; %转置样本 [N,m] = size(X); distance = zeros(N,N); for i=1:N for j=1:N for k=1:m distance(i,j) =distance(i,j)+(X(i,k)-X(j,k))^2; %利用欧式距离确定K近邻 end distance(i,j)=sqrt(distance(i,j)); end end [~,index]=sort(distance,2); %前K列表示距离最近的K个样本所在的列数 for i=1:N for j=K+1:N distance(i,index(i,j))=inf; end end %采用MDS算法 %step1调用最短路径法得到距离矩阵(Dijkstra) % dis = zeros(N,1); %存储每一行的最短路径 idx = []; %存储最短路径对应的编号 % for i=1:N for i=1:N % dis = distance(i,:); j = 1; while j<N+1 [~,idx] = sort(distance(i,:)); for k=1:N if(distance(idx(j),k)~=inf) if(distance(i,k)>distance(idx(j),k)+distance(i,idx(j))) distance(i,k)=distance(idx(j),k)+distance(i,idx(j)); end end end j=j+1; end end for i=1:N for j=1:N distance(i,j) = min(distance(i,j),distance(j,i)); end end %step2构造矩阵D2 D2 = distance.*distance; %step3构造矩阵B e = ones(N,d); H = eye(N,N)-1/N*(e*e'); B = -1/2*H'*D2*H; %step4将B特征值分解，得到Z [V,U]=eig(B); U = diag(U); [~, pos] = sort(U,'descend'); index = pos(1:d); V = V(:, index); Z = diag(U(index))^(0.5) * V';