黎曼MDS降维算法MATLAB代码

以下是黎曼MDS降维算法的MATLAB代码，仅供参考：

function [Y, eigvalue] = RiemannMDS(X, d)
% X: input SPD matrices in the cell format (N x 1), N is the number of matrices
% d: the number of dimensions for the embedding space
% Y: output low-dimensional embedding vectors (N x d)
% eigvalue: the eigenvalues of the covariance matrix

    N = length(X);
    P = zeros(N, N);
    for i = 1:N
        for j = 1:N
            P(i,j) = log(det(X{i} + X{j})) - 0.5 * (log(det(X{i})) + log(det(X{j})));
        end
    end
    P = -0.5 * P;
    H = eye(N) - ones(N, N)/N;
    B = H * P * H;
    [V, D] = eig(B);
    [~, index] = sort(diag(D), 'descend');
    Y = V(:, index(1:d)) * sqrt(D(index(1:d), index(1:d)));
    eigvalue = diag(D);

end

该代码实现了Riemannian MDS算法，对输入的SPD矩阵进行降维。具体实现过程为：计算输入矩阵的黎曼距离矩阵，将其转化为半正定矩阵，并进行特征值分解，选取前d个特征值对应的特征向量作为输出矩阵的降维结果。