IS散度的NMF/MU算法matlab代码

以下是基于IS散度的NMF/MU算法的Matlab代码：

function [W,H] = nmf_is(X,r,max_iter)
% NMF based on IS divergence
% Input:
%   X: data matrix (n x m)
%   r: number of basis vectors
%   max_iter: maximum number of iterations
% Output:
%   W: basis matrix (n x r)
%   H: activation matrix (r x m)
% Reference:
%   Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects
%   by non-negative matrix factorization. Nature, 401(6755), 788-791.

% Initialize W and H
[n,m] = size(X);
W = rand(n,r);
H = rand(r,m);

% Calculate initial objective value
obj = sum(sum(X.*log(X./(W*H)) - X + W*H));

% Perform multiplicative updates
for iter = 1:max_iter
    % Update H
    H = H.*(W'*((X./(W*H)).^2))./(W'*X);
    
    % Update W
    W = W.*(((X./(W*H)).^2)*H')./(W*(H*H'));
    
    % Calculate objective value
    new_obj = sum(sum(X.*log(X./(W*H)) - X + W*H));
    
    % Check convergence
    if abs(new_obj - obj) < 1e-6
        break;
    end
    
    obj = new_obj;
end

end

其中，`X` 是输入数据矩阵，`r` 是要分解的基向量数量， `max_iter` 是最大迭代次数。函数返回基矩阵 `W` 和激活矩阵 `H`。算法的具体实现采用了基于IS散度的NMF/MU算法，参考文献为Lee和Seung在Nature上发表的论文：Learning the parts of objects by non-negative matrix factorization。