基于EM算法的IS散度NMF算法的matlab代码

以下是基于EM算法的IS散度NMF算法的matlab代码示例：

function [W, H] = is_nmf_em(V, r, max_iter)
% V: 数据矩阵，r: 分解的秩，max_iter: 最大迭代次数
% W: 基矩阵，H: 系数矩阵

% 初始化W和H
W = rand(size(V, 1), r);
H = rand(r, size(V, 2));

% 迭代更新W和H
for i = 1:max_iter
    % 更新H
    V_hat = W * H;
    H = H .* (W' * (V ./ V_hat)) ./ (W' * ones(size(V)));
    
    % 更新W
    V_hat = W * H;
    W = W .* ((V ./ V_hat) * H') ./ (ones(size(V, 1)) * H');
end
end

该代码实现了基于EM算法的IS散度NMF算法，输入参数为数据矩阵V、分解秩r和最大迭代次数max_iter，输出结果为基矩阵W和系数矩阵H。在迭代更新W和H时，分别使用了V和V_hat的IS散度作为损失函数。

相关问题

IS散度的NMF算法matlab代码

以下是IS散度的NMF算法的MATLAB代码：

function [W,H] = nmf_isdiv(X,k,max_iter)
% NMF using IS divergence
% X: input matrix
% k: number of basis vectors
% max_iter: maximum number of iterations
% W: basis matrix
% H: coefficient matrix

% initialize W and H with random values
[n,m] = size(X);
W = rand(n,k);
H = rand(k,m);

% set small value for avoiding division by zero
eps = 1e-16;

% iterate until convergence or max_iter
for iter = 1:max_iter
    % update H
    for j = 1:m
        H(:,j) = H(:,j) .* (W' * (X(:,j) ./ (W * H(:,j) + eps))) ./ sum(W,1)';
    end
    
    % update W
    for i = 1:n
        W(i,:) = W(i,:) .* ((X(i,:) ./ (W(i,:) * H + eps)) * H') ./ sum(H,2)';
    end
    
    % calculate IS divergence
    div = sum(sum(X .* log(X./(W*H+eps)) - X + W*H));
    
    % check for convergence
    if iter > 1 && abs(div-prev_div) < 1e-6
        break
    end
    prev_div = div;
end

end

使用方法：

假设X为输入矩阵，k为基向量的数量，max_iter为最大迭代次数。调用函数nmf_isdiv(X,k,max_iter)即可进行IS散度的NMF算法计算，返回值为W和H矩阵。

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。