Question

我正在matlab中实现期望最大化算法。算法在214096 x 2数据矩阵上运行，并且在计算概率时，存在（214096 x 2）*（2 x 2）*（2 x 214096）矩阵的乘法，这导致matlab中的内存不足错误。有没有办法解决这个问题？

Equation

Matlab代码：

          enter image description here  D = size(X,2); % dimension
            N = size(X,1); % number of samples
            K = 4; % number of Gaussian Mixture components ( Also number of clusters )

            % Initialization
            p = [0.2, 0.3, 0.2, 0.3]; % arbitrary pi, probabilities of clusters, apriori probability of cluster
            [idx,mu] = kmeans(X,K); % initial means of the components, theta is mu and variance

            % compute the covariance of the components
            sigma = zeros(D,D,K);
            for k = 1:K
                tempmat = X(idx==k,:);
                sigma(:,:,k) = cov(tempmat);  % Sigma j
                sigma_det(k) = det(sigma(:,:,k));
            end

            % calculate x-mu
            for k=1: K
                            check=length( X(idx == k,1))
                            for  lidx = 1: length( X(idx == k,1))

                                cidx = find( idx == k) ;
                                Xmu(cidx(lidx),:) = X(cidx(lidx),:) - mu(k,:); %( x-mu ) calculation on cluster level
                            end
            end


            % compute P(Cj|x; theta(t)), and take log to simplified calculation

            %Eq 14.14 denominator 
            denom = 0;
            for k=1:K
                calc_sigma_1_2 = sigma_det(k)^(-1/2);
                calc_x_mu = Xmu(idx == k,:);
                calc_sigma_inv = inv(sigma(:,:,k)); 
                calc_x_mu_tran = calc_x_mu.';
                factor = calc_sigma_1_2 * exp (-1/2 * calc_x_mu * calc_sigma_inv * calc_x_mu_tran  ) * p(k);

                denom = denom + factor;
            end


            for k =1:K 
                calc_sigma_1_2 = sigma_det(k)^(-1/2);
                calc_x_mu = Xmu(idx == k,:);
                calc_sigma_inv = inv(sigma(:,:,k)); 
                calc_x_mu_tran = calc_x_mu.';
                factor = calc_sigma_1_2 * exp (-1/2 * calc_x_mu_tran * calc_sigma_inv * calc_x_mu ) * p(k);

                pdf(k) = factor/denom;
            end

            %%%% Equation 14.14 ends

Answer 1

似乎你试图通过简单地用向量代替矩阵来应用基于向量的方程，这不是它的工作原理

section.box

应该是（x-mu）的 mahalanobis 范数，并且您希望每个矩阵X的每一行获得此值，因此

(x - mu).' * Inv(sigma) * (x-mu)

现在你必须做逐点 A乘以（X-mu），而不是点积，最后求和第二轴（列），这样你最终得到(X - mu).' * Inv(sigma) =: A <- this is ok, this results in N x d matrix元素向量，每个元素向量包含来自X的相应行的马哈拉诺比斯范数。

期望最大化算法matlab内存不足错误

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