期望最大化算法matlab内存不足错误

我在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，这会导致matlab内存不足。有没有办法解决这个问题？期望最大化算法matlab内存不足错误

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

来源

2016-05-11 Umar

是214096维数/特征的数量？ – lejlot

214096是2个维度中每个维度的观察次数 – Umar

在EM算法中，您会得到N^2个元素的矩阵吗？它似乎不正确。你为什么需要Gramian？ – lejlot

看来你试图通过简单的矩阵替代向量应用基于矢量方程，这是不是它是如何工作

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

是应该是mahalanobis（x-mu）的范数，并且您想要获得每行矩阵的这个值X，从而

(X - mu).' * Inv(sigma) =: A <- this is ok, this results in N x d matrix

，现在你要做的逐点乘法与（X - 亩），而不是一个点的产品，最后总结了第二轴（列），这样一来你结束与N元素矢量相关，每个元素包含从X起对应行的mahalanobis范数。

来源

2016-05-12 00:10:37 lejlot

非常感谢@lejlot，即时修复这个问题 – Umar

期望最大化算法matlab内存不足错误

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