Spherical K-Means Clustering

spkmeans.m

function [U,V,idx] = spkmeans(X,k,tol,imax)

  [d,n] = size(X);
  
  U = zeros(d,k);
  V = zeros(k,n);
  
  % random clusters and normalize to unit sphere.
  for j = 1:n
    V(randi(k),j) = 1;
    X(:,j)        = X(:,j) ./ norm(X(:,j));
  end
  
  % monitor convergence.
  olderr = 0;
  
  for iter = 0:imax
    % recompute assignments.
    if iter > 0
      for i = 1:n
        dots    = X(:,i)' * U;
        [~,ix]  = max(dots);
        
        col       = zeros(k,1);
        col(ix,1) = 1;
        
        V(:,i) = col;
      end
    end
    
    % monitor cost.
    newerr = 0;
    
    % update or initialize concept vectors.
    for i = 1:k
      ix = find(V(i,:) == 1);
      m  = (1/numel(ix)) * sum(X(:,ix),2);
      c  = m / norm(m);
      
      U(:,i) = c;
      newerr = newerr + sum(X(:,ix)' * c);
    end
    
    fprintf('Iteration %f\tCost function: %f\n', iter, newerr);
    
    if newerr > 0 && olderr > 0 && newerr - olderr < tol
      break;
    end
    
    olderr = newerr;
  end
  
  % which clusters?
  [~,idx] = max(V);
  
end