function [cid,nr,centers] = cskmeans(x,k,nc)
　　% CSKMEANS K-Means clustering - general method.
　　% 
　　% This implements the more general k-means algorithm, where 
　　% HMEANS is used to find the initial partition and then each
　　% observation is examined for further improvements in minimizing
　　% the within-group sum of squares.
　　%
　　% [CID,NR,CENTERS] = CSKMEANS(X,K,NC) Performs K-means
　　% clustering using the data given in X. 
　　% 
　　% INPUTS: X is the n x d matrix of data,
　　% where each row indicates an observation. K indicates
　　% the number of desired clusters. NC is a k x d matrix for the
　　% initial cluster centers. If NC is not specified, then the
　　% centers will be randomly chosen from the observations.
　　%
　　% OUTPUTS: CID provides a set of n indexes indicating cluster
　　% membership for each point. NR is the number of observations
　　% in each cluster. CENTERS is a matrix, where each row
　　% corresponds to a cluster center.
　　%
　　% See also CSHMEANS
　　% W. L. and A. R. Martinez, 9/15/01
　　% Computational Statistics Toolbox 
　　warning off
　　[n,d] = size(x);
　　if nargin < 3
　　% Then pick some observations to be the cluster centers.
　　ind = ceil(n*rand(1,k));
　　% We will add some noise to make it interesting.
　　nc = x(ind,:) + randn(k,d);
　　end
　　% set up storage
　　% integer 1,...,k indicating cluster membership
　　cid = zeros(1,n); 
　　% Make this different to get the loop started.
　　oldcid = ones(1,n);
　　% The number in each cluster.
　　nr = zeros(1,k); 
　　% Set up maximum number of iterations.
　　maxiter = 100;
　　iter = 1;
　　while ~isequal(cid,oldcid) & iter < maxiter
　　% Implement the hmeans algorithm
　　% For each point, find the distance to all cluster centers
　　for i = 1:n
　　dist = sum((repmat(x(i,:),k,1)-nc).^2,2);
　　[m,ind] = min(dist); % assign it to this cluster center
　　cid(i) = ind;
　　end
　　% Find the new cluster centers
　　for i = 1:k
　　% find all points in this cluster
　　ind = find(cid==i);
　　% find the centroid
　　nc(i,:) = mean(x(ind,:));
　　% Find the number in each cluster;
　　nr(i) = length(ind);
　　end
　　iter = iter + 1;
　　end
　　% Now check each observation to see if the error can be minimized some more. 
　　% Loop through all points.
　　maxiter = 2;
　　iter = 1;
　　move = 1;
　　while iter < maxiter & move ~= 0 
　　move = 0;
　　% Loop through all points.
　　for i = 1:n
　　% find the distance to all cluster centers
　　dist = sum((repmat(x(i,:),k,1)-nc).^2,2);
　　r = cid(i); % This is the cluster id for x
　　%%nr,nr+1;
　　dadj = nr./(nr+1).*dist'; % All adjusted distances
　　[m,ind] = min(dadj); % minimum should be the cluster it belongs to
　　if ind ~= r % if not, then move x
　　cid(i) = ind;
　　ic = find(cid == ind);
　　nc(ind,:) = mean(x(ic,:));
　　move = 1;
　　end
　　end
　　iter = iter+1;
　　end
　　centers = nc;
　　if move == 0
　　disp('No points were moved after the initial clustering procedure.')
　　else
　　disp('Some points were moved after the initial clustering procedure.')
　　end