(matlab)kmeans.m

关于k-means聚类算法的MATLAB实现

        % Deal with clusters that have just lost all their members
        empties = changed(m(changed) == 0);
        if ~isempty(empties)
            switch emptyact
            case 'error'
                error(sprintf('Empty cluster created at iteration %d.',iter));
            case 'drop'
                % Remove the empty cluster from any further processing
                D(:,empties) = NaN;
                changed = changed(m(changed) > 0);
                if display > 0
                    warning(sprintf('Empty cluster created at iteration %d.',iter));
                end
            case 'singleton'
                if display > 0
                    warning(sprintf('Empty cluster created at iteration %d.',iter));
                end
                
                for i = empties
                    % Find the point furthest away from its current cluster.
                    % Take that point out of its cluster and use it to create
                    % a new singleton cluster to replace the empty one.
                    [dlarge, lonely] = max(d);
                    from = idx(lonely); % taking from this cluster
                    C(i,:) = X(lonely,:);
                    m(i) = 1;
                    idx(lonely) = i;
                    d(lonely) = 0;
                    
                    % Update clusters from which points are taken
                    [C(from,:), m(from)] = gcentroids(X, idx, from, distance, Xsort, Xord);
                    changed = unique([changed from]);
                end
            end
        end
    end % phase one

    % Initialize some cluster information prior to phase two
    switch distance
    case 'cityblock'
        Xmid = zeros([k,p,2]);
        for i = 1:k
            if m(i) > 0
                % Separate out sorted coords for points in i'th cluster,
                % and save values above and below median, component-wise
                Xsorted = reshape(Xsort(idx(Xord)==i), m(i), p);
                nn = floor(.5*m(i));
                if mod(m(i),2) == 0
                    Xmid(i,:,1:2) = Xsorted([nn, nn+1],:)';
                elseif m(i) > 1
                    Xmid(i,:,1:2) = Xsorted([nn, nn+2],:)';
                else
                    Xmid(i,:,1:2) = Xsorted([1, 1],:)';
                end
            end
        end
    case 'hamming'
        Xsum = zeros(k,p);
        for i = 1:k
            if m(i) > 0
                % Sum coords for points in i'th cluster, component-wise
                Xsum(i,:) = sum(X(idx==i,:), 1);
            end
        end
    end
    
    %
    % Begin phase two:  single reassignments
    %
    changed = find(m' > 0);
    lastmoved = 0;
    nummoved = 0;
    iter1 = iter;
    while iter < maxit
        % Calculate distances to each cluster from each point, and the
        % potential change in total sum of errors for adding or removing
        % each point from each cluster.  Clusters that have not changed
        % membership need not be updated.
        %
        % Singleton clusters are a special case for the sum of dists
        % calculation.  Removing their only point is never best, so the
        % reassignment criterion had better guarantee that a singleton
        % point will stay in its own cluster.  Happily, we get
        % Del(i,idx(i)) == 0 automatically for them.
		switch distance
		case 'sqeuclidean'
            for i = changed
                mbrs = (idx == i);
                sgn = 1 - 2*mbrs; % -1 for members, 1 for nonmembers
                if m(i) == 1
                    sgn(mbrs) = 0; % prevent divide-by-zero for singleton mbrs
                end
                Del(:,i) = (m(i) ./ (m(i) + sgn)) .* sum((X - C(repmat(i,n,1),:)).^2, 2);
            end
        case 'cityblock'
            for i = changed
                if mod(m(i),2) == 0 % this will never catch singleton clusters
                    ldist = Xmid(repmat(i,n,1),:,1) - X;
                    rdist = X - Xmid(repmat(i,n,1),:,2);
                    mbrs = (idx == i);
                    sgn = repmat(1-2*mbrs, 1, p); % -1 for members, 1 for nonmembers
                    Del(:,i) = sum(max(0, max(sgn.*rdist, sgn.*ldist)), 2);
                else
                    Del(:,i) = sum(abs(X - C(repmat(i,n,1),:)), 2);
                end
            end
        case {'cosine','correlation'}
            % The points are normalized, centroids are not, so normalize them
            normC(changed) = sqrt(sum(C(changed,:).^2, 2));
            if any(normC < eps) % small relative to unit-length data points
                error(sprintf('Zero cluster centroid created at iteration %d.',iter));
            end
            % This can be done without a loop, but the loop saves memory allocations
            for i = changed
                XCi = X * C(i,:)';
                mbrs = (idx == i);
                sgn = 1 - 2*mbrs; % -1 for members, 1 for nonmembers
                Del(:,i) = 1 + sgn .*...
                      (m(i).*normC(i) - sqrt((m(i).*normC(i)).^2 + 2.*sgn.*m(i).*XCi + 1));
            end
        case 'hamming'
            for i = changed
                if mod(m(i),2) == 0 % this will never catch singleton clusters
                    % coords with an unequal number of 0s and 1s have a
                    % different contribution than coords with an equal
                    % number
                    unequal01 = find(2*Xsum(i,:) ~= m(i));
                    numequal01 = p - length(unequal01);
                    mbrs = (idx == i);
                    Di = abs(X(:,unequal01) - C(repmat(i,n,1),unequal01));
                    Del(:,i) = (sum(Di, 2) + mbrs*numequal01) / p;
                else
                    Del(:,i) = sum(abs(X - C(repmat(i,n,1),:)), 2) / p;
                end
            end
		end

        % Determine best possible move, if any, for each point.  Next we
        % will pick one from those that actually did move.
        previdx = idx;
        prevtotsumD = totsumD;
        [minDel, nidx] = min(Del, [], 2);
        moved = find(previdx ~= nidx);
        if length(moved) > 0
            % Resolve ties in favor of not moving
            moved = moved(Del((previdx(moved)-1)*n + moved) > minDel(moved));
        end
        if length(moved) == 0
            % Count an iteration if phase 2 did nothing at all, or if we're
            % in the middle of a pass through all the points
            if (iter - iter1) == 0 | nummoved > 0
                iter = iter + 1;
                if display > 2 % 'iter'
                    disp(sprintf(dispfmt,iter,2,nummoved,totsumD));
                end
            end
            converged = true;
            break;
        end
        
        % Pick the next move in cyclic order
        moved = mod(min(mod(moved - lastmoved - 1, n) + lastmoved), n) + 1;
        
        % If we've gone once through all the points, that's an iteration
        if moved <= lastmoved
            iter = iter + 1;
            if display > 2 % 'iter'
                disp(sprintf(dispfmt,iter,2,nummoved,totsumD));
            end
            if iter >= maxit, break; end
            nummoved = 0;
        end
        nummoved = nummoved + 1;
        lastmoved = moved;
        
        oidx = idx(moved);
        nidx = nidx(moved);
        totsumD = totsumD + Del(moved,nidx) - Del(moved,oidx);
        
        % Update the cluster index vector, and rhe old and new cluster
        % counts and centroids
        idx(moved) = nidx;
        m(nidx) = m(nidx) + 1;
        m(oidx) = m(oidx) - 1;
        switch distance
        case 'sqeuclidean'
            C(nidx,:) = C(nidx,:) + (X(moved,:) - C(nidx,:)) / m(nidx);
            C(oidx,:) = C(oidx,:) - (X(moved,:) - C(oidx,:)) / m(oidx);
        case 'cityblock'
            for i = [oidx nidx]
                % Separate out sorted coords for points in each cluster.
                % New centroid is the coord median, save values above and
                % below median.  All done component-wise.
                Xsorted = reshape(Xsort(idx(Xord)==i), m(i), p);
                nn = floor(.5*m(i));
                if mod(m(i),2) == 0
                    C(i,:) = .5 * (Xsorted(nn,:) + Xsorted(nn+1,:));
                    Xmid(i,:,1:2) = Xsorted([nn, nn+1],:)';
                else
                    C(i,:) = Xsorted(nn+1,:);
                    if m(i) > 1
                        Xmid(i,:,1:2) = Xsorted([nn, nn+2],:)';
                    else
                        Xmid(i,:,1:2) = Xsorted([1, 1],:)';
                    end
                end
            end
        case {'cosine','correlation'}
            C(nidx,:) = C(nidx,:) + (X(moved,:) - C(nidx,:)) / m(nidx);
            C(oidx,:) = C(oidx,:) - (X(moved,:) - C(oidx,:)) / m(oidx);
        case 'hamming'
            % Update summed coords for points in each cluster.  New
            % centroid is the coord median.  All done component-wise.
            Xsum(nidx,:) = Xsum(nidx,:) + X(moved,:);
            Xsum(oidx,:) = Xsum(oidx,:) - X(moved,:);
            C(nidx,:) = .5*sign(2*Xsum(nidx,:) - m(nidx)) + .5;
            C(oidx,:) = .5*sign(2*Xsum(oidx,:) - m(oidx)) + .5;
        end
        changed = sort([oidx nidx]);
    end % phase two
    
    if (~converged) & (display > 0)
        warning(sprintf('Failed to converge in %d iterations.', maxit));
    end

    % Calculate cluster-wise sums of distances
    nonempties = find(m(:)'>0);
    D(:,nonempties) = distfun(X, C(nonempties,:), distance, iter);
    d = D((idx-1)*n + (1:n)');
    sumD = zeros(k,1);
    for i = 1:k
        sumD(i) = sum(d(idx == i));
    end
    if display > 1 % 'final' or 'iter'
        disp(sprintf('%d iterations, total sum of distances = %g',iter,totsumD));
    end

    % Save the best solution so far
    if totsumD < totsumDBest
        totsumDBest = totsumD;
        idxBest = idx;
        Cbest = C;
        sumDBest = sumD;
        if nargout > 3
            Dbest = D;
        end
    end
end

% Return the best solution
idx = idxBest;
C = Cbest;
sumD = sumDBest;
if nargout > 3
    D = Dbest;
end


%------------------------------------------------------------------

function D = distfun(X, C, dist, iter)
%DISTFUN Calculate point to cluster centroid distances.
[n,p] = size(X);
D = zeros(n,size(C,1));
clusts = 1:size(C,1);

switch dist
case 'sqeuclidean'
    for i = clusts
        D(:,i) = sum((X - C(repmat(i,n,1),:)).^2, 2);
    end
case 'cityblock'
    for i = clusts
        D(:,i) = sum(abs(X - C(repmat(i,n,1),:)), 2);
    end
case {'cosine','correlation'}
    % The points are normalized, centroids are not, so normalize them
    normC = sqrt(sum(C.^2, 2));
    if any(normC < eps) % small relative to unit-length data points
        error(sprintf('Zero cluster centroid created at iteration %d.',iter));
    end
    % This can be done without a loop, but the loop saves memory allocations
    for i = clusts
        D(:,i) = 1 - (X * C(i,:)') ./ normC(i);
    end
case 'hamming'
    for i = clusts
        D(:,i) = sum(abs(X - C(repmat(i,n,1),:)), 2) / p;
    end
end


%------------------------------------------------------------------

function [centroids, counts] = gcentroids(X, index, clusts, dist, Xsort, Xord)
%GCENTROIDS Centroids and counts stratified by group.
[n,p] = size(X);
num = length(clusts);
centroids = repmat(NaN, [num p]);
counts = zeros(num,1);
for i = 1:num
    members = find(index == clusts(i));
    if length(members) > 0
        counts(i) = length(members);
        switch dist
        case 'sqeuclidean'
            centroids(i,:) = sum(X(members,:),1) / counts(i);
        case 'cityblock'
            % Separate out sorted coords for points in i'th cluster,
            % and use to compute a fast median, component-wise
            Xsorted = reshape(Xsort(index(Xord)==clusts(i)), counts(i), p);
            nn = floor(.5*counts(i));
            if mod(counts(i),2) == 0
                centroids(i,:) = .5 * (Xsorted(nn,:) + Xsorted(nn+1,:));
            else
                centroids(i,:) = Xsorted(nn+1,:);
            end
        case {'cosine','correlation'}
            centroids(i,:) = sum(X(members,:),1) / counts(i); % unnormalized
        case 'hamming'
            % Compute a fast median for binary data, component-wise
            centroids(i,:) = .5*sign(2*sum(X(members,:), 1) - counts(i)) + .5;
        end
    end
end