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%APCLUSTERMEX Affinity Propagation Clustering (Frey/Dueck, Science 2007)
% [idx,netsim,dpsim,expref]=APCLUSTERMEX(s,p) clusters data, using a set
% of real-valued pairwise data point similarities as input. Clusters
% are each represented by a cluster center data point (the "exemplar").
% The method is iterative and searches for clusters so as to maximize
% an objective function, called net similarity.
%
% For N data points, there are potentially N^2-N pairwise similarities;
% this can be input as an N-by-N matrix 's', where s(i,k) is the
% similarity of point i to point k (s(i,k) needn’t equal s(k,i)). In
% fact, only a smaller number of relevant similarities are needed; if
% only M similarity values are known (M < N^2-N) they can be input as
% an M-by-3 matrix with each row being an (i,j,s(i,j)) triple.
%
% APCLUSTERMEX automatically determines the number of clusters based on
% the input preference 'p', a real-valued N-vector. p(i) indicates the
% preference that data point i be chosen as an exemplar. Often a good
% choice is to set all preferences to median(s); the number of clusters
% identified can be adjusted by changing this value accordingly. If 'p'
% is a scalar, APCLUSTERMEX assumes all preferences are that shared value.
%
% The clustering solution is returned in idx. idx(j) is the index of
% the exemplar for data point j; idx(j)==j indicates data point j
% is itself an exemplar. The sum of the similarities of the data points to
% their exemplars is returned as dpsim, the sum of the preferences of
% the identified exemplars is returned in expref and the net similarity
% objective function returned is their sum, i.e. netsim=dpsim+expref.
%
% [ ... ]=apclustermex(s,p,'NAME',VALUE,...) allows you to specify
% optional parameter name/value pairs as follows:
%
% 'maxits' maximum number of iterations (default: 500)
% 'convits' if the estimated exemplars stay fixed for convits
% iterations, APCLUSTERMEX terminates early (default: 50)
% 'dampfact' update equation damping level in [0.5, 1). Higher
% values correspond to heavy damping, which may be needed
% if oscillations occur.
% 'plot' (no value needed) Plots netsim after each iteration
% 'details' (no value needed) Outputs iteration-by-iteration
% details (greater memory requirements)
% 'nonoise' (no value needed) APCLUSTERMEX adds a small amount of
% noise to 's' to prevent degenerate cases; this disables that.
% 'callback' provide a callback m-function invoked each iteration
% 0=action=fn(a,r,idx,netsim,dpsim,expref,iter)
%
% Copyright (c) B.J. Frey & D. Dueck (2006). This software may be
% freely used and distributed for non-commercial purposes.
function [idx,netsim,dpsim,expref] = apclustermex(s,p,varargin)
start = clock;
if ~issparse(s) && size(s,1)==size(s,2), % full+square matrix
si=[]; sj=[]; sij=s(:); [I,J]=size(s); sij(sub2ind([I J],1:I,1:I))=p(:)';
else % non-full+square matrix
if size(s,2)==3, si=s(:,1);sj=s(:,2); sij=s(:,3); elseif issparse(s), [si,sj,sij]=find(s); end;
I=max(si); J=max(sj);
ii=find(si==sj); if isempty(ii), si=[si; (1:max(I,J))']; sj=[sj; (1:max(I,J))']; ii=find(si==sj); end; % if no diagonal elements are given, add the full set
[junk,order]=sort(si(ii)); sij(ii(order))=p; % set "all" diagonal elements to the preference(s)
if isempty(find(sisj,1,'first')), warning('s(i,j) does not imply s(j,i) -- check if all desired (i,j) pairs are included'); end;
end;
N=length(sij);
% set up apcluster options (including computing platform)
options.cbSize=40;
options.lambda=0.9;
options.minimum_iterations=1;
options.converge_iterations=50;
options.maximum_iterations=500;
options.details=0;
options.nonoise=0;
options.progressfunction=[];
options.kcc=0; options.vsh=0;
switch(computer),
case {'PCWIN'}, options.cbSize=40; kccoptions.cbSize=32;
case {'GLNXA64'}, options.cbSize=48; kccoptions.cbSize=40;
case {'GLNX86'}, options.cbSize=36;
otherwise, error('Affinity Propagation not supported on %s platform [yet]',computer);
end;
while numel(varargin),
switch(varargin{1}),
case {'nokcc','pure','nofixup','nocleanup'}, options.kcc=0; varargin(1)=[];
case {'novsh'}, options.vsh=0; varargin(1)=[];
case {'vsh'}, options.vsh=1; varargin(1)=[];
case {'kcc','fixup','cleanup'}, options.kcc=1; varargin(1)=[];
case {'details','det'}, options.details=1; varargin(1)=[];
case {'nodetails','nodet'}, options.details=0; varargin(1)=[];
case {'noise','plusnoise','+noise','addnoise'}, options.nonoise=0;
case {'nonoise','-noise'}, options.nonoise=1; varargin(1)=[];
case {'plot','plt'}, warning('plotting not supported within compiled MEX-files'); varargin(1)=[];
case {'convits','cnvits','conv','cnv'}, options.converge_iterations=varargin{2}; varargin(1:2)=[];
case {'dampfact','damping','dmpfact','lambda'}, options.lambda=varargin{2}; varargin(1:2)=[];
case {'maxiter','mxiter','maxits','mxits'}, options.maximum_iterations=varargin{2}; varargin(1:2)=[];
case {'callback','callbackfunction','callbackfcn','callbackfn','progressfn','progressfcn','progressfunction','progress','function'}, options.progressfunction=varargin{2}; varargin(1:2)=[];
otherwise, varargin(1)=[];
end;
end;
if isa(options.progressfunction,'function_handle'), options.progressfunction=func2str(options.progressfunction); end;
if strcmp(options.progressfunction,''), options.progressfunction=[]; end;
if exist(options.progressfunction), if exist(options.progressfunction)~=2, options.progressfunction=[]; warning('nonexistent callback function specified'); end; end;
if I<2^16-1, si=uint16(si-1); sj=uint16(sj-1); else si=uint32(si-1); sj=uint32(sj-1); end;
if options.details, % set up return arguments (reference parameters)
idx = -ones(I,options.maximum_iterations,'int32');
netsim = zeros(1,options.maximum_iterations);
dpsim = zeros(1,options.maximum_iterations);
expref = zeros(1,options.maximum_iterations);
else
idx=-ones(I,1,'int32');
netsim = 0;
dpsim = 0;
expref = 0;
end; netsim(1)=1e-38; dpsim(1)=1e-38; expref(1)=1e-38; % this makes sure the memory is allocated (compatibility reasons)
ret=apclustermex_(sij,si,sj,idx,netsim,dpsim,expref,options);
if ret<0, error('apclustermex returned error code %d',ret); end;
T = max([find(netsim,1,'last'),find(dpsim,1,'last'),find(expref,1,'last')]);
netsim=netsim(1:T); dpsim=dpsim(1:T); expref=expref(1:T); idx=idx(:,1:T);
finish = clock;
if options.details,
fprintf('\nNumber of exemplars identified: %d (for %d data points)\n',length(unique(idx(:,end))),I);
fprintf('Fitness (net similarity): %g\n',netsim(end));
fprintf(' Similarities of data points to exemplars: %g\n',dpsim(end));
fprintf(' Preferences of selected exemplars: %g\n',expref(end));
fprintf('Number of iterations: %d\n',T);
% if options.kcc, fprintf(' + KCC cleanup\n'); else fprintf('\n'); end;
fprintf('Elapsed time: %g sec\n',etime(finish,start));
end;
if options.kcc,
kccoptions.use_input_exemplars=1; kccoptions.number_of_restarts=1;
temp=unique(idx(:,end)); temp=temp(temp>0); kccidx=zeros(I,1,'int32'); kccidx(temp)=1;
kccnetsim=1e-10; kccdpsim=2e-10; kccexpref=3e-10;
ret=kcentersmex_(sij,si,sj,sum(kccidx),kccidx,kccnetsim,kccdpsim,kccexpref,kccoptions);
if ret<0, error('kcentersmex returned error code %d',ret); end;
idx=[idx kccidx]; netsim=[netsim kccnetsim]; dpsim=[dpsim kccdpsim]; expref=[expref kccexpref];
fprintf(' KCC cleanup: netsim=%g, dpsim=%g, expref=%g\n',netsim(end),dpsim(end),expref(end));
fprintf(' Additional Elapsed time: %g sec\n',etime(clock,finish));
end;
if options.vsh,
init=unique(double(idx(:,end))); K=length(init);
if isempty(si), S=reshape(sij,[I I]); else S=zeros(I,I); S(sub2ind([I I],double(si),double(sj)))=sij; end;
[idx,netsim,dpsim,expref]=vshmex(S,K,'pref',p,'init',init);
end;
return
% sample callback function
function action = progressfunction(a,r,curridx,currnetsim,currdpsim,currexpref,iter)
hold on; plot(iter,currnetsim,'ro');
action = 0; % returning zero means to continue
return