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% /******************************************************************************
%
% This program, "NCDM", the associated MATLAB scripts and all
% provided data, are copyright (C) 2014 Andrew R. Cohen, All rights reserved.
%
% This program uses bzip2 compressor as a static library.
% A built version for windows 64 is included. for other platforms, see
% the files in the bzlib project on https://git-bioimage.coe.drexel.edu
%
% This software may be referenced as:
%
% A.R. Cohen, C. Bjornsson, S. Temple, G. Banker, and B. Roysam,
% "Automatic Summarization of Changes in Biological Image Sequences
% using Algorithmic Information Theory". IEEE Transactions on Pattern
% Analysis and Machine Intelligence, 2009. 31(8): p. 1386-1403.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions
% are met:
%
% 1. Redistributions of source code must retain the above copyright
% notice, this list of conditions and the following disclaimer.
%
% 2. The origin of this software must not be misrepresented; you must
% not claim that you wrote the original software. If you use this
% software in a product, an acknowledgment in the product
% documentation would be appreciated but is not required.
%
% 3. Altered source versions must be plainly marked as such, and must
% not be misrepresented as being the original software.
%
% 4. The name of the author may not be used to endorse or promote
% products derived from this software without specific prior written
% permission.
%
% THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
% OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
% DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
% GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
% WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
% NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
% SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
%
% Andrew R. Cohen acohen@coe.drexel.edu
% GapSpectral version 1.0 (release) November 2014
%
% ******************************************************************************/
function [kGap Gap S idx] = GapSpectral(DistanceMatrix,nMaxClusters,bAlgorithmicInformationDistance)
if nargin<3
bAlgorithmicInformationDistance=1;
end
B = 50; % size of Monte Carlo distribution
if nMaxClusters>size(DistanceMatrix,1)
nMaxClusters = size(DistanceMatrix,1)-1;
end
D = Regularize(DistanceMatrix);
bound=D;
for i=1: size(bound,1)
bound(i,i)=NaN;
end
a = min(min(bound));%;
b = max(max(bound));
UV = a + (b-a)*rand(size (D,1),size (D,2),B); % uniform distribution
for k=1:nMaxClusters
if (1==k) %
% one happy cluster
idx = ones(size (D,1),1);
else
idx = SpectralCluster(D,k);
end
W(k)=WkSpectral(k,idx,D);
for ib =1:B
uni = UV(:,:,ib);
uni = Regularize(uni); % make uni a valid distance matrix
if (1==k) %
% one happy cluster
idx = ones(size (D,1),1);
else
idx = SpectralCluster(uni,k);
end
Wb(ib,k)=WkSpectral(k,idx,uni);;
end
Wkb = Wb(:,k);
lkb = log(Wkb);
if bAlgorithmicInformationDistance
Gap(k) = 1/B*sum(Wkb) - W(k);
sdk = std(Wkb,1);
else
Gap(k) = 1/B*sum(lkb) - log(W(k));
sdk = std(lkb,1);
end
S(k)=sdk * sqrt(1+1/B);
% Gap
% S
end
figure
errorbar( [1:nMaxClusters],Gap,S)
set(gca,'XTick',[1:nMaxClusters])
k=1;
while ((k<nMaxClusters) && (Gap(k) < Gap(k+1)-S(k+1)))
k=k+1;
end
kGap=k;
if (kGap>1)
idx = SpectralCluster(D,kGap);
else
idx = ones(size (D,1),1);
end
function w=WkSpectral(k,idx,DistanceMatrix)
% called by GapSpectral
for r =1:k
% find points in cluster r
pr = find(idx==r);
D(r) = 0;
for i=1:size(pr,1)
for j=i:size(pr,1)
D(r) = D(r)+DistanceMatrix(pr(i),pr(j));
end
end
D(r) = D(r)/(2*size(pr,1)); %(2) in paper
end
w = sum(D);