NCDM.m

% /******************************************************************************
% 
% This program, "NCDM", the associated MATLAB scripts and all 
% provided data, are copyright (C) 2018 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 and P.M.B. Vitanyi, Normalized Compression Distance of Multisets
%       with Applications, IEEE Transactions on Pattern Analysis and Machine 
%       Intelligence. 2015 Aug;37(8):1602-14, 
%
% 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 andrew.r.cohen@drexel.edu
% 
% ******************************************************************************/

% NCDM
% Returns the normalized compression distance for the multiset X
% each row of x is assumed to be a single member x of set X
% this is the multiset NCD

function ncd = NCD(X)

if size(X,1)<2
    ncd=0;
    fprintf(1,'single element x of X : d=0\n');
    return
end
GX = Press(X',[]);
cxi=[];
for i=1:size(X,1)
    xi=X(i,:);
    cxi(i)=Press(xi,[]);
end
gx = min([cxi]);

gExclude =[];
xExclude=[];
for i=1:size(X,1)
    xExclude=X;
    xExclude(i,:)=[];
    gExclude(i)=Press(xExclude',[]); % G(X\x)
end

ncd = (GX - gx)/(max(gExclude));



end