% MATCORR - Find matching rows in two matrices and their corrs.
% Uses the Hungarian (default), VAM, or maxcorr assignment methods.
% (Follow with MATPERM to permute and sign x -> y).
%
% Usage: >> [corr,indx,indy,corrs] = matcorr(x,y,rmmean,method,weighting);
%
% Inputs:
% x = first input matrix
% y = matrix with same number of columns as x
%
% Optional inputs:
% rmmean = When present and non-zero, remove row means prior to correlation
% {default: 0}
% method = Method used to find assignments.
% 0= Hungarian Method - maximize sum of abs corrs {default: 2}
% 1= Vogel's Assignment Method -find pairs in order of max contrast
% 2= Max Abs Corr Method - find pairs in order of max abs corr
% Note that the methods 0 and 1 require matrices to be square.
% weighting = An optional weighting matrix size(weighting) = size(corrs) that
% weights the corrs matrix before pair assignment {def: 0/[] -> ones}
% Outputs:
% corr = a column vector of correlation coefficients between
% best-correlating rows of matrice x and y
% indx = a column vector containing the index of the maximum
% abs-correlated x row in descending order of abs corr
% (no duplications)
% indy = a column vector containing the index of the maximum
% abs-correlated row of y in descending order of abs corr
% (no duplications)
% corrs = an optional square matrix of row-correlation coefficients
% between matrices x and y
%
% Note: outputs are sorted by abs(corr)
%
% Authors: Scott Makeig & Sigurd Enghoff, SCCN/INC/UCSD, La Jolla, 11-30-96
% Copyright (C) 11-30-96 Scott Makeig, SCCN/INC/UCSD, scott@sccn.ucsd.edu
%
% This file is part of EEGLAB, see http://www.eeglab.org
% for the documentation and details.
%
% 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. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "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 COPYRIGHT HOLDER OR CONTRIBUTORS 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.
% 04-22-99 Re-written using VAM by Sigurd Enghoff, CNL/Salk
% 04-30-99 Added revision of algorithm loop by SE -sm
% 05-25-99 Added Hungarian method assignment by SE
% 06-15-99 Maximum correlation method reinstated by SE
% 08-02-99 Made order of outputs match help msg -sm
% 02-16-00 Fixed order of corr output under VAM added method explanations,
% and returned corr signs in abs max method -sm
% 01-25-02 reformated help & license, added links -ad
% Uses function hungarian.m
function [corr,indx,indy,corrs] = matcorr(x,y,rmmean,method,weighting)
%
if nargin < 2 || nargin > 5
help matcorr
return
end
if nargin < 4
method = 2; % default: Max Abs Corr - select successive best abs(corr) pairs
end
[m,n] = size(x);
[p,q] = size(y);
m = min(m,p);
if m~=n || p~=q
if nargin>3 && method~=2
fprintf('matcorr(): Matrices are not square: using max abs corr method (2).\n');
end
method = 2; % Can accept non-square matrices
end
if n~=q
error('Rows in the two input matrices must be the same length.');
end
if nargin < 3 || isempty(rmmean)
rmmean = 0;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if rmmean
x = x - mean(x')'*ones(1,n); % optionally remove means
y = y - mean(y')'*ones(1,n);
end
dx = sum(x'.^2);
dy = sum(y'.^2);
dx(find(dx==0)) = 1;
dy(find(dy==0)) = 1;
corrs = x*y'./sqrt(dx'*dy);
if nargin > 4 && ~isempty(weighting) && norm(weighting) > 0,
if any(size(corrs) ~= size(weighting))
fprintf('matcorr(): weighting matrix size must match that of corrs\n.')
return
else
corrs = corrs.*weighting;
end
end
cc = abs(corrs);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch method
case 0
ass = hungarian(-cc); % Performs Hungarian algorithm matching
idx1 = sub2ind(size(cc),ass,1:m);
[dummy idx2] = sort(-cc(idx1));
corr = corrs(idx1);
corr = corr(idx2)';
indy = [1:m]';
indx = ass(idx2)';
indy = indy(idx2);
case 1 % Implements the VAM assignment method
indx = zeros(m,1);
indy = zeros(m,1);
corr = zeros(m,1);
for i=1:m,
[sx ix] = sort(cc); % Looks for maximum salience along a row/column
[sy iy] = sort(cc'); % rather than maximum correlation.
[sxx ixx] = max(sx(end,:)-sx(end-1,:));
[syy iyy] = max(sy(end,:)-sy(end-1,:));
if sxx == syy
if sxx == 0 && syy == 0
[sxx ixx] = max((sx(end,:)-sx(end-1,:)) .* sx(end,:));
[syy iyy] = max((sy(end,:)-sy(end-1,:)) .* sy(end,:));
else
sxx = sx(end,ixx); % takes care of identical vectors
syy = sy(end,iyy); % and zero vectors
end
end
if sxx > syy
indx(i) = ix(end,ixx);
indy(i) = ixx;
else
indx(i) = iyy;
indy(i) = iy(end,iyy);
end
cc(indx(i),:) = -1;
cc(:,indy(i)) = -1;
end
i = sub2ind(size(corrs),indx,indy);
corr = corrs(i);
[tmp j] = sort(-abs(corr)); % re-sort by abs(correlation)
corr = corr(j);
indx = indx(j);
indy = indy(j);
case 2 % match successive max(abs(corr)) pairs
indx = zeros(size(cc,1),1);
indy = zeros(size(cc,1),1);
corr = zeros(size(cc,1),1);
for i = 1:size(cc,1)
[tmp j] = max(cc(:));
% [corr(i) j] = max(cc(:));
[indx(i) indy(i)] = ind2sub(size(cc),j);
corr(i) = corrs(indx(i),indy(i));
cc(indx(i),:) = -1; % remove from contention
cc(:,indy(i)) = -1;
end
otherwise
error('Unknown method');
end
Datasets
Models
