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MOT_ANA/Matlab_Scripts/GlobalUtilities/01_Graph_Construction/construct_epsilon_graph.m
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construct_epsilon_graph.m
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%% Constructs an epsilon-like graph of the data, constrained so that only
% the temporally closest frames belonging to the same subject are selected
function W = construct_epsilon_graph(X,epsilon,n_TP,n_Subj)
% Computes a subject index vector
disp('Computing subject index vector...');
S_idx = [];
for i = 1:n_Subj
S_idx = [S_idx,i*ones(1,n_TP)];
end
disp('Computing distances between data points...');
% Computes the distance between all data points
D = distance(X',X');
% Adjacency matrix, initilly filled with zeros
W = zeros(size(D));
disp('Filling adjacency matrix...');
j = 1:size(D,1);
% For all data points, we will consider the epsilon temporally closest
% frames
for i = 1:size(D,1)
% Takes all distances to the considered data point
tmp = D(i,:);
% Only keeps the ones of closeby data points temporally (in both
% directions) AND of data points belonging to the same subjects
tmp = tmp( (abs(j-i)<=epsilon) & (S_idx(i)==S_idx(j)) );
divide_factor = epsilon;
% Those have a distance value computed
tmp = exp(-tmp.^2/(divide_factor^2));
tmp(isnan(tmp)) = 0;
% Adjacency filled accordingly
W(i,(abs(j-i)<=epsilon) & (S_idx(i)==S_idx(j))) = tmp;
end
end
function d = distance(a,b)
% DISTANCE - computes Euclidean distance matrix
%
% E = distance(A,B)
%
% A - (DxM) matrix
% B - (DxN) matrix
%
% Returns:
% E - (MxN) Euclidean distances between vectors in A and B
%
%
% Description :
% This fully vectorized (VERY FAST!) m-file computes the
% Euclidean distance between two vectors by:
%
% ||A-B|| = sqrt ( ||A||^2 + ||B||^2 - 2*A.B )
%
% Example :
% A = rand(400,100); B = rand(400,200);
% d = distance(A,B);
% Author : Roland Bunschoten
% University of Amsterdam
% Intelligent Autonomous Systems (IAS) group
% Kruislaan 403 1098 SJ Amsterdam
% tel.(+31)20-5257524
% bunschot@wins.uva.nl
% Last Rev : Oct 29 16:35:48 MET DST 1999
% Tested : PC Matlab v5.2 and Solaris Matlab v5.3
% Thanx : Nikos Vlassis
% Copyright notice: You are free to modify, extend and distribute
% this code granted that the author of the original code is
% mentioned as the original author of the code.
if (nargin ~= 2)
error('Not enough input arguments');
end
if (size(a,1) ~= size(b,1))
error('A and B should be of same dimensionality');
end
aa=sum(a.*a,1); bb=sum(b.*b,1); ab=a'*b;
d = sqrt(abs(repmat(aa',[1 size(bb,2)]) + repmat(bb,[size(aa,2) 1]) - 2*ab));
end
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