%% 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