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iCAPs/packages/gspbox/embedding/gsp_weight2distance.m
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gsp_weight2distance.m
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function D = gsp_weight2distance(G, method, sigma)
%GSP_WEIGHT2DISTANCE Distance matrix from weight matrix
% Usage: D = gsp_weight2distance(G);
% D = gsp_weight2distance(G, method);
% D = gsp_weight2distance(G, method, nnn);
%
% Input parameters
% G : Graph or weight matrix
% method : Type of kernel used to compute the weight matrix
% sigma : kernel paramter
%
%
% Output parameters
% D : Distance matrix (sparse)
%
% This function uses the weight matrix of a graph in order to compute the
% distance matrix D. If G is a structure it is considered as a graph
% otherwise it is considered as a weight matrix. The resulting matrix is
% in sparse form. The indices idx are of the nearest neighbors or (if k
% is not used) the indices of all non zero elements of the weight matrix.
% In both cases indices are saved in a cell where idx{ii} contains a
% vector jj of indices where D(ii, jj) are the Distances of the nearest
% neighbours of element ii.
%
% The type of method one can use are the following:
% 'exp' : exponential kernel (e^(frac{-d_{ij}}{sigma^2}))
% '1/x' : inverse of x kernel (frac{1}{sigma+d_{ij}})
% '1/x^2' : inverse of x^2 kernel (frac{1}{(sigma+d_{ij})^2})
% 'resistance' : Resistance distance.
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/embedding/gsp_weight2distance.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% Authors : Dion O. E. Tzamarias
% Date : 20/11/2015
if isstruct(G)
W = G.W;
else
W = G;
end
if nargin<2
method = 'exp';
end
if nargin<3
sigma = 1;
end
switch lower (method)
case 'exp'
if sum(W(:)>1)
error('W cannot have entries bigger than 1')
end
% d = - log(w) * sigma;
% D = sparse(rows,cols,d);
D = spfun(@(w) sqrt(abs(- log(w))) * sigma, W);
% w = 1/d =>
case '1/x'
if any(W(:) >= sigma)
error('W cannot have entries bigger than 1/sigma')
end
% d = 1./w - sigma;
% D = sparse(rows,cols,d);
D = spfun(@(w) 1./w - sigma, W);
case '1/x^2'
if any(W(:) >= sigma^2)
error('W cannot have entries bigger than 1/sigma^2')
end
% d = sqrt(1./w) - sigma;
% D = sparse(rows,cols,d);
D = spfun(@(w) sqrt(1./w) - sigma, W);
case 'resistance'
D = gsp_resistance_distances(G);
% d = d(rows,cols);
D = sparse(D);
otherwise
end
end
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