gsp_laplacian_eigenmaps.m
2cb18aae5832master

gsp_laplacian_eigenmaps.m
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			function coords = gsp_laplacian_eigenmaps(G, dim, param)
			%GSP_LAPLACIAN_EIGENMAPS Laplacian eigenmaps embedding
			% Usage: coords = gsp_laplacian_eigenmaps(G, dim);
			% coords = gsp_laplacian_eigenmaps(G, dim, param);
			%
			% Input parameters
			% G : Graph
			% dim : Dimension of the embedding
			% param : Structure of optional paramters
			% Output parameters
			% coords : Coordinates of the embedding
			%
			% This function uses the weight matrix of a graph G, in order to compute
			% a dim -dimensional embedding (output coordinates). The algorithm used
			% is Laplacian eigenmaps. Warning, this function might not work if the
			% graph is not connected.
			%
			% param is a structure optional parameters:
			%
			% param.tol : Tolerance for the spectral gap (default 1e-6).
			%
			%
			% See also: gsp_update_coordinates gsp_isomap gsp_lle
			%
			% Demo: gsp_demo_graph_embedding
			%
			% References:
			% M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques
			% for embedding and clustering. In NIPS, volume 14, pages 585--591, 2001.
			%
			%
			%
			% Url: http://lts2research.epfl.ch/gsp/doc/embedding/gsp_laplacian_eigenmaps.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 nargin<3
			param = struct;
			end

			if ~isfield(param,'tol'), param.tol = 1e-6; end


			% Laplacian Eigenmaps
			options.disp = 0;
			options.isreal = 1;
			options.issym = 1;
			% only need bottom (no_dims + 1) eigenvectors
			if strcmp(G.type,'normalized') % Bug G.type
			[coords, e] = eigs(G.L, dim + 1, param.tol, options);
			else
			[coords, e] = eigs(G.L, sparse(diag(G.d)), dim + 1, param.tol, options);
			end
			e = diag(e);

			if nnz(e < param.tol) > 1
			warning('Multiple zero eigenvalues')
			end

			[~, ind] = sort(e, 'ascend');
			coords = coords(:, ind);
			coords = coords(:, 2:end);
			end

iCAPs/packages/gspbox/embedding/gsp_laplacian_eigenmaps.m2cb18aae5832master

gsp_laplacian_eigenmaps.mView Options

iCAPs/packages/gspbox/embedding/gsp_laplacian_eigenmaps.m
2cb18aae5832master

gsp_laplacian_eigenmaps.m
View Options