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iCAPs/packages/gspbox/graphs/gsp_rmse_mv_graph.m
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gsp_rmse_mv_graph.m
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function G = gsp_rmse_mv_graph(X,param)
%GSP_RMSE_MV_GRAPH Root meean square error missing value graph
% Usage : G = gsp_rmse_mv_graph( Xin );
% G = gsp_rmse_mv_graph( Xin, param );
%
% Input parameters:
% Xin : Input points (with missing value (nan))
% param : Structure of optional parameters
%
% Output parameters:
% G : Resulting graph
%
% 'gsp_rmse_mv_graph(X,param)' creates a graph from positional data. The points are
% connected to their neighbors (either belonging to the k nearest
% neighbors or to the epsilon-closest neighbors. This function ignore all
% nan value. But it is much slower than GSP_NN_GRAPH.
%
% Additional parameters
% ---------------------
%
% param.type : ['knn', 'radius'] the type of graph (default 'knn')
% param.sigma : float the variance of the distance kernel
% param.k : int number of neighbors for knn
% param.epsilon : float the radius for the range search
% param.symmetrize_type*: ['average','full'] symmetrization type (default 'full')
% param.center : [0, 1] center the data
% param.rescale : [0, 1] rescale the data (in a 1-ball)
%
% Url: http://lts2research.epfl.ch/gsp/doc/graphs/gsp_rmse_mv_graph.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
% Author: Nathanael Perraudin
% Date : 12 March 2015
% Testing: test_rmse
if nargin<2
param = struct;
end
if ~isfield(param, 'epsilon'), param.epsilon = 0.01; end
if ~isfield(param, 'verbose'), param.verbose = 1; end
if ~isfield(param, 'k'), param.k = 10; end
if ~isfield(param, 'symmetrize_type'), param.symmetrize_type = 'average'; end
if ~isfield(param, 'type'), param.type = 'knn'; end
if ~isfield(param, 'center'), param.center = 1; end
if ~isfield(param, 'rescale'), param.rescale = 1; end
[N, d] = size(X);
if N> 5000
error('This code is not optimized and cannot handle such a big graphs!');
end
Xout = X;
%Center the point cloud
if param.center
for ii = 1:d
mask = 1-isnan(X(:,ii));
mask = mask .* (1:N)';
mask = find(mask);
Xout(mask,ii) = X(mask,ii) - mean(X(mask,ii));
end
end
%Rescale the point cloud
if param.rescale
bounding_radius = 0;
for ii = 1:d
mask = 1-isnan(X(:,ii));
mask = mask .* (1:N)';
mask = find(mask);
bounding_radius = bounding_radius+ abs(max(Xout(mask,ii)) - min(Xout(mask,ii)))^2;
end
bounding_radius = 0.5 * sqrt(bounding_radius);
scale = nthroot(N, min(d, 3)) / 10;
Xout = Xout .* (scale / bounding_radius);
end
p.verbose = param.verbose;
C = gsp_rmse_mv(transpose(Xout),p);
C = C*sqrt(d);
% sparsification
switch param.type
case 'knn'
for ii=1:size(C,1)
[~,sortIndex] = sort(C(ii,:),'ascend'); %# Sort the values in
%# descending order
C(ii,sortIndex(param.k+2:end)) = 0;
end
if ~isfield(param, 'sigma'), param.sigma = mean(C(C>0))^2; end
W = spfun(@(x) exp(-x.^2/param.sigma),sparse(C));
W = W-diag(diag(W));
W = gsp_symmetrize(W,param.symmetrize_type);
case 'radius'
if ~isfield(param, 'sigma'), param.sigma = param.epsilon.^2/2; end
C(C>param.epsilon) = 0;
W = spfun(@(x) exp(-x.^2/param.sigma),sparse(C));
W = W-diag(diag(W));
otherwise
error('Unknown type : allowed values are knn, radius');
end
% Create the graph
G = gsp_graph(W,Xout);
G.type = 'RMSE MV';
G.sigma = param.sigma;
end
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