GSP_GRAPH_MULTIRESOLUTION - Compute a multiresolution of graphs

Usage

[Gs]=gsp_graph_multiresolution(G,num_levels);
[Gs]=gsp_graph_multiresolution(G,num_levels,param);

Input parameters

Output parameters

Description

'gsp_graph_multiresolution(G,num_levels)' computes a multiresolution of graph by repeatedly downsampling and performing graph reduction. The default downsampling method is the largest eigenvector method based on the polarity of the components of the eigenvector associated with the largest graph Laplacian eigenvalue. The default graph reduction method is Kron reduction followed by a graph sparsification step. param is a structure of optional parameters containing the following fields:

• sparsify: To perform a spectral sparsification step immediately after the graph reduction (default=1)
• sparsify_epsilon: Parameter epsilon used in the spectral sparsification (default=min(10/sqrt(G.N),.3))
• downsampling_method: The graph downsampling method (default='largest_eigenvector')
• reduction_method: The graph reduction method (default='Kron')
• compute_full_eigen: To also compute the graph Laplacian eigenvalues and eigenvectors for every graph in the multiresolution sequence (default=0)

Example:

N = 500;
G = gsp_sensor(N);
Nlevel = 5;

Gs = gsp_graph_multiresolution(G, Nlevel);

figure;
for ii = 1:numel(Gs)
    subplot(2,3,ii)
    gsp_plot_graph(Gs{ii})
    title(['Reduction level: ', num2str(ii-1)]);
end

Demo: gsp_demo_pyramid

Authors : David I Shuman, Elle Weeks, Andre Archer, Stefan Faridani, Yan Jin, Nathanael Perraudin. Date: 26 November 2015 Testing: test_operators