commGSP/commGSP_optimal_subgraph.m
234a68af8299master

commGSP_optimal_subgraph.m
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			function S = commGSP_optimal_subgraph(A, type, BW, K)
			% Finds subgraph optimal for subsampling signals of a certain class
			% (e.g. modular, smooth) existing on the given graph
			% INPUT:
			% A - (symmetric) adjacency matrix
			% type - string defining type of the signals which are optimally
			% subsampled by the resulting subgraph:
			% 'smooth', 'non-smooth' (Laplacian-based),
			% 'modular', 'anti-modular' (modularity-based)
			% BW - number of eigenvectors kept in the signal bandwidth
			% K - number of nodes in the optimal subgraph

			% OUTPUT
			% S - diagonal matrix with entry (i,i) equal to 1 if i^th node belongs
			% to the subgraph, 0 otherwise

			N=size(A,1);
			if strcmp(type, 'smooth') \|\| strcmp(type, 'non-smooth')
			[U, ~] = commGSP_eig_implicit(A, 'laplacian');
			else
			if strcmp(type, 'modular') \|\| strcmp(type, 'anti-modular')
			[U, ~] = commGSP_eig_implicit(A, 'modularity');
			end
			end

			if strcmp(type, 'smooth') \|\| strcmp(type, 'modular')
			w=1:BW;
			else
			if strcmp(type, 'non-smooth') \|\| strcmp(type, 'anti-modular')
			w=(N-BW+1):N;
			end
			end
			W = sparse(w,w,ones(length(BW),1),N,N);

			l2=vecnorm(W*(U'));
			[~,ind]=sort(l2,'descend');
			S=sparse(ind(1:K), ind(1:K), ones(K,1), N, N);

			end