Sparse Graph Learning Under Laplacian-Related Constraints

We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these cons...

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Main Author:	Jitendra K. Tugnait
Format:	article
Language:	EN
Published:	IEEE 2021
Subjects:	Sparse graph learning graph estimation graph Laplacian undirected graph inverse covariance estimation Electrical engineering. Electronics. Nuclear engineering TK1-9971
Online Access:	https://doaj.org/article/57fb50f62d6341fc965c97b77f4da80b
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id	oai:doaj.org-article:57fb50f62d6341fc965c97b77f4da80b
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spelling	oai:doaj.org-article:57fb50f62d6341fc965c97b77f4da80b2021-11-17T00:00:54ZSparse Graph Learning Under Laplacian-Related Constraints2169-353610.1109/ACCESS.2021.3126675https://doaj.org/article/57fb50f62d6341fc965c97b77f4da80b2021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9606894/https://doaj.org/toc/2169-3536We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these constraints the off-diagonal elements of the precision matrix are non-positive (total positivity), and the precision matrix may not be full-rank. We investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. The graph Laplacian can then be extracted from the off-diagonal precision matrix. An alternating direction method of multipliers (ADMM) algorithm is presented and analyzed for constrained optimization under Laplacian-related constraints and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches. We also evaluate our approach on real financial data.Jitendra K. TugnaitIEEEarticleSparse graph learninggraph estimationgraph Laplacianundirected graphinverse covariance estimationElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 151067-151079 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Sparse graph learning graph estimation graph Laplacian undirected graph inverse covariance estimation Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Sparse graph learning graph estimation graph Laplacian undirected graph inverse covariance estimation Electrical engineering. Electronics. Nuclear engineering TK1-9971 Jitendra K. Tugnait Sparse Graph Learning Under Laplacian-Related Constraints
description	We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these constraints the off-diagonal elements of the precision matrix are non-positive (total positivity), and the precision matrix may not be full-rank. We investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. The graph Laplacian can then be extracted from the off-diagonal precision matrix. An alternating direction method of multipliers (ADMM) algorithm is presented and analyzed for constrained optimization under Laplacian-related constraints and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches. We also evaluate our approach on real financial data.
format	article
author	Jitendra K. Tugnait
author_facet	Jitendra K. Tugnait
author_sort	Jitendra K. Tugnait
title	Sparse Graph Learning Under Laplacian-Related Constraints
title_short	Sparse Graph Learning Under Laplacian-Related Constraints
title_full	Sparse Graph Learning Under Laplacian-Related Constraints
title_fullStr	Sparse Graph Learning Under Laplacian-Related Constraints
title_full_unstemmed	Sparse Graph Learning Under Laplacian-Related Constraints
title_sort	sparse graph learning under laplacian-related constraints
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/57fb50f62d6341fc965c97b77f4da80b
work_keys_str_mv	AT jitendraktugnait sparsegraphlearningunderlaplacianrelatedconstraints
_version_	1718426048328105984

Sparse Graph Learning Under Laplacian-Related Constraints

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