Gaussian graphical models for proper quaternion distributions

Alba Sloin, Ami Wiesel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

In this paper we extend Gaussian graphical models to proper quaternion Gaussian distributions. The properness assumption reduces the number of unknowns by a factor of four and allow for improved accuracy. We begin by showing that the unconstrained proper quaternion maximum likelihood problem is convex and has a closed form solution that resembles the classical sample covariance. Then, we proceed and add convex sparsity constraints to the inverse covariance matrix and minimize them using convex optimization toolboxes. Finally, we show that in the special case of chordal graphs, the estimates follow a simple closed form which aggregates the unconstrained solutions in each of the cliques. We demonstrate the performance of our suggested estimators on both synthetic and real data.

Original languageAmerican English
Title of host publication2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
Pages117-120
Number of pages4
DOIs
StatePublished - 2013
Event2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013 - Saint Martin, France
Duration: 15 Dec 201318 Dec 2013

Publication series

Name2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013

Conference

Conference2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
Country/TerritoryFrance
CitySaint Martin
Period15/12/1318/12/13

Keywords

  • Quaternions
  • chordal graphs
  • covariance estimation
  • graphical models

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