On the role of ML estimation and Bregman divergences in sparse representation of covariance and precision matrices

TL;DR

This paper explores the use of machine learning estimation techniques and Bregman divergences to improve sparse representations of covariance and precision matrices, which are crucial in structured signal modeling.

Contribution

It introduces novel problem formulations and solutions for sparse matrix representation, emphasizing the role of ML estimation and Bregman divergences.

Findings

Enhanced sparse representation methods for covariance matrices

Improved precision matrix modeling techniques

Potential for better structured signal analysis

Abstract

Sparse representation of structured signals requires modelling strategies that maintain specific signal properties, in addition to preserving original information content and achieving simpler signal representation. Therefore, the major design challenge is to introduce adequate problem formulations and offer solutions that will efficiently lead to desired representations. In this context, sparse representation of covariance and precision matrices, which appear as feature descriptors or mixture model parameters, respectively, will be in the main focus of this paper.