Learning averages over the lie group of symmetric positive-definite matrices

Authors:
Simone Fiori;Toshihisa Tanaka
Affiliations:
Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni, Facoltà di Ingegneria, Università Politecnica delle Marche, Ancona, Italy;Department of Electrical and Electronic Engineering, Faculty of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

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Abstract

In the present paper, we treat the problem of learning averages out of a set of symmetric positive-definite matrices (SPDMs). We discuss a possible learning technique based on the differential geometrical properties of the SPDM-manifold which was recently shown to possess a Lie-group structure under appropriate group definition. We first recall some relevant notions from differential geometry, mainly related to Lie-group theory, and then we propose a scheme of learning averages. Some numerical experiments will serve to illustrate the features of the learnt averages.