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

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. ©2009 IEEE.