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.
Learning averages over the Lie group of symmetric positive-definite matrices / Fiori, Simone; T., Tanaka. - (2009), pp. 828-832. [10.1109/IJCNN.2009.5178598]
Learning averages over the Lie group of symmetric positive-definite matrices
FIORI, Simone;
2009-01-01
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. ©2009 IEEE.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.