Title: Computation of the Frechet mean, variance and interpolation for a pool of neural networks over the manifold of special orthogonal matrices

Authors: S. Fiori

Addresses: Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni (DIBET), Facolta di Ingegneria, Universita Politecnica delle Marche, Via Brecce Bianche, Ancona I-60131, Italy

Abstract: The present manuscript tackles the problem of merging the connection patterns learnt by a pool of neural networks that share the manifold of special orthogonal matrices as parameter space. The merging technique is implemented as an averaging algorithm over the curved manifold of special orthogonal matrices. In the present manuscript, averaging is computed via the notion of Frechet mean and the associated metric dispersion is interpreted as the variance of the patterns around the Frechet mean. Also, continuous interpolation of two connection patterns is considered as an extension of the Frechet principle.

Keywords: computational intelligence; Frechet mean computation; curved spaces; interpolation; optimisation; differential manifolds; special orthogonal matrices; neural networks; connection patterns.

DOI: 10.1504/IJCISTUDIES.2009.025338

International Journal of Computational Intelligence Studies, 2009 Vol.1 No.1, pp.50 - 71

Published online: 19 May 2009 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article