Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis

Authors:
Yasunori Nishimori;Shotaro Akaho;Mark D. Plumbley
Affiliations:
Neuroscience Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), , Tsukuba, Japan 305-8568;Neuroscience Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), , Tsukuba, Japan 305-8568;Department of Electronic Engineering, Queen Mary University of London, London, UK E1 4NS
Venue:
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Year:
2008

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Abstract

We study the problem of complex-valued independent subspace analysis (ISA). We introduce complex flag manifolds to tackle this problem, and, based on Riemannian geometry, propose the natural conjugate gradient method on this class of manifolds. Numerical experiments demonstrate that the natural conjugate gradient method yields better convergence compared to the natural gradient geodesic search method.