Partial extraction of edge filters by cumulant-based ICA under highly overcomplete model

Authors:
Yoshitatsu Matsuda;Kazunori Yamaguchi
Affiliations:
Department of Integrated Information Technology, Aoyama Gakuin University, Sagamihara-shi, Kanagawa, Japan;Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
Venue:
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: models and applications - Volume Part II
Year:
2010

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Abstract

It has been well known that ICA can extract edge filters from natural scenes. However, it has been also known that the existing cumulant-based ICA can not extract edge filters. It suggests that the simple ICA model is insufficient for explaining the properties of natural scenes. In this paper, we propose a highly overcomplete model for natural scenes. Besides, we show that the 4-th order covariance has a positive constant lower bound under this model. Then, a new cumulant-based ICA algorithm is proposed by utilizing this lower bound. Numerical experiments show that this cumulant-based algorithm can extract edge filters.