Learning Natural Image Structure with a Horizontal Product Model

Authors:
Urs Köster;Jussi T. Lindgren;Michael Gutmann;Aapo Hyvärinen
Affiliations:
Department of Computer Science, and Helsinki Institute for Information Technology,;Department of Computer Science, and Helsinki Institute for Information Technology,;Department of Computer Science, and Helsinki Institute for Information Technology,;Department of Computer Science, and Helsinki Institute for Information Technology, and Department of Mathematics and Statistics, University of Helsinki, Finland
Venue:
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Year:
2009

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Abstract

We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.