Estimating Overcomplete Independent Component Bases for Image Windows
Journal of Mathematical Imaging and Vision
Topographic Independent Component Analysis
Neural Computation
Learning Overcomplete Representations
Neural Computation
A fixed-point algorithm of topographic ICA
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
The infomin principle for ICA and topographic mappings
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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It is known that the number of the edge detectors significantly exceeds that of input signals in the visual system of the brains. This phenomenon has been often regarded as overcomplete independent component analysis (ICA) and some generative models have been proposed. Though the models are effective, they need to assume some ad-hoc prior probabilistic models. Recently, the InfoMin principle was proposed as a comprehensive framework with minimal prior assumptions for explaining the information processing in the brains and its usefulness has been verified in the classic non-overcomplete cases. In this paper, we propose a new ICA contrast function for overcomplete cases, which is deductively derived from the the InfoMin and InfoMax principles without any prior models. Besides, we construct an efficient fixed-point algorithm for optimizing it by an approximate Newton's method. Numerical experiments verify the effectiveness of the proposed method.