Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A unifying objective function for topographic mappings
Neural Computation
A fast fixed-point algorithm for independent component analysis
Neural Computation
Factorizing multivariate function classes
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Modeling surround suppression in V1 neurons with a statistically-derived normalization model
Proceedings of the 1998 conference on Advances in neural information processing systems II
Self-Organizing Maps
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
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Independent component analysis (ICA), which is equivalent to linear sparse coding, has been recently used as a model of natural image statistics and V1 receptive fields. Olshausen and Field applied the principle of maximizing the sparseness of the coefficients of a linear representation to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and V1 simple cell receptive fields. In this paper, we extend this model to explain emergence of V1 topography. This is done by ordering the basis vectors so that vectors with strong higher-order correlations are near to each other. This is a new principle of topographic organization, and may be more relevant to natural image statistics than the more conventional topographic ordering based on Euclidean distances. For example, this topographic ordering leads to simultaneous emergence of complex cell properties: neighbourhoods act like complex cells.