Topographic ICA as a model of V1 receptive fields

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: each neighbourhood acts like a complex cell