Overcomplete topographic independent component analysis

Topographic and overcomplete representations of natural images/videos are important problems in computational neuroscience. We propose a new method using both topographic and overcomplete representations of natural images, showing emergence of properties similar to those of complex cells in primary visual cortex (V1). This method can be considered as an extension of model in Hyvärinen et al. [Topographic independent component analysis, Neural Comput. 13 (7) (2001) 1527–1558], which uses complete topographic representation. We utilize a sparse and approximately uncorrelated decompositions and define a topographic structure on coefficients (the dot products between basis vectors and whitened observed data vectors). The overcomplete topographic basis vectors can be learned via estimation of independent component analysis (ICA) model based on the prior assumption upon basis vectors. Computer simulations are provided to show the relationship between our model and the basic properties of complex cells in V1 cortex. The learned bases are shown to have better coding efficiency than ordinary topographic ICA (TICA) bases.