Learning Topographic Representations for Linearly Correlated Components

Recently, some variants of independent component analysis (ICA) have been proposed to estimate topographic representations. In these models, the assumptions of ICA are slightly relaxed: adjacent components are allowed to have higher order correlations while being linearly uncorrelated. In this paper, we propose a new statistical model for the estimation of topographic representations. In the proposed model, the estimated components are sparse and linearly correlated. To confirm the behavior of the model, we perform experiments on artificial data. In applications of the model to real data, we find emergence of a new kind of topographic representation for natural images and the outputs of simulated complex cells in the primary visual cortex.