Aapo Hyvärinen, Patrik Hoyer
Independent component analysis of natural images leads to emer(cid:173) gence of simple cell properties, Le. linear filters that resemble wavelets or Gabor functions. In this paper, we extend ICA to explain further properties of VI cells. First, we decompose natural images into independent subspaces instead of scalar components. This model leads to emergence of phase and shift invariant fea(cid:173) tures, similar to those in VI complex cells. Second, we define a topography between the linear components obtained by ICA. The topographic distance between two components is defined by their higher-order correlations, so that two components are close to each other in the topography if they are strongly dependent on each other. This leads to simultaneous emergence of both topography and invariances similar to complex cell properties.