A fixed-point algorithm of topographic ICA

Topographic ICA is a well-known ICA-based technique, which generates a topographic mapping consisting of edge detectors from natural scenes. Topographic ICA uses a complicated criterion derived from a two-layer generative model and minimizes it by a gradient descent algorithm. In this paper, we propose a new simple criterion for topographic ICA and construct a fixed-point algorithm minimizing it. Our algorithm can be regarded as an expansion of the well-known fast ICA algorithm to topographic ICA, and it does not need any tuning of the stepsize. Numerical experiments show that our fixed-point algorithm can generate topographic mappings similar to those in topographic ICA.