松田 源立

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.

It has been known that several Jacobi algorithms (e.g. JADE, MaxKurt, EML, and so on) are useful in independent component analysis (ICA). This paper shows that the sum of 4th-order (iijj-) cumulants over all the pairs of components is a "semi-invariant" function of such Jacobi algorithms. Then we prove that MaxKurt algorithm converges monotonically without loss to a local minimum of the semi-invariant function, which is consistent with the result obtained by the symmetrical maximization of kurtoses. In addition, a new algorithm combining EML and JADE is proposed. The EML-JADE algorithm not only uses both maximization and minimization of kurtoses suitably like EML but also utilizes JADE in the cases where super- and sub-gaussian sources are highly mixed.