Algorithms for Independent Components Analysis and Higher Order Statistics

Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)

Bibtex Metadata Paper


Daniel Lee, Uri Rokni, Haim Sompolinsky


A latent variable generative model with finite noise is used to de(cid:173) scribe several different algorithms for Independent Components Anal(cid:173) ysis (lCA). In particular, the Fixed Point ICA algorithm is shown to be equivalent to the Expectation-Maximization algorithm for maximum likelihood under certain constraints, allowing the conditions for global convergence to be elucidated. The algorithms can also be explained by their generic behavior near a singular point where the size of the opti(cid:173) mal generative bases vanishes. An expansion of the likelihood about this singular point indicates the role of higher order correlations in determin(cid:173) ing the features discovered by ICA. The application and convergence of these algorithms are demonstrated on a simple illustrative example.