Novel Characteristic Function Based Criteria for Ica

We introduce two nonparametric independent component analysis (ICA) criteria based on factorization of characteristic functions. This approach has potential to separate wide class of distributions because characteristic function always exists. A simple criterion allowing for efficient search of the separating matrix and a more advanced criterion possessing desirable consistency property are presented. These criteria may easily be used in orthogonal ICA algorithms. Separating matrix is estimated by establishing pairwise independence among the source signals. Theoretical characteristic functions used in the criteria are replaced by empirical ones. In the examples, the reliable performance of the methods is demonstrated using a variety of source distributions including skewed and heavy-tailed distributions.