Independent Component Analysis Using Maximization of L-Kurtosis

This paper presents a new approach towards independent component analysis (ICA) for small samples of data, utilizing the linear combination of expectations of order statistics, also termed as L-moments. The main advantage of using L-moments is the relatively low bias in their estimation for small samples compared to the conventional moments. In the present work, arguments leading to kurtosis maximization ICA are first explored and a criterion based on the maximization of L-kurtosis is developed. The optimality criterion based on the extraction of a single source is then assessed. The independent components of the mixture are extracted sequentially using a deflationary approach. The quality of separation of independent components from a mixture is re-interpreted in terms of the distribution parameters of the recovered sources. The robustness of the proposed algorithm is demonstrated through simulation examples of separation of 2-source mixtures, a large-scale problem and a case study from health monitoring of civil structures.