Invariant Coordinate Selection (ICS): A Robust Statistical Perspective on Independent Component Analysis (ICA)

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ABSTRACTIndependent component analysis (ICA) is an increasingly popular method for analyzing multivariate data within many diverse disciplines, such as computer vision, psychology, electrical engineering, physics and meteorology. Although essentially a multivariate statistical method, the primary development of ICAhas come from outside the area of statistics. Methods developed for ICA presume somewhat specialized models for multivariate data. Nevertheless, these methods tend to possess some natural robustness properties, and consequently, have been used for exploratory data analysis in general and for cluster analysis or unsupervised learning in particular. At present, the statistical properties of ICA methods are not well understood. One goal of the proposed research is thus to conduct a study of the statistical and robustness properties of ICA methods. Another goal of the proposed research is to study the use of ICA methods as general multivariate statistical methods rather than simply as solutions to the ICA problem. To accomplish this, a new model free interpretation of ICA methods, together with some extensions of these methods, is to be introduced and developed. The principal investigator refers to this model free approach as invariant coordinate selection (ICS).The proposed research should have an impact on the many scientific and engineering disciples using ICA models by providing a better statistical understanding of their methods, consequently leading to improved methods and applications. An important application of ICA models, for example, is in the unraveling of convoluted signals or sources. The proposed research will also help call further attention to these important statistical problems to the general statistics research community. In addition, it is anticipated that the proposed introduction and development of the ICS methodology will provide important and potentially very popular new methods for exploring and analyzing multivariate data, perhaps similar to the importance of principal component analysis or discriminant analysis. These more general ICS methods should have impact not only within the statistics community but also within the varied disciplines, such as psychology, biology, geology, and others, that routinely deal with multivariate data.