Measuring non-gaussianity by phi-transformed and fuzzy histograms

Authors:
Claudia Plant;Son Mai Thai;Junming Shao;Fabian J. Theis;Anke Meyer-Baese;Christian Böhm
Affiliations:
Dirac Science Library, Florida State University, Tallahassee, FL;Department for Informatics, Research Unit for Database Systems, University of Munich, Munich, Germany;Klinikum rechts der Isar der TUM, Munich, Germany;Helmholtz Zentrum München, Neuherberg, Germany;Dirac Science Library, Florida State University, Tallahassee, FL;Department for Informatics, Research Unit for Database Systems, University of Munich, Munich, Germany
Venue:
Advances in Artificial Neural Systems - Special issue on Advances in Unsupervised Learning Techniques Applied to Biosciences and Medicine
Year:
2012

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Abstract

Independent component analysis (ICA) is an essential building block for data analysis in many applications. Selecting the truly meaningful components from the result of an ICA algorithm, or comparing the results of different algorithms, however, is nontrivial problems. We introduce a very general technique for evaluating ICA results rooted in information-theoretic model selection. The basic idea is to exploit the natural link between non-Gaussianity and data compression: the better the data transformation represented by one or several ICs improves the effectiveness of data compression, the higher is the relevance of the ICs. We propose two different methods which allow an efficient data compression of non-Gaussian signals: Phi-transformed histograms and fuzzy histograms. In an extensive experimental evaluation, we demonstrate that our novel information-theoretic measures robustly select non-Gaussian components from data in a fully automatic way, that is, without requiring any restrictive assumptions or thresholds.