Measuring Non-Gaussianity by Phi-Transformed and Fuzzy Histograms

Claudia Plant, Thai Son Mai, Junming Shao, Fabian J. Theis, Anke Meyer-Baese, Christian Boehm

Research output: Contribution to journalArticle

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.
Original languageEnglish
Number of pages13
JournalAdvances in Artificial Neural Systems
DOIs
Publication statusPublished - 2012

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