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Dimension Selection for Feature Selection and Dimension Reduction with Principal and Independent Component Analysis

inge{at}maths.unsw.edu.au Department of Statistics, School of Mathematics, University of New South Wales, Sydney, NSW 2052 Australia

Kanta Naito

naito{at}riko.shimane-u.ac.jp Department of Mathematics, Faculty of Science and Engineering, Shimane University, Matsue 690-8504 Japan

This letter is concerned with the problem of selecting the best or most informative dimension for dimension reduction and feature extraction in high-dimensional data. The dimension of the data is reduced by principal component analysis; subsequent application of independent component analysis to the principal component scores determines the most nongaussian directions in the lower-dimensional space. A criterion for choosing the optimal dimension based on bias-adjusted skewness and kurtosis is proposed. This new dimension selector is applied to real data sets and compared to existing methods. Simulation studies for a range of densities show that the proposed method performs well and is more appropriate for nongaussian data than existing methods.