Set-Oriented dimension reduction: localizing principal component analysis via hidden markov models

Authors:
Illia Horenko;Johannes Schmidt-Ehrenberg;Christof Schütte
Affiliations:
Department of Mathematics and Informatics, Freie Universität Berlin, Berlin, Germany;Zuse Institute Berlin (ZIB), Berlin;Department of Mathematics and Informatics, Freie Universität Berlin, Berlin, Germany
Venue:
CompLife'06 Proceedings of the Second international conference on Computational Life Sciences
Year:
2006

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Abstract

We present a method for simultaneous dimension reduction and metastability analysis of high dimensional time series. The approach is based on the combination of hidden Markov models (HMMs) and principal component analysis. We derive optimal estimators for the log-likelihood functional and employ the Expectation Maximization algorithm for its numerical optimization. We demonstrate the performance of the method on a generic 102-dimensional example, apply the new HMM-PCA algorithm to a molecular dynamics simulation of 12–alanine in water and interpret the results.