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Set-Oriented Dimension Reduction: Localizing Principal Component Analysis Via Hidden Markov Models

  • Illia Horenko
  • Johannes Schmidt-Ehrenberg
  • Christof Schütte
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4216)

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.

Keywords

Hide Markov Model Independent Component Analysis Dimension Reduction Independent Component Analysis Hide State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Illia Horenko
    • 1
  • Johannes Schmidt-Ehrenberg
    • 2
  • Christof Schütte
    • 1
  1. 1.Department of Mathematics and InformaticsFreie Universität BerlinBerlinGermany
  2. 2.Zuse Institute Berlin (ZIB)Berlin

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