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Summary: Set-Oriented Dimension Reduction: Localizing
Principal Component Analysis via Hidden
Markov Models
Illia Horenko1
, Johannes Schmidt-Ehrenberg2
, and Christof Sch¨utte1
1
Freie Universit¨at Berlin, Department of Mathematics and Informatics,
Arnimallee 6, D-14195 Berlin, Germany
{horenko,schuette}@mi.fu-berlin.de
2
Zuse Institute Berlin (ZIB), Takustr. 7, D-14195 Berlin
schmidt-ehrenberg@zib.de
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 algo-
rithm for its numerical optimization. We demonstrate the performance
of the method on a generic 102-dimensional example, apply the new
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