Set-oriented dimension reduction: Localizing principal component analysis via hidden Markov models

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 loglikelihood 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. © Springer-Verlag Berlin Heidelberg 2006.