A locally optimal algorithm for estimating a generating partition from an observed time series

David J. Miller, Najah F. Ghalyan, Asok Ray

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Estimation of a generating partition is critical for symbolization of measurements from discrete-time dynamical systems, where a sequence of symbols from a (finite-cardinality) alphabet uniquely specifies the underlying time series. Such symbolization is useful for computing measures (e.g., Kolmogorov-Sinai entropy) to characterize the (possibly unknown) dynamical system. It is also useful for time series classification and anomaly detection. Previous work attemps to minimize a clustering objective function that measures discrepancy between a set of reconstruction values and the points from the time series. Unfortunately, the resulting algorithm is non-convergent, with no guarantee of finding even locally optimal solutions. The problem is a heuristic 'nearest neighbor' symbol assignment step. Alternatively, we introduce a new, locally optimal algorithm. We apply iterative 'nearest neighbor' symbol assignments with guaranteed discrepancy descent, by which joint, locally optimal symbolization of the time series is achieved. While some approaches use vector quantization to partition the state space, our approach only ensures a partition in the space consisting of the entire time series (effectively, clustering in an infinite-dimensional space). Our approach also amounts to a novel type of sliding block lossy source coding. We demonstrate improvement, with respect to several measures, over a popular method used in the literature.

Original languageEnglish (US)
Title of host publication2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings
EditorsNaonori Ueda, Jen-Tzung Chien, Tomoko Matsui, Jan Larsen, Shinji Watanabe
PublisherIEEE Computer Society
Pages1-6
Number of pages6
ISBN (Electronic)9781509063413
DOIs
StatePublished - Dec 5 2017
Event2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Tokyo, Japan
Duration: Sep 25 2017Sep 28 2017

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
Volume2017-September
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Other

Other2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017
CountryJapan
CityTokyo
Period9/25/179/28/17

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All Science Journal Classification (ASJC) codes

  • Human-Computer Interaction
  • Signal Processing

Cite this

Miller, D. J., Ghalyan, N. F., & Ray, A. (2017). A locally optimal algorithm for estimating a generating partition from an observed time series. In N. Ueda, J-T. Chien, T. Matsui, J. Larsen, & S. Watanabe (Eds.), 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings (pp. 1-6). (IEEE International Workshop on Machine Learning for Signal Processing, MLSP; Vol. 2017-September). IEEE Computer Society. https://doi.org/10.1109/MLSP.2017.8168162