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

David Jonathan Miller, Najah F. Ghalyan, Asok Ray

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

1 Citation (Scopus)

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
PublisherIEEE Computer Society
Pages1-6
Number of pages6
Volume2017-September
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

Other

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

Fingerprint

Time series
Dynamical systems
Vector quantization
Entropy

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 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings (Vol. 2017-September, pp. 1-6). IEEE Computer Society. https://doi.org/10.1109/MLSP.2017.8168162
Miller, David Jonathan ; Ghalyan, Najah F. ; Ray, Asok. / A locally optimal algorithm for estimating a generating partition from an observed time series. 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings. Vol. 2017-September IEEE Computer Society, 2017. pp. 1-6
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Miller, DJ, Ghalyan, NF & Ray, A 2017, A locally optimal algorithm for estimating a generating partition from an observed time series. in 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings. vol. 2017-September, IEEE Computer Society, pp. 1-6, 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017, Tokyo, Japan, 9/25/17. https://doi.org/10.1109/MLSP.2017.8168162

A locally optimal algorithm for estimating a generating partition from an observed time series. / Miller, David Jonathan; Ghalyan, Najah F.; Ray, Asok.

2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings. Vol. 2017-September IEEE Computer Society, 2017. p. 1-6.

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

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Miller DJ, Ghalyan NF, Ray A. A locally optimal algorithm for estimating a generating partition from an observed time series. In 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings. Vol. 2017-September. IEEE Computer Society. 2017. p. 1-6 https://doi.org/10.1109/MLSP.2017.8168162