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 language | English (US) |
|---|---|
| Title of host publication | 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings |
| Publisher | IEEE Computer Society |
| Pages | 1-6 |
| Number of pages | 6 |
| Volume | 2017-September |
| ISBN (Electronic) | 9781509063413 |
| DOIs | |
| State | Published - Dec 5 2017 |
| Event | 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Tokyo, Japan Duration: Sep 25 2017 → Sep 28 2017 |
Other
| Other | 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 |
|---|---|
| Country | Japan |
| City | Tokyo |
| Period | 9/25/17 → 9/28/17 |
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All Science Journal Classification (ASJC) codes
- Human-Computer Interaction
- Signal Processing
Cite this
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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 proceeding › Conference contribution
TY - GEN
T1 - A locally optimal algorithm for estimating a generating partition from an observed time series
AU - Miller, David Jonathan
AU - Ghalyan, Najah F.
AU - Ray, Asok
PY - 2017/12/5
Y1 - 2017/12/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85042254824&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042254824&partnerID=8YFLogxK
U2 - 10.1109/MLSP.2017.8168162
DO - 10.1109/MLSP.2017.8168162
M3 - Conference contribution
AN - SCOPUS:85042254824
VL - 2017-September
SP - 1
EP - 6
BT - 2017 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2017 - Proceedings
PB - IEEE Computer Society
ER -