### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Human-Computer Interaction
- Signal Processing

### Cite this

*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

}

*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.

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 -