Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification

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

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Abstract

Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new trajectory labels using Sinkhorn divergences on the space of diagram KDEs to quantify proximity. We show that this approach accurately discriminates between states of chaotic systems that are close in parameter space, and its performance is robust to noise.
Original languageEnglish
Title of host publicationProceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018
EditorsM. Arif Wani, Moamar Sayed-Mouchaweh, Edwin Lughofer, Joao Gama, Mehmed Kantardzic
PublisherIEEE
Pages714-721
Number of pages8
ISBN (Electronic)978-1-5386-6805-4
ISBN (Print)978-1-5386-6806-1
DOIs
Publication statusPublished - 17 Jan 2019
Event17th IEEE International Conference on Machine Learning and Applications - Orlando, United States
Duration: 17 Dec 201820 Dec 2018
Conference number: 17
https://www.icmla-conference.org/icmla18/

Conference

Conference17th IEEE International Conference on Machine Learning and Applications
Abbreviated titleICMLA 2018
CountryUnited States
CityOrlando
Period17/12/1820/12/18
Internet address

Fingerprint

Time series
Chaotic systems
Fault detection
Quality control
Labels
Dynamical systems
Classifiers
Trajectories
Health
Monitoring

Bibliographical note

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • Time series analysis
  • Measurement
  • Entropy
  • Pipelines
  • Histograms
  • Machine learning
  • Chaos
  • Time series
  • Dynamical system
  • Sinkhorn
  • Persistence diagram
  • TDA
  • Topological data analysis

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Safety, Risk, Reliability and Quality
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications
  • Computer Science Applications

Cite this

Stephen, C. (2019). Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification. In M. A. Wani, M. Sayed-Mouchaweh, E. Lughofer, J. Gama, & M. Kantardzic (Eds.), Proceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018 (pp. 714-721). [8614138] IEEE. https://doi.org/10.1109/ICMLA.2018.00113

Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification. / Stephen, Colin.

Proceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018. ed. / M. Arif Wani; Moamar Sayed-Mouchaweh; Edwin Lughofer; Joao Gama; Mehmed Kantardzic. IEEE, 2019. p. 714-721 8614138.

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

Stephen, C 2019, Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification. in MA Wani, M Sayed-Mouchaweh, E Lughofer, J Gama & M Kantardzic (eds), Proceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018., 8614138, IEEE, pp. 714-721, 17th IEEE International Conference on Machine Learning and Applications, Orlando, United States, 17/12/18. https://doi.org/10.1109/ICMLA.2018.00113
Stephen C. Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification. In Wani MA, Sayed-Mouchaweh M, Lughofer E, Gama J, Kantardzic M, editors, Proceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018. IEEE. 2019. p. 714-721. 8614138 https://doi.org/10.1109/ICMLA.2018.00113
Stephen, Colin. / Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification. Proceedings - 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018. editor / M. Arif Wani ; Moamar Sayed-Mouchaweh ; Edwin Lughofer ; Joao Gama ; Mehmed Kantardzic. IEEE, 2019. pp. 714-721
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