Skip to main content
View expanded cover

Australasian Joint Conference on Artificial Intelligence

AI 2022: AI 2021: Advances in Artificial Intelligence pp 543–555Cite as

Multivariate Ordinal Patterns for Symmetry Approximation in Dynamic Probabilistic Relational Models

  • 375 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 13151)

Abstract

Exploiting symmetries is an important topic to obtain sparse (lifted) representations, reduce complexity and achieve good performance in dynamic probabilistic relational models (DPRMs). DPRMs factorise a full joint probability distribution by encoding multivariate time series through a set of conditionally dependent random variables. As obtaining exact symmetries throughout multivariate time series is often not realistic in real-world contexts and counteracts lifted representations, we propose to approximate the multivariate time series with a symbolisation scheme that encodes the overarching trend in up and down movements. In this work, we introduce MOP4SA, an approach for the approximation of symmetries based on multivariate ordinal pattern encodings and spectral clustering. Understanding symmetrical behaviour has several benefits that we evaluate in two use cases. We use MOP4SA (a) to detect structures in model symmetries over time, and (b) to avoid model splits and groundings in DPRMs.

Keywords

  • Symmetry
  • Multivariate time series
  • Multivariate ordinal pattern
  • Relational models
  • Lifting

N. Finke and M. Mohr—Contributed equally to this work.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-97546-3_44
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-97546-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   119.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Notes

  1. 1.

    Pronounced deeper models.

  2. 2.

    https://www.dma.dk/SikkerhedTilSoes/Sejladsinformation/AIS/.

  3. 3.

    https://github.com/FinkeNils/Processed-AIS-Data-Baltic-Sea-2020-v2.

References

  1. Agostini, A., Celaya, E.: Exploiting domain symmetries in reinforcement learning with continuous state and action spaces. In: 2009 International Conference on Machine Learning and Applications, Miami, FL, USA, pp. 331–336. IEEE (2009)

    Google Scholar 

  2. Agrawal, R., Faloutsos, C., Swami, A.: Efficient similarity search in sequence databases. In: Lomet, D.B. (ed.) FODO 1993. LNCS, vol. 730, pp. 69–84. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57301-1_5

    CrossRef  Google Scholar 

  3. Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 4 (2002)

    CrossRef  Google Scholar 

  4. Bellman, R.: Adaptive Control Processes: A guided Tour. Princeton Legacy Library, Princeton University Press, Princeton (2015)

    Google Scholar 

  5. Bertozzi, A.L., Merkurjev, E.: Chapter 12 - Graph-based optimization approaches for machine learning, uncertainty quantification and networks. In: Kimmel, R., Tai, X.C. (eds.) Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Handbook of Numerical Analysis, vol. 20, pp. 503–531. Elsevier (2019)

    Google Scholar 

  6. Chiu, B., Keogh, E., Lonardi, S.: Probabilistic discovery of time series motifs. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 493–498 (2003)

    Google Scholar 

  7. Dieleman, S., Fauw, J.D., Kavukcuoglu, K.: Exploiting cyclic symmetry in convolutional neural networks. In: Proceedings of the 33rd International Conference on Machine Learning, pp. 1889–1898 (2016)

    Google Scholar 

  8. Finke, N., Gehrke, M., Braun, T., Potten, T., Möller, R.: Investigating matureness of probabilistic graphical models for dry-bulk shipping. In: Proceedings of the 10th International Conference on Probabilistic Graphical Models, pp. 197–208 (2020)

    Google Scholar 

  9. Finke, N., Mohr, M.: A priori approximation of symmetries in dynamic probabilistic relational models. In: Edelkamp, S., Möller, R., Rueckert, E. (eds.) KI 2021. LNCS (LNAI), vol. 12873, pp. 309–323. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-87626-5_23

    CrossRef  Google Scholar 

  10. Gehrke, M., Braun, T., Möller, R.: Lifted dynamic junction tree algorithm. In: Chapman, P., Endres, D., Pernelle, N. (eds.) ICCS 2018. LNCS (LNAI), vol. 10872, pp. 55–69. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91379-7_5

    CrossRef  Google Scholar 

  11. Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S.: Dimensionality reduction for fast similarity search in large time series databases. In: Knowledge and Information Systems, pp. 263–286 (2001). https://doi.org/10.1021/acsami.7b03579

  12. Kramer, S.: A brief history of learning symbolic higher-level representations from data (and a curious look forward). In: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20, pp. 4868–4876 (2020)

    Google Scholar 

  13. Kruskal, J.B., Liberman, M.: The symmetric time warping problem: From continuous to discrete. In: Time Warps, String Edits and Macromolecules: The Theory and Practice of Sequence Comparison. Addison-Wesley Publishing Co. (1983)

    Google Scholar 

  14. Mohr, M., Wilhelm, F., Hartwig, M., Möller, R., Keller, K.: New approaches in ordinal pattern representations for multivariate time series. In: Proceedings of the 33rd International Florida Artificial Intelligence Research Society Conference (2020)

    Google Scholar 

  15. Myers, A., Khasawneh, F.A.: On the automatic parameter selection for permutation entropy. Chaos: an Interdis. J. Nonlinear Sci. 30(3), 033130 (2020)

    Google Scholar 

  16. Niepert, M., Van den Broeck, G.: Tractability through exchangeability: a new perspective on efficient probabilistic inference. In: AAAI-14 Proceedings of the 28th AAAI Conference on Artificial Intelligence, pp. 2467–2475. AAAI Press (2014)

    Google Scholar 

  17. Petitjean, F., Inglada, J., Gancarski, P.: Satellite image time series analysis under time warping. IEEE Trans. Geosci. Remote Sens. 50(8) (2012)

    Google Scholar 

  18. Poole, D.: First-order probabilistic inference. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 985–991 (2003)

    Google Scholar 

  19. Salvador, S., Chan, P.: FastDTW: toward accurate dynamic time warping in linear time and space. In: KDD Workshop on Mining Temporal and Sequential Data, pp. 70–80 (2004)

    Google Scholar 

  20. Sato, T.: A Statistical learning method for logic programs with distribution semantics. In: Proceedings of the 12th International Conference on Logic Programming, pp. 715–729 (1995)

    Google Scholar 

  21. Satorras, V.G., Hoogeboom, E., Welling, M.: E(n) equivariant graph neural networks. In: Proceedings of the 38th ICML (2021)

    Google Scholar 

  22. Yeh, C.C.M., et al.: Matrix profile I: all pairs similarity joins for time series: a unifying view that includes motifs, discords and shapelets. In: 2016 IEEE 16th International Conference on Data Mining (ICDM), pp. 1317–1322 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Systems, University of Lübeck, Lübeck, Germany

    Nils Finke, Ralf Möller & Marisa Mohr

  2. inovex GmbH, Hamburg, Germany

    Marisa Mohr

Authors
  1. Nils Finke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ralf Möller
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marisa Mohr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nils Finke .

Editor information

Editors and Affiliations

  1. University of Technology Sydney, Sydney, NSW, Australia

    Guodong Long

  2. RMIT University, Melbourne, SA, Australia

    Prof. Xinghuo Yu

  3. University of Queensland, Brisbane, QLD, Australia

    Sen Wang

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Finke, N., Möller, R., Mohr, M. (2022). Multivariate Ordinal Patterns for Symmetry Approximation in Dynamic Probabilistic Relational Models. In: Long, G., Yu, X., Wang, S. (eds) AI 2021: Advances in Artificial Intelligence. AI 2022. Lecture Notes in Computer Science(), vol 13151. Springer, Cham. https://doi.org/10.1007/978-3-030-97546-3_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-97546-3_44

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97545-6

  • Online ISBN: 978-3-030-97546-3

  • eBook Packages: Computer ScienceComputer Science (R0)