Abstract
Periodicity or repetition detection has a wide varieties of use cases in human activity tracking, music pattern discovery, physiological signal monitoring and more. While there exists a broad range of research, often the most practical approaches are those based on simple quantities that are conserved over periodic repetition, such as auto-correlation or Fourier transform. Unfortunately, these periodicity-based approaches do not generalise well to quasi-periodic (variable period) scenarios. In this research, we exploit the time warping invariance of path signatures to find linearly accumulating quantities with respect to quasi-periodic repetition, and propose a novel repetition detection algorithm Recurrence Point Signed Area Persistence. We show that our approach can effectively deal with repetition detection with period variations, which similar unsupervised methods tend to struggle with.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110(1–2), 43–50 (1997). https://doi.org/10.1016/S0167-2789(97)00118-8
Chen, K.T.: Integration of paths, geometric invariants and a generalized baker-hausdorff formula. Ann. Math. 163–178 (1957). https://doi.org/10.2307/1969671
Chevyrev, I., Kormilitzin, A.: A primer on the signature method in machine learning. arXiv preprint arXiv:1603.03788 (2016)
De Paepe, D., Van Hoecke, S.: Mining recurring patterns in real-valued time series using the radius profile. In: 2020 IEEE International Conference on Data Mining (ICDM), pp. 984–989. IEEE (2020). https://doi.org/10.1109/ICDM50108.2020.00113
Hsu, J.L., Chen, A.L., Chen, H.C.: Finding approximate repeating patterns from sequence data. In: ISMIR, p. 2004 (2004)
Li, C.T., Cao, J., Liu, X., Stojmenovic, M.: mSIMPAD: efficient and robust mining of successive similar patterns of multiple lengths in time series. ACM Trans. Comput. Healthcare 1(4), 1–19 (2020). https://doi.org/10.1145/3396250
Li, C.T., Shen, J., Yang, Y., Cao, J., Stojmenovic, M.: Repetitive activity monitoring from multivariate time series: a generic and efficient approach. In: 2021 IEEE 18th International Conference on Mobile Ad Hoc and Smart Systems (MASS), pp. 36–45. IEEE (2021). https://doi.org/10.1109/MASS52906.2021.00014
Lyons, T., McLeod, A.D.: Signature methods in machine learning. arXiv preprint arXiv:2206.14674 (2022)
Lyons, T.: Rough paths, signatures and the modelling of functions on streams. In: Proceedings of the International Congress of Mathematicians Seoul 2014 (2014)
Mirmomeni, M., Kulik, L., Bailey, J.: A transferable technique for detecting and localising segments of repeating patterns in time series. In: 2021 International Joint Conference on Neural Networks (IJCNN), pp. 1–10. IEEE (2021). https://doi.org/10.1109/IJCNN52387.2021.9534157
Morris, D., Saponas, T.S., Guillory, A., Kelner, I.: Recofit: using a wearable sensor to find, recognize, and count repetitive exercises. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 3225–3234 (2014). https://doi.org/10.1145/2556288.2557116
Müller, M.: Dynamic time warping. In: Müller, M. (ed.) Information Retrieval for Music and Motion, pp. 69–84. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74048-3_4
Panagiotakis, C., Karvounas, G., Argyros, A.: Unsupervised detection of periodic segments in videos. In: 2018 25th IEEE International Conference on Image Processing (ICIP), pp. 923–927. IEEE (2018). https://doi.org/10.1109/ICIP.2018.8451336
Rai, A., Chintalapudi, K.K., Padmanabhan, V.N., Sen, R.: Zee: zero-effort crowdsourcing for indoor localization. In: Proceedings of the 18th Annual International Conference on Mobile Computing and Networking, pp. 293–304 (2012). https://doi.org/10.1145/2348543.2348580
Rehm, G.B., Kuhn, B.T., Nguyen, J., Anderson, N.R., Chuah, C.N., Adams, J.Y.: Improving mechanical ventilator clinical decision support systems with a machine learning classifier for determining ventilator mode. Stud. Health Technol. Inform. 264, 318–322 (2019). https://doi.org/10.3233/SHTI190235
Reiss, A., Stricker, D.: Introducing a new benchmarked dataset for activity monitoring. In: 2012 16th International Symposium on Wearable Computers, pp. 108–109. IEEE (2012). https://doi.org/10.1109/ISWC.2012.13
Shen, C., Ho, B.J., Srivastava, M.: MiLift: efficient smartwatch-based workout tracking using automatic segmentation. IEEE Trans. Mob. Comput. 17(7), 1609–1622 (2017). https://doi.org/10.1109/TMC.2017.2775641
Soro, A., Brunner, G., Tanner, S., Wattenhofer, R.: Recognition and repetition counting for complex physical exercises with deep learning. Sensors 19(3), 714 (2019). https://doi.org/10.3390/s19030714
Stillwell, J.: Naive Lie Theory. Springer, New York (2008). https://doi.org/10.1007/978-0-387-78214-0
Torres-Soto, J., Ashley, E.A.: Multi-task deep learning for cardiac rhythm detection in wearable devices. NPJ Digit. Med. 3(1), 1–8 (2020). https://doi.org/10.1038/s41746-020-00320-4
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Wang, C., Luo, L., Aickelin, U. (2023). Quasi-Periodicity Detection via Repetition Invariance of Path Signatures. In: Kashima, H., Ide, T., Peng, WC. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2023. Lecture Notes in Computer Science(), vol 13938. Springer, Cham. https://doi.org/10.1007/978-3-031-33383-5_24
Download citation
DOI: https://doi.org/10.1007/978-3-031-33383-5_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-33382-8
Online ISBN: 978-3-031-33383-5
eBook Packages: Computer ScienceComputer Science (R0)