Skip to main content
SpringerLink
Log in
Book cover

Pacific-Asia Conference on Knowledge Discovery and Data Mining

PAKDD 2022: Advances in Knowledge Discovery and Data Mining pp 511–525Cite as

Tlife-GDN: Detecting and Forecasting Spatio-Temporal Anomalies via Persistent Homology and Geometric Deep Learning

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13281))

Abstract

Most recently, the tools of geometric deep learning (GDL) and, in particular, graph neural networks emerge as a promising new alternative in unsupervised anomaly detection problems where the data exhibit a sophisticated nonlinear dependence structure such as various geospatial surveillance systems. However, prevailing GDL-based methods for anomaly detection tend to exhibit limited capabilities to capture multiscale spatio-temporal variability which is ubiquitous in many applications, particularly, related to biosurveillance and biothreats. Motivated by the problem of assessing COVID-19 severity, we develop a novel approach to unsupervised anomaly detection in spatio-temporal data by fusing the notion of GDL with the emerging direction of persistent homologies and topological data analysis. In particular, our key idea is to bolster the GDL performance by leveraging the complementary insight on the intrinsic multiscale data organization which topological descriptors can provide. We also go one step further and show how our ideas at the interface of topological and geometric deep learning can be used not only for detection but for prediction of future anomalies. We show the utility of the new approach to detecting, forecasting and interpreting risks in COVID-19 clinical severity, measured in terms of hospitalization rates, in three U.S. states: California, Texas, and Pennsylvania.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Generation details are available in Algorithm 1.

  2. 2.

    Available at https://covidactnow.org/?s=24821397.

  3. 3.

    Available at https://github.com/CSSEGISandData/COVID-19.

  4. 4.

    Available at https://github.com/d-ailin/GDN/tree/main/data/msl.

  5. 5.

    Further details at https://itrust.sutd.edu.sg/testbeds/water-distribution-wadi/ [3].

  6. 6.

    https://github.com/ZhiweiZhen/Tlife-GDN.

References

  1. Adams, H., et al.: Persistence images: a stable vector representation of persistent homology. JMLR 18, 1–35 (2017)

    MathSciNet  Google Scholar 

  2. Aggarwal, C.C.: Data Mining: The Textbook. Springer, Cham (2015)

    MATH  Google Scholar 

  3. Ahmed, C.M., Palleti, V.R., Mathur, A.P.: WADI: a water distribution testbed for research in the design of secure cyber physical systems. In: CySWATER (2017)

    Google Scholar 

  4. Alonso, J., Belanche, L., Avresky, D.R.: Predicting software anomalies using machine learning techniques. In: IEEE NCA, pp. 163–170 (2011)

    Google Scholar 

  5. Angiulli, F., Pizzuti, C.: Fast outlier detection in high dimensional spaces. In: ECML PKDD (2002)

    Google Scholar 

  6. Basak, D., Pal, S., Patranabis, D.C.: Support vector regression. Neural Inf. Process. Lett. Rev. 11(10), 203–224 (2007)

    Google Scholar 

  7. Brar, G., et al.: COVID-19 severity and outcomes in patients with cancer: a matched cohort study. J. Cl. Oncol. 38(33), 3914–3924 (2020)

    Article  Google Scholar 

  8. Cai, Q., et al.: Obesity and COVID-19 severity in a designated hospital in Shenzhen. China Diab. care 43(7), 1392–1398 (2020)

    Google Scholar 

  9. Carlsson, G.: Topology and data. BAMS 46(2), 255–308 (2009)

    Article  MathSciNet  Google Scholar 

  10. Chaudhary, A., Mittal, H., Arora, A.: Anomaly detection using graph neural networks. In: COMITCon, pp. 346–350. IEEE (2019)

    Google Scholar 

  11. Chazal, F., Michel, B.: An introduction to topological data analysis: fundamental and practical aspects for data scientists. Frontiers in Artificial Intelligence (2021)

    Google Scholar 

  12. Chen, Y., Segovia-Dominguez, I., Coskunuzer, B., Gel, Y.R.: TAMP-S2GCNets: coupling time-aware multipersistence knowledge representation with spatio-supra graph convolutional networks for time-series forecasting. In: ICLR (2022)

    Google Scholar 

  13. Chen, Y., Segovia-Dominguez, I., Gel, Y.R.: Z-GCNETs: time zigzags at graph convolutional networks for time series forecasting. In: ICML (2021)

    Google Scholar 

  14. Deng, A., Hooi, B.: Graph neural network-based anomaly detection in multivariate time series. In: AAAI (2021)

    Google Scholar 

  15. Dey, T.K., Wang, Y.: Computational Topology for Data Analysis. Cambridge University Press, Cambridge (2022)

    Book  Google Scholar 

  16. Gallo Marin, B., et al.: Predictors of COVID-19 severity: a literature review. Rev. in Med. Virol. 31(1), 1–10 (2021)

    Google Scholar 

  17. Goh, J., Adepu, S., Junejo, K.N., Mathur, A.P.: A dataset to support research in the design of secure water treatment systems. In: CRITIS (2016)

    Google Scholar 

  18. Golan, I., El-Yaniv, R.: Deep anomaly detection using geometric transformations. arXiv:1805.10917 (2018)

  19. Hickok, A., Needell, D., Porter, M.A.: Analysis of spatiotemporal anomalies using persistent homology: case studies with COVID-19 data. arXiv:2107.09188 (2021)

  20. Hofer, C.D., Graf, F., Rieck, B., Niethammer, M., Kwitt, R.: Graph filtration learning. In: ICML, vol. 119, pp. 4314–4323. PMLR (2020)

    Google Scholar 

  21. Hundman, K., Constantinou, V., Laporte, C., Colwell, I., Soderstrom, T.: Detecting spacecraft anomalies using LSTMs and nonparametric dynamic thresholding. arXiv:1802.04431 (2018)

  22. Islambekov, U., Yuvaraj, M., Gel, Y.R.: Harnessing the power of topological data analysis to detect change points in time series. Environmetrics 31(1), e2612 (2020)

    Google Scholar 

  23. Jin, W., Tung, A.K.H., Han, J., Wang, W.: Ranking outliers using symmetric neighborhood relationship. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 577–593. Springer, Heidelberg (2006). https://doi.org/10.1007/11731139_68

  24. Karadayi, Y., Aydin, M.N., Öǧrenci, A.S.: Unsupervised anomaly detection in multivariate spatio-temporal data using deep learning: early detection of COVID-19 outbreak in Italy. IEEE Access 8, 164155–164177 (2020)

    Google Scholar 

  25. Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv:1312.6114 (2013)

  26. Li, D., Chen, D., Goh, J., Ng, S.k.: Anomaly detection with generative adversarial networks for multivariate time series. arXiv:1809.04758 (2018)

  27. Li, Y., Islambekov, U., Akcora, C., Smirnova, E., Gel, Y.R., Kantarcioglu, M.: Dissecting ethereum blockchain analytics: What we learn from topology and geometry of the ethereum graph? In: SDM, pp. 523–531. SIAM (2020)

    Google Scholar 

  28. Liang, L., Gong, P.: Climate change and human infectious diseases: a synthesis of research findings from global and spatio-temporal perspectives. Environ. Int. 103, 99–108 (2017)

    Google Scholar 

  29. Liu, D., Veeramachaneni, K., Geiger, A., Li, V.O.K., Qu, H.: AQEyes: visual analytics for anomaly detection and examination of air quality data. arXiv:2103.12910 (2021)

  30. Ma, X., Wu, J., Xue, S., Yang, J., Zhou, C., Sheng, Q.Z., Xiong, H., Akoglu, L.: A comprehensive survey on graph anomaly detection with deep learning. IEEE Trans. Knowl. Data Eng. (2021)

    Google Scholar 

  31. Malhotra, P., Vig, L., Shroff, G., Agarwal, P.: Long short term memory networks for anomaly detection in time series. In: ESANN, vol. 89, pp. 89–94 (2015)

    Google Scholar 

  32. Moore, M., Landree, E., Hottes, A.K., Shelton, S.R.: Environmental biodetection and human biosurveillance research and development for national security. Tech. rep, Homeland Security Operational Analysis Center, RAND Corp (2018)

    Google Scholar 

  33. Ofori-Boateng, D., Dominguez, I.S., Kantarcioglu, M., Akcora, C.G., Gel, Y.R.: Topological anomaly detection in dynamic multilayer blockchain networks. In: ECML (2021)

    Google Scholar 

  34. Ruff, L., et al.: Deep one-class classification. In: ICML, vol. 80, pp. 4393–4402 (2018)

    Google Scholar 

  35. Sanchez-Hernandez, C., Boyd, D.S., Foody, G.M.: One-class classification for mapping a specific land-cover class: SVDD classification of fenland. GRSS-IEEE 45(4), 1061–1073 (2007)

    Google Scholar 

  36. Segovia Dominguez, I., Lee, H., Chen, Y., Garay, M., Gorski, K.M., Gel, Y.R.: Does air quality really impact COVID-19 clinical severity: coupling NASA satellite datasets with geometric deep learning. In: ACM SIGKDD, pp. 3540–3548 (2021)

    Google Scholar 

  37. Segovia-Dominguez, I., et al.: Using NASA satellite data sources and geometric deep learning to uncover hidden patterns in COVID-19 clinical severity. arXiv:2110.10849 (2021)

  38. Segovia-Dominguez, I., Zhen, Z., Wagh, R., Lee, H., Gel, Y.R.: TLife-LSTM: Forecasting future COVID-19 progression with topological signatures of atmospheric conditions. In: PAKDD, pp. 201–212 (2021)

    Google Scholar 

  39. Shyu, M.L., Chen, S.C., Sarinnapakorn, K., Chang, L.: A novel anomaly detection scheme based on principal component classifier. Miami Univ Coral Gables Fl Dept of Electrical and Computer Engineering, Technical report (2003)

    Google Scholar 

  40. Stolz, B.J., Harrington, H.A., Porter, M.A.: Persistent homology of time-dependent functional networks constructed from coupled time series. Chaos 27(4), 047410 (2017)

    Google Scholar 

  41. Tack, A.J., Thrall, P.H., Barrett, L.G., Burdon, J.J., Laine, A.L.: Variation in infectivity and aggressiveness in space and time in wild host-pathogen systems: causes and consequences. J. Evol. Biol. 25(10), 1918–1936 (2012)

    Google Scholar 

  42. Tang, J., Chen, Z., Fu, A.W., Cheung, D.W.: Enhancing effectiveness of outlier detections for low density patterns. In: Chen, M.-S., Yu, P.S., Liu, B. (eds.) PAKDD 2002. LNCS (LNAI), vol. 2336, pp. 535–548. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47887-6_53

  43. Umeda, Y., Kaneko, J., Kikuchi, H.: Topological data analysis and its application to time-series data analysis. Fujitsu Sci. Tech. J. 55(2), 65–71 (2019)

    Google Scholar 

  44. Van Donkelaar, A., Martin, R.V., Brauer, M., Kahn, R., Levy, R., Verduzco, C., Villeneuve, P.J.: Global estimates of ambient fine particulate matter concentrations from satellite-based aerosol optical depth: development and application. Environ. Health Perspectives 118(6), 847–855 (2010)

    Google Scholar 

  45. Vapnik, V.N.: An overview of statistical learning theory. IEEE Trans. Neural Netw. 10(5), 988–999 (1999)

    Google Scholar 

  46. Vries, D., Van Den Akker, B., Vonk, E., De Jong, W., Van Summeren, J.: Application of machine learning techniques to predict anomalies in water supply networks. Water Sci. Technol. 16(6), 1528–1535 (2016)

    Google Scholar 

  47. Zeng, S., Graf, F., Hofer, C., Kwitt, R.: Topological attention for time series forecasting. In: NeurIPS (2021)

    Google Scholar 

  48. Zong, B., Song, Q., Min, M.R., Cheng, W., Lumezanu, C., Cho, D., Chen, H.: Deep autoencoding gaussian mixture model for unsupervised anomaly detection. In: ICLR (2018)

    Google Scholar 

Download references

Acknowledgement

This work has been supported in part by grants NSF DMS 1925346, NSF ECCS 2039701, NASA 20-RRNES20-0021, and the Department of the Navy, Office of Naval Research under ONR award number N00014-21-1-2530. Part of this material is also based upon work supported by (while serving at) the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation and/or the Office of Naval Research. The authors are grateful to Huikyo Lee, NASA’s Jet Propulsion Lab for the motivating discussion.

Author information

Authors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, 75080, USA

    Zhiwei Zhen, Ignacio Segovia-Dominguez & Yulia R. Gel

  2. Princeton University, Princeton, NJ, 08544, USA

    Yuzhou Chen

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Yuzhou Chen

  4. Jet Propulsion Laboratory, Pasadena, CA, 91109, USA

    Ignacio Segovia-Dominguez

  5. National Science Foundation, Alexandria, VA, 22314, Egypt

    Yulia R. Gel

Authors
  1. Zhiwei Zhen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuzhou Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ignacio Segovia-Dominguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yulia R. Gel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiwei Zhen .

Editor information

Editors and Affiliations

  1. Laboratory of Artificial Intelligence and Decision Support, University of Porto, Porto, Portugal

    João Gama

  2. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, China

    Tianrui Li

  3. National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China

    Yang Yu

  4. School of Computer Science and Technology, University of Science and Technology of China, Hefei, China

    Enhong Chen

  5. JD iCity, JD Technology & JD Intelligent Cities Research, Beijing, China

    Yu Zheng

  6. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, China

    Fei Teng

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhen, Z., Chen, Y., Segovia-Dominguez, I., Gel, Y.R. (2022). Tlife-GDN: Detecting and Forecasting Spatio-Temporal Anomalies via Persistent Homology and Geometric Deep Learning. In: Gama, J., Li, T., Yu, Y., Chen, E., Zheng, Y., Teng, F. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2022. Lecture Notes in Computer Science(), vol 13281. Springer, Cham. https://doi.org/10.1007/978-3-031-05936-0_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-05936-0_40

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-05935-3

  • Online ISBN: 978-3-031-05936-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation