Skip to main content
SpringerLink
Log in

A Practical Hands-on for Learning Graph Data Communities on Manifolds

  • Conference paper
  • First Online:
Geometric Structures of Statistical Physics, Information Geometry, and Learning (SPIGL 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 361))

  • 1426 Accesses

Abstract

Learning graph-structured data with hyperbolic geometry has received considerable attention in the last years. This paper reviews recent approaches based on hyperbolic embeddings, Riemannian K-means and Expectation Maximisation algorithms for supervised and unsupervised learning problems on graphs. The presentation is aimed to provide a practical and technical support for users interested in this topic. It is focused on illustrative examples, visualisations and Pytorch codes which are commented in details (The package implementing the algorithms is available online from https://github.com/tgeral68/HyperbolicGraphAndGMM).

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

Access this chapter

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 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Notes

  1. 1.

    https://www.aminer.org/billboard/aminernetwork.

References

  1. Alekseevskij, D., Vinberg, E.B., Solodovnikov, A.: Geometry of spaces of constant curvature. In: Geometry II, pp. 1–138. Springer (1993)

    Google Scholar 

  2. Arnaudon, M., Barbaresco, F., Yang, L.: Riemannian medians and means with applications to radar signal processing. J. Sel. Top. Sig. Process. 7(4), 595–604 (2013)

    Article  Google Scholar 

  3. Bonnabel, S.: Stochastic gradient descent on Riemannian manifolds. IEEE Trans. Autom. Control 122(4), 2217–2229 (2013)

    Article  MathSciNet  Google Scholar 

  4. Cavallari, S., Zheng, V.W. Cai, H., Chang, K.C.-C., Cambria, E.: Learning community embedding with community detection and node embedding on graphs. In: Proceedings of the 2017 ACM on Conference on Information and Knowledge Management (CIKM), pp. 377–386. ACM (2017)

    Google Scholar 

  5. Cho, H., DeMeo, B., Peng, J., Berger, B.: Large-margin classification in hyperbolic space. In: Proceedings of Machine Learning Research, vol. 89 , pp. 1832–1840. PMLR, 16–18 April 2019

    Google Scholar 

  6. Dhingra, B., Shallue, C.J., Norouzi, M., Dai, A.M., Dahl, G.E.: Embedding text in hyperbolic spaces. In: TextGraphs@NAACL-HLT, pp. 59–69. Association for Computational Linguistics (2018)

    Google Scholar 

  7. Ganea, O., Becigneul, G., Hofmann, T.: Hyperbolic neural networks. In: Advances in Neural Information Processing Systems 31 (NIPS), pp. 5345–5355. Curran Associates, Inc. (2018)

    Google Scholar 

  8. Gerald, T., Zaatiti, H., Hajri, H., Baskiotis, N., Schwander, O.: From node embedding to community embedding: a hyperbolic approach (2020)

    Google Scholar 

  9. Hajri, H., Zaatiti, H., Hébrail, G., Aknin, P.: Apprentissage automatique sur des données de type graphe utilisant le plongement de poincaré et les algorithmes stochastiques riemanniens. In: Conférence Nationale d’Intelligence Artificielle Année 2019 (2019)

    Google Scholar 

  10. Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. American Mathematical Society (2001)

    Google Scholar 

  11. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), (2008)

    Google Scholar 

  12. Leimeister, M., Wilson, B.J.: Skip-gram word embeddings in hyperbolic space. CoRR, abs/1809.01498 (2018)

    Google Scholar 

  13. Liu, S., Chen J., Pan, L., Ngo, C., Chua, T., Jiang, Y.: Hyperbolic visual embedding learning for zero-shot recognition. In: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, 13–19 June 2020, pp. 9270–9278. IEEE (2020)

    Google Scholar 

  14. Mathieu, E., Le Lan, C., Maddison, C.J., Tomioka, R., Teh, Y.W.: Continuous hierarchical representations with poincaré variational auto-encoders. In: Wallach, H. Larochelle, H., Beygelzimer, A., d Alché-Buc, F., Fox, E., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32, pp. 12565–12576. Curran Associates, Inc. (2019)

    Google Scholar 

  15. Miller, G.A.: Wordnet: a lexical database for English. Commun. ACM 38(11), 39–41 (1995)

    Article  Google Scholar 

  16. Miolane, N., Guigui, N., Le Brigant, A., Mathe, J., Hou, B., Thanwerdas, Y., Heyder, S., Peltre, O., Koep, N., Zaatiti, H., et al.: Geomstats: a python package for Riemannian geometry in machine learning. J. Mach. Learn. Res. 21(223), 1–9 (2020)

    MathSciNet  MATH  Google Scholar 

  17. Miolane, N., Guigui, N., Zaatiti, H., Shewmake, C., Hajri, H., Brooks, D., Le Brigant, A., Mathe, J., Hou, B., Thanwerdas, Y., et al.: Introduction to geometric learning in python with geomstats. In: Proceedings of the 19th Python in Science Conference, vol. 2020 (2020)

    Google Scholar 

  18. Nickel, M., Kiela, D.: Poincaré embeddings for learning hierarchical representations. In: Advances in Neural Information Processing Systems 30 (NIPS), pp. 6338–6347. Curran Associates, Inc. (2017)

    Google Scholar 

  19. Pennec, X.: Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. J. Math. Imaging Vis. 25(1), 127 (2006)

    Article  MathSciNet  Google Scholar 

  20. Perozzi, B., Al-Rfou, R., Skiena, S.: Deepwalk: online learning of social representations. In: Proceedings of the 20th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), KDD 2014, pp. 701–710 (2014)

    Google Scholar 

  21. Said, S., Hajri, H., Bombrun, L., Vemuri, B.C.: Gaussian distributions on Riemannian symmetric spaces: Statistical learning with structured covariance matrices. IEEE Trans. Inf. Theory 64(2), 752–772 (2018)

    Article  MathSciNet  Google Scholar 

  22. Skovgaard, L.T.: A Riemannian geometry of the multivariate normal model. Scandinavian J. Stat., 211–223 (1984)

    Google Scholar 

  23. Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., Mei, Q.: Line: large-scale information network embedding. In: Proceedings of the 24th International Conference on World Wide Web, pp. 1067–1077 (2015)

    Google Scholar 

  24. Tang, J., Zhang, J., Yao, L., Li, J., Zhang, L., Su, Z.: Arnetminer: extraction and mining of academic social networks. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 990–998 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Science Sorbonne University, Lip6, 75005, Paris, France

    Thomas Gerald

  2. Institute of Research and Technology SystemX, 8 avenue de la Vauve, 91120, Palaiseau, France

    Hadi Zaatiti & Hatem Hajri

Authors
  1. Thomas Gerald
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hadi Zaatiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hatem Hajri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Zaatiti .

Editor information

Editors and Affiliations

  1. Thales Land & Air Systems, Technical Directorate, Thales, Limours, France

    Frédéric Barbaresco

  2. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

Rights and permissions

Reprints and permissions

Copyright information

© 2021 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

Gerald, T., Zaatiti, H., Hajri, H. (2021). A Practical Hands-on for Learning Graph Data Communities on Manifolds. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_21

Download citation

Publish with us

Policies and ethics

Search

Navigation