Skip to main content
SpringerLink
Log in

Topological Data Analysis Approach for Weighted Networks Embedding

  • Conference paper
  • First Online:
Networks in the Global World V (NetGloW 2020)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 181))

Included in the following conference series:

  • 302 Accesses

Abstract

Efficient node representation for weighted networks is an important problem for many domains in real-world network analysis. Network exploration usually comes down to description of some structural features which give information about network properties in general, but not about specific nodes. Whereas information about node profile is very important in any network with attributed nodes. Recently, the network embedding approach has emerged, which could be formalized as mapping each node in the undirected and weighted graph into a d-dimensional vector that captures its structural properties. The output representation can be used as the input for a variety of data analysis tasks as well as for individual node analysis. We suggested using an additional approach for node description based on the topological structure of the network. Some interesting topological features of such data can be revealed with topological data analysis. Each node in this case may be described in terms of participation in topological cavities of different sizes and their persistence. Such representation was used as an alternative node description and demonstrated their efficiency in the community detection task. In order to test the approach, we used a weighted stochastic block model with different parameters as a network generative process.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Similar content being viewed by others

References

  1. Newman, M.E.J.: Analysis of weighted networks. Phys. Rev. E 70, 056131 (2004)

    Article  Google Scholar 

  2. Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, pp. 631–640 (2010)

    Google Scholar 

  3. Aicher, C., Jacobs, A.Z., Clauset, A.: Learning latent block structure in weighted networks. J. Complex Networks 3(2), 221–248 (2015)

    Article  MathSciNet  Google Scholar 

  4. Cui, P., Wang, X., Pei, J., Zhu, W.: A survey on network embedding. IEEE Trans. Knowl. Data Eng. 31(5), 833–852 (2018)

    Article  Google Scholar 

  5. Giusti, C., Ghrist, R., Bassett, D.S.: Two’s company, three (or more) is a simplex. J. Comput. Neurosci. 41(1), 1–14 (2016)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  7. Mikolov, T., Chen, K., Corrado, G., Dean, J.: Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781 (2013)

  8. Sizemore, A.E., Giusti, C., Kahn, A., Vettel, J.M., Betzel, R.F., Bassett, D.S.: Cliques and cavities in the human connectome. J. Comput. Neurosci. 44(1), 115–145 (2018)

    Article  MathSciNet  Google Scholar 

  9. Wang, S., Aggarwal, C., Tang, J., Liu, H.: Attributed signed network embedding. In: Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp. 137–146 (2017)

    Google Scholar 

  10. Faskowitz, J., Yan, X., Zuo, X.N., Sporns, O.: Weighted stochastic block models of the human connectome across the life span. Sci. Rep. 8(1), 1–16 (2018)

    Article  Google Scholar 

  11. Karrer, B., Newman, M.E.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83(1), 016107 (2011)

    Article  MathSciNet  Google Scholar 

  12. Giusti, C., Pastalkova, E., Curto, C., Itskov, V.: Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Natl. Acad. Sci. 112(44), 13455–13460 (2015)

    Article  MathSciNet  Google Scholar 

  13. Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61–75 (2008)

    Article  MathSciNet  Google Scholar 

  14. Knyazeva, I., Poyda, A., Orlov, V., Verkhlyutov, V., Makarenko, N., Kozlov, S., Velichkovsky, B., Ushakov, V.: Resting state dynamic functional connectivity: network topology analysis. Biol. Insp. Cognit. Archit. 23, 43–53 (2018)

    Google Scholar 

  15. Rabadán, R., Blumberg, A.J.: Topological Data Analysis for Genomics and Evolution: Topology in Biology. Cambridge University Press, Cambridge (2019)

    Book  Google Scholar 

  16. Zomorodian, A., Carlsson, G.: Computing persistent homology. Discr. Comput. Geom. 33(2), 249–274 (2005)

    Article  MathSciNet  Google Scholar 

  17. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. In: Proceedings 41st Annual Symposium on Foundations of Computer Science, pp. 454–463. IEEE (2000)

    Google Scholar 

  18. Henselman, G., Ghrist, R.: Matroid Filtrations and Computational Persistent Homology. ArXiv e-prints, June 2016

    Google Scholar 

  19. Edelsbrunner, H., Harer, J.: Persistent homology-a survey. Contemp. math. 453, 257–282 (2008)

    Article  MathSciNet  Google Scholar 

  20. Wasserman, L.: Topological data analysis. Ann. Rev. Stat. Appl. 5(1), 501–532 (2018)

    Article  MathSciNet  Google Scholar 

  21. Makarenko, I., Shukurov, A., Henderson, R., Rodrigues, L.F., Bushby, P., Fletcher, A.: Topological signatures of interstellar magnetic fields–i. betti numbers and persistence diagrams. Monthly Not. Roy. Astronom. Soc. 475(2), 1843–1858 (2018)

    Google Scholar 

  22. Ahmed, A., Shervashidze, N., Narayanamurthy, S., Josifovski, V., Smola, A.J.: Distributed large-scale natural graph factorization. In: Proceedings of the 22nd International Conference on World Wide Web, pp. 37–48 (2013)

    Google Scholar 

  23. Cao, S., Lu, W., Xu, Q.: Grarep: Learning graph representations with global structural information. In: Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, pp. 891–900 (2015)

    Google Scholar 

  24. Ou, M., Cui, P., Pei, J., Zhang, Z., Zhu, W.: Asymmetric transitivity preserving graph embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1105–1114 (2016)

    Google Scholar 

  25. Wang, X., Cui, P., Wang, J., Pei, J., Zhu, W., Yang, S.: Community preserving network embedding. In: Thirty-first AAAI Conference on Artificial Intelligence (2017)

    Google Scholar 

  26. Wang, D., Cui, P., Zhu, W.: Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225–1234 (2016)

    Google Scholar 

  27. Cao, S., Lu, W., Xu, Q.: Deep neural networks for learning graph representations. In: Thirtieth AAAI Conference on Artificial Intelligence (2016)

    Google Scholar 

  28. Dai, Q., Li, Q., Tang, J., Wang, D.: Adversarial network embedding. In: Thirty-Second AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  29. Shen, X., Dai, Q., Chung, F.l., Lu, W., Choi, K.S.: Adversarial deep network embedding for cross-network node classification. arXiv preprint arXiv:2002.07366 (2020)

  30. Grover, A., Leskovec, J.: node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855–864 (2016)

    Google Scholar 

  31. Perozzi, B., Kulkarni, V., Skiena, S.: Walklets: Multiscale graph embeddings for interpretable network classification. arXiv preprint arXiv:1605.02115 (2016)

  32. Cho, H., Berger, B., Peng, J.: Diffusion component analysis: unraveling functional topology in biological networks. In: International Conference on Research in Computational Molecular Biology, pp. 62–64. Springer (2015)

    Google Scholar 

  33. Palumbo, E., Rizzo, G., Troncy, R., Baralis, E., Osella, M., Ferro, E.: Knowledge graph embeddings with node2vec for item recommendation. In: European Semantic Web Conference, pp. 117–120. Springer (2018)

    Google Scholar 

  34. Peng, J., Guan, J., Shang, X.: Predicting Parkinson’s disease genes based on node2vec and autoencoder. Front. Genet. 10 (2019)

    Google Scholar 

  35. Hu, F., Liu, J., Li, L., Liang, J.: Community detection in complex networks using node2vec with spectral clustering. Physica A: Stat. Mech. Appl. 123633 (2019)

    Google Scholar 

  36. McInnes, L., Healy, J., Melville, J.: Umap: uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426 (2018)

Download references

Acknowledgments

The reported study was funded by Russian Foundation for Basic Research (RFBR), project number 19-07-00337 and by the Institute of Information and Computational Technologies (Grant AR05134227, Kazakhstan).

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    Irina Knyazeva & Olga Talalaeva

  2. Institute of Information and Computational Technologies, Almaty, Kazakhstan

    Irina Knyazeva

Authors
  1. Irina Knyazeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olga Talalaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina Knyazeva .

Editor information

Editors and Affiliations

  1. St. Petersburg University, Centre for German and European Studies, St. Petersburg, Russia

    Artem Antonyuk

  2. St. Petersburg University, Centre for German and European Studies, St. Petersburg, Russia

    Nikita Basov

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and 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

Knyazeva, I., Talalaeva, O. (2021). Topological Data Analysis Approach for Weighted Networks Embedding. In: Antonyuk, A., Basov, N. (eds) Networks in the Global World V. NetGloW 2020. Lecture Notes in Networks and Systems, vol 181. Springer, Cham. https://doi.org/10.1007/978-3-030-64877-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation