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Structural iterative lexicographic autoencoded node representation

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Abstract

Graph representation learning approaches are effective to automatically extract relevant hidden features from graphs. Previous related work in graph representation learning can be divided into connectivity and structural-based. Connectivity-based representation learning methods work on the assumption that neighboring nodes should have similar representations. While structural node representation learning assumes that nodes with the same structure should have identical representations; structural representation learning is suitable for node classification and regression tasks. Possible drawbacks of current structural node representation learning approaches are prohibitive execution time complexity and the inability to entirely preserve structural information. In this work, we propose SILA, a Structural Iterative Lexicographic Autoencoded approach for node representation learning. This new iterative approach presents a small number of iterations, and compared with the method presented in the literature, shows better performance in preserving structural information for both classification and regression tasks.

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  1. The code will be made publicly available after paper acceptance.

References

  • Bengio Y, Courville A, Vincent P (2013) Representation learning: a review and new perspectives. IEEE Trans Pattern Anal Mach Intell 35(8):1798–1828

    Article  Google Scholar 

  • Cook DJ, Holder LB (2006) Mining graph data. Wiley, New York

    Book  MATH  Google Scholar 

  • Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    Article  MATH  Google Scholar 

  • Donnat C, Zitnik M, Hallac D, Leskovec J (2018) Learning structural node embeddings via diffusion wavelets. In: Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1320–1329. ACM

  • Geurts P, Ernst D, Wehenkel L (2006) Extremely randomized trees. Mach Learn 63(1):3–42

    Article  MATH  Google Scholar 

  • Gilmer J, Schoenholz SS, Riley PF, Vinyals O, Dahl GE (2017) Neural message passing for quantum chemistry. In: International conference on machine learning, pp 1263–1272. PMLR

  • Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

    MATH  Google Scholar 

  • Grover A, Leskovec J (2016) node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, pp 855–864. ACM

  • Hamilton W, Ying Z, Leskovec J (2017) Inductive representation learning on large graphs. In: Advances in neural information processing systems, pp 1024–1034

  • Harzheim E (2006) Ordered sets, vol 7. Springer, New York

    MATH  Google Scholar 

  • Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  Google Scholar 

  • Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980

  • Kipf TN, Welling M (2016) Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907

  • Leskovec J, Krevl A (2014) Snap datasets: stanford large network dataset collection

  • Lou Z, You J, Wen C, Canedo A, Leskovec J, et al (2020) Neural subgraph matching. arXiv preprint arXiv:2007.03092

  • Meng Q, Catchpoole D, Skillicom D, Kennedy PJ (2017) Relational autoencoder for feature extraction. In: 2017 International joint conference on neural networks (IJCNN), pp 364–371. IEEE

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

  • Mikolov T, Sutskever I, Chen K, Corrado GS, Dean J (2013) Distributed representations of words and phrases and their compositionality. In: Advances in neural information processing systems, pp 3111–3119

  • Pan S, Hu R, Long G, Jiang J, Yao L, Zhang C (2018) Adversarially regularized graph autoencoder for graph embedding. arXiv preprint arXiv:1802.04407

  • Pan Y, Li DH, Liu JG, Liang JZ (2010) Detecting community structure in complex networks via node similarity. Physica A 389(14):2849–2857

    Article  Google Scholar 

  • Pedarsani P, Grossglauser M (2011) On the privacy of anonymized networks. In: Proceedings of the 17th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1235–1243. ACM

  • Perozzi B, Al-Rfou R, Skiena S (2014) Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 701–710. ACM

  • Ribeiro LF, Saverese PH, Figueiredo DR (2017) struc2vec: Learning node representations from structural identity. In: Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pp 385–394. ACM

  • Shervashidze N, Schweitzer P, Van Leeuwen EJ, Mehlhorn K, Borgwardt KM (2011) Weisfeiler-Lehman graph kernels. J Mach Learn Res 12(9):2539–2561

    MathSciNet  MATH  Google Scholar 

  • Sutskever I, Vinyals O, Le QV (2014) Sequence to sequence learning with neural networks. Adv Neural Inf Process Syst 2:3104–3112

    Google Scholar 

  • Symeonidis P, Tiakas E, Manolopoulos Y (2010) Transitive node similarity for link prediction in social networks with positive and negative links. In: Proceedings of the fourth ACM conference on Recommender systems, pp 183–190. ACM

  • Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015) Line: large-scale information network embedding. In: Proceedings of the 24th international conference on world wide web conferences steering committee, pp 1067–1077

  • Tsitsulin A, Mottin D, Karras P, Müller E (2018) Verse. Proceedings of the 2018 world wide web conference on world wide web—WWW ’18. https://doi.org/10.1145/3178876.3186120

  • Tu K, Cui P, Wang X, Yu PS, Zhu W (2018) Deep recursive network embedding with regular equivalence. In: Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery and data mining, pp 2357–2366

  • Veličković P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y (2017) Graph attention networks. arXiv preprint arXiv:1710.10903

  • Velickovic P, Fedus W, Hamilton WL, Liò P, Bengio Y, Hjelm RD (2019) Deep graph infomax. ICLR (Poster) 2(3):4

    Google Scholar 

  • Weisfeiler B, Leman A (1968) The reduction of a graph to canonical form and the algebgra which appears therein. NTI, Series 2

  • Wold S, Esbensen K, Geladi P (1987) Principal component analysis. Chemom Intell Lab Syst 2(1–3):37–52

    Article  Google Scholar 

  • Wu Z, Pan S, Chen F, Long G, Zhang C, Philip SY (2020) A comprehensive survey on graph neural networks. IEEE Trans Neural Netw Learn Syst 32:4–24

    Article  MathSciNet  Google Scholar 

  • Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? arXiv preprint arXiv:1810.00826

  • Yin Y, Wei Z (2019) Scalable graph embeddings via sparse transpose proximities. CoRR arXiv:1905.07245

  • Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33(4):452–473

    Article  Google Scholar 

  • Zhang D, Yin J, Zhu X, Zhang C (2018) Network representation learning: a survey. IEEE Trans Big Data

  • Zhang Z, Cui P, Wang X, Pei J, Yao X, Zhu W (2018) Arbitrary-order proximity preserved network embedding. In: Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery and data mining, KDD ’18, pp 2778–2786. Association for computing machinery, New York, USA. https://doi.org/10.1145/3219819.3219969

  • Zhou J, Cui G, Zhang Z, Yang C, Liu Z, Wang L, Li C, Sun M (2018) Graph neural networks: a review of methods and applications. arXiv preprint arXiv:1812.08434

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Acknowledgements

This research was funded by a National Centers of Academic Excellence in Cybersecurity grant (H98230-22-1-0300), which is part of the National Security Agency.

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  1. Computer Science Department, Boise State University, 777 W Main St, Boise, ID, 83702, USA

    Mikel Joaristi & Edoardo Serra

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  1. Mikel Joaristi
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  2. Edoardo Serra
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Correspondence to Edoardo Serra.

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Responsible editor: B. Aditya Prakash.

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Joaristi, M., Serra, E. Structural iterative lexicographic autoencoded node representation. Data Min Knowl Disc 37, 289–317 (2023). https://doi.org/10.1007/s10618-022-00880-x

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