Abstract
Network embedding can effectively dig out potentially useful information and discover the relationships and rules which exist in the data, that has attracted increasing attention in many real-world applications. The goal of network embedding is to map high-dimensional and sparse networks into low-dimensional and dense vector representations. In this paper, we propose a network embedding method based on high-degree penalty and adaptive negative sampling (NEPS). First, we analyze the problem of imbalanced node training in random walk and propose an indicator base on high-degree penalty, which can control the random walk and avoid over-sampling high-degree neighbor node. Then, we propose a two-stage adaptive negative sampling strategy, which can dynamically obtain negative samples suitable for the current training according to the training stage to improve training effect. By comparing with seven well-known network embedding algorithms on eight real-world data sets, experiments show that the NEPS has good performance in node classification, network reconstruction and link prediction. The code is available at: https://github.com/Andrewsama/NEPS-master.
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Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M, et al. (2016) Tensorflow: a system for large-scale machine learning. In: 12th \(\{\)USENIX\(\}\) symposium on operating systems design and implementation (\(\{\)OSDI\(\}\) 16), pp 265–283
Adhikari B, Zhang Y, Ramakrishnan N, Prakash BA (2018) Sub2vec: Feature learning for subgraphs. In: Pacific-Asia conference on knowledge discovery and data mining, Springer, pp 170–182
Alanis-Lobato G, Mier P, Andrade-Navarro MA (2016) Efficient embedding of complex networks to hyperbolic space via their Laplacian. Sci Rep 6(1):1–10
Armandpour M, Ding P, Huang J, Hu X (2019) Robust negative sampling for network embedding. In: Proceedings of the AAAI conference on artificial intelligence 33:3191–3198
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6):1373–1396
Bu D, Zhao Y, Cai L, Xue H, Zhu X, Lu H, Zhang J, Sun S, Ling L, Zhang N et al (2003) Topological structure analysis of the protein-protein interaction network in budding yeast. Nucleic Acids Res 31(9):2443–2450
Cao S, Lu W, Xu Q (2015) 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
Cao S, Lu W, Xu Q (2016) Deep neural networks for learning graph representations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 30
Chang S, Han W, Tang J, Qi GJ, Aggarwal CC, Huang TS (2015) Heterogeneous network embedding via deep architectures. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp 119–128
Chen H, Perozzi B, Hu Y, Skiena S (2018) Harp: Hierarchical representation learning for networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 32
Cox MA, Cox TF (2008) Multidimensional scaling. In: Handbook of data visualization, Springer, pp 315–347
Dai Q, Li Q, Tang J, Wang D (2018) Adversarial network embedding. In: Proceedings of the AAAI conference on artificial intelligence, vol 32
Donahue J, Simonyan K (2019) Large scale adversarial representation learning. arXiv preprint arXiv:1907.02544
Dong Y, Chawla NV, Swami A (2017) metapath2vec: Scalable representation learning for heterogeneous networks. In: Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pp 135–144
Feng R, Yang Y, Hu W, Wu F, Zhang Y (2018) Representation learning for scale-free networks. In: Proceedings of the AAAI conference on artificial intelligence, vol 32
Gao H, Huang H (2018) Self-paced network embedding. In: Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining, pp 1406–1415
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
Hamilton WL, Ying R, Leskovec J (2017) Inductive representation learning on large graphs. In: Proceedings of the 31st international conference on neural information processing systems, pp 1025–1035
Hou Z, Cen Y, Dong Y, Zhang J, Tang J (2021) Automated unsupervised graph representation learning. IEEE Trans Knowl Data Eng 35:2285–2298
Hu B, Fang Y, Shi C (2019) Adversarial learning on heterogeneous information networks. In: Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pp 120–129
Huang X, Li J, Hu X (2017) Label informed attributed network embedding. In: Proceedings of the tenth ACM international conference on web search and data mining, pp 731–739
Kendall MG (1938) A new measure of rank correlation. Biometrika 30(1/2):81–93
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, Kleinberg J, Faloutsos C (2007) Graph evolution: Densification and shrinking diameters. ACM transactions on Knowledge Discovery from Data (TKDD) 1(1):2–es
Li AQ, Ahmed A, Ravi S, Smola AJ (2014) Reducing the sampling complexity of topic models. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 891–900
Lü L, Zhou T (2011) Link prediction in complex networks: a survey. Phys A: Stat Mech Appl 390(6):1150–1170
Mahoney M (2011) Large text compression benchmark
Mikolov T, Chen K, Corrado G, Dean J (2013a) Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781
Mikolov T, Sutskever I, Chen K, Corrado GS, Dean J (2013b) Distributed representations of words and phrases and their compositionality. In: Advances in neural information processing systems, pp 3111–3119
Narayanan A, Chandramohan M, Chen L, Liu Y, Saminathan S (2016) subgraph2vec: Learning distributed representations of rooted sub-graphs from large graphs. arXiv preprint arXiv:1606.08928
Newman ME (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104
Ou M, Cui P, Pei J, Zhang Z, Zhu W (2016) Asymmetric transitivity preserving graph embedding. In: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, pp 1105–1114
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
Perozzi B, Kulkarni V, Chen H, Skiena S (2017) Don’t walk, skip! online learning of multi-scale network embeddings. In: Proceedings of the 2017 IEEE/ACM international conference on advances in social networks analysis and mining 2017, pp 258–265
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
Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326
Rozemberczki B, Allen C, Sarkar R (2021) Multi-scale attributed node embedding. J Complex Netw cnab9(2):014
Shao J (2006) Mathematical statistics: exercises and solutions. Springer Science & Business Media
Shaw B, Jebara T (2009) Structure preserving embedding. In: Proceedings of the 26th annual international conference on machine learning, pp 937–944
Spearman C (1987) The proof and measurement of association between two things. Am J Psychol 100(3/4):441–471
Tang J, Qu M, Mei Q (2015a) Pte: Predictive text embedding through large-scale heterogeneous text networks. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1165–1174
Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015b) Line: large-scale information network embedding. In: Proceedings of the 24th international conference on world wide web, pp 1067–1077
Tenenbaum JB, De Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323
Veličković P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y (2017) Graph attention networks. arXiv preprint arXiv:1710.10903
Wang D, Cui P, Zhu W (2016) Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, pp 1225–1234
Wang J, Yu L, Zhang W, Gong Y, Xu Y, Wang B, Zhang P, Zhang D (2017) Irgan: a minimax game for unifying generative and discriminative information retrieval models. In: Proceedings of the 40th International ACM SIGIR conference on Research and Development in Information Retrieval, pp 515–524
Wang J, Huang P, Zhao H, Zhang Z, Zhao B, Lee DL (2018) Billion-scale commodity embedding for e-commerce recommendation in alibaba. In: Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining, pp 839–848
Wang X, Zhang Y, Shi C (2019) Hyperbolic heterogeneous information network embedding. In: Proceedings of the AAAI conference on artificial intelligence 33:5337–5344
Wang Z, Ye X, Wang C, Cui J, Yu P (2020) Network embedding with completely-imbalanced labels. IEEE Trans Knowl Data Eng 33:3634–3647
Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? arXiv preprint arXiv:1810.00826
Yang C, Liu Z, Zhao D, Sun M, Chang E (2015) Network representation learning with rich text information. In: Twenty-fourth international joint conference on artificial intelligence
Yang Z, Ding M, Zhou C, Yang H, Zhou J, Tang J (2020) Understanding negative sampling in graph representation learning. In: Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pp 1666–1676
Yin H, Benson AR, Leskovec J, Gleich DF (2017) Local higher-order graph clustering. In: Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pp 555–564
Zhang J, Shi X, Xie J, Ma H, King I, Yeung DY (2018) Gaan: Gated attention networks for learning on large and spatiotemporal graphs. arXiv preprint arXiv:1803.07294
Zhang J, Dong Y, Wang Y, Tang J, Ding M (2019) Prone: Fast and scalable network representation learning. IJCAI 19:4278–4284
Zhang W, Chen T, Wang J, Yu Y (2013) Optimizing top-n collaborative filtering via dynamic negative item sampling. In: Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval, pp 785–788
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This work is supported by the National Natural Science Foundation of China (No. 61773448 and 62176236.)
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Ma, GF., Yang, XH., Ye, W. et al. Network embedding based on high-degree penalty and adaptive negative sampling. Data Min Knowl Disc 38, 597–622 (2024). https://doi.org/10.1007/s10618-023-00973-1
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DOI: https://doi.org/10.1007/s10618-023-00973-1