Abstract
Higher-order clustering is a hot research topic which searches higher-order organization of networks at the level of small subgraphs (motifs). However, in bipartite networks, there are no higher-order structures such as triangles, quadrangles or cliques. In this paper, we study the problem of identifying clusters with motif of dense butterflies in bipartite networks. First, we propose a framework of higher-order clustering algorithm by optimizing motif conductance. Then, we prove that the problem can be transformed to computing the conductance of a weight graph constructed by butterflies, so it can be solved by eigenvalue decomposition techniques. Next, we analyse the computational complexity of the proposed algorithms and find that it is indeed efficient to cluster motif of butterflies in bipartite networks. Finally, numerous experiments prove the effectiveness, efficiency and scalability of the proposed algorithm.
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References
Alon, U.: Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8(6), 450–461 (2007)
Benson, A.R., Gleich, D.F., Leskovec, J.: Higher-order organization of complex networks. Science 353(6295), 163–166 (2016)
Colfen, H., Mann, S.: Higher-order organization by mesoscale self-assembly and transformation of hybrid nanostructures. Angew. Chem. 42(21), 2350–2365 (2003)
Cooper, D.M., Crossthwaite, A.J.: Higher-order organization and regulation of adenylyl cyclases. Trends Pharmacol. Sci. 27(8), 426–431 (2006)
Farid, H.: Detecting hidden messages using higher-order statistical models. In: IEEE IPIP, vol. 2, p. II (2002)
Hou, Y., Whang, J.J., Gleich, D.F., Dhillon, I.S.: Non-exhaustive, overlapping clustering via low-rank semidefinite programming, pp. 427–436 (2015)
Jain, S., Govindu, V.M.: Efficient higher-order clustering on the grassmann manifold. In: ICCV 2013, USA, pp. 3511–3518. IEEE (2013)
Mangan, S., Alon, U.: Structure and function of the feed-forward loop network motif. Proc. Natl. Acad. Sci. U.S.A. 100(21), 11980–11985 (2003)
Milo, R., Shenorr, S.S., Itzkovitz, S., Kashtan, N., Chklovskii, D.B., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)
Saneimehri, S., Sariyuce, A.E., Tirthapura, S.: Butterfly counting in bipartite networks, pp. 2150–2159 (2018)
Schaub, M.T., Trefois, M., Van Dooren, P., Delvenne, J.: Sparse matrix factorizations for fast linear solvers with application to laplacian systems. SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017)
Seshadhri, C., Pinar, A., Kolda, T.G.: Wedge sampling for computing clustering coefficients and triangle counts on large graphs. Stat. Anal. Data Mining 7(4), 294–307 (2014)
Smith, K.: On neighbourhood degree sequences of complex networks. Sci. Rep. 9(1), 8340 (2019)
Wang, K., Lin, X., Qin, L., Zhang, W., Zhang, Y.: Vertex priority based butterfly counting for large-scale bipartite networks. Proc. VLDB Endow. 12(10), 1139–1152 (2019). https://doi.org/10.14778/3339490.3339497
Yang, J., Leskovec, J.: Overlapping communities explain core-periphery organization of networks. Proc. IEEE 102(12), 1892–1902 (2014)
Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. Knowl. Inf. Syst. 42(1), 181–213 (2013). https://doi.org/10.1007/s10115-013-0693-z
Yaveroglu, O.N., et al.: Revealing the hidden language of complex networks. Sci. Rep. 4(1), 4547–4547 (2015)
Yin, H., Benson, A.R., Leskovec, J.: Higher-order clustering in networks. Phys. Rev. E 97(5), 052306 (2018)
Yin, H., Benson, A.R., Leskovec, J., Gleich, D.F.: Local higher-order graph clustering. In: KDD 2017, pp. 555–564. ACM, New York (2017)
Acknowledgements
This research was supported by the National Key Research and Development Program of China (No. 2018YFB1004402).
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Zheng, Y., Qin, H., Zheng, J., Jin, F., Li, RH. (2020). Butterfly-Based Higher-Order Clustering on Bipartite Networks. In: Li, G., Shen, H., Yuan, Y., Wang, X., Liu, H., Zhao, X. (eds) Knowledge Science, Engineering and Management. KSEM 2020. Lecture Notes in Computer Science(), vol 12274. Springer, Cham. https://doi.org/10.1007/978-3-030-55130-8_42
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DOI: https://doi.org/10.1007/978-3-030-55130-8_42
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