Abstract
Multiplex networks convey more valuable information than single-layer networks; thus, performing the community detection task involving these networks has become a subject of extensive research on the exploration of latent community structures. The non-negative matrix factorization (NMF) algorithm has proven successful in community detection scenarios by offering good interpretations of community structures. However, directly obtaining consensus community assignments using the traditional NMF algorithm poses a challenge due to the presence of complex structures spanning across different layers in the multiplex network. In this paper, we propose a novel algorithm called Deep Structure-Preserving Non-negative Matrix Factorization (DSP-NMF) to perform community detection in multiplex networks. Specifically, DSP-NMF constructs a deep autoencoder-like NMF model to generate meaningful network embeddings that are represented by multiple basis matrices and reconstructed by corresponding transposed basis matrices. By integrating the similarity relationships of nodes into the proposed DSP-NMF algorithm, the corresponding Laplacian matrices in each network layer are regularized to preserve the community structure during the learning process. Simultaneously, a consensus network embedding can be learned to obtain the final community partition. In this manner, the proposed DSP-NMF algorithm not only uncovers robust community structures in multiplex networks but also maintains the coherence between layers without losing complementary features. The experimental results obtained on five multiplex network datasets show that our proposed DSP-NMF algorithm outperforms other competitive methods in community detection tasks involving multiplex networks.
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All the experiments are conducted utilizing publicly accessible datasets which are available in http://mlg.ucd.ie/aggregation.
References
Kumar S, Singhla L, Jindal K, Grover K, Panda B (2021) Im-elpr: Influence maximization in social networks using label propagation based community structure. Applied Intell 51:7647–7665
Dey A, Kumar BR, Das B, Ghoshal AK (2023) Outlier detection in social networks leveraging community structure. Inf Sci 634:578–586
Doluca O, Oğuz K (2021) Apal: Adjacency propagation algorithm for overlapping community detection in biological networks. Inf Sci 579:574–590
Chatterjee S, Sanjeev B (2023) Community detection in epstein-barr virus associated carcinomas and role of tyrosine kinase in etiological mechanisms for oncogenesis. Microbial Pathogen 180:106115
Samie M E, Behbood E, Hamzeh A (2023) Local community detection based on influence maximization in dynamic networks. Applied Intell 1–25
Baltsou G, Tsichlas K, Vakali A (2022) Local community detection with hints. Applied Intell 52:9599–9620
Chagas GO, Lorena LAN, dos Santos RDC (2022) A hybrid heuristic for overlapping community detection through the conductance minimization. Physica A: Stat Mech Appl 592:126887
Reihanian A, Feizi-Derakhshi M-R, Aghdasi HS (2023) An enhanced multi-objective biogeography-based optimization for overlapping community detection in social networks with node attributes. Inf Sci 622:903–929
Karimi F, Lotfi S, Izadkhah H (2020) Multiplex community detection in complex networks using an evolutionary approach. Exp Syst Appl 146:113184
Guo K et al (2022) Network representation learning based on community-aware and adaptive random walk for overlapping community detection. Applied Intell 52:9919–9937
Xu X-L, Xiao Y-Y, Yang X-H, Wang L, Zhou Y-B (2022) Attributed network community detection based on network embedding and parameter-free clustering. Applied Intell 52:8073–8086
Hao J, Zhu W (2023) Deep graph clustering with enhanced feature representations for community detection. Applied Intell 53:1336–1349
Yue Y, Wang G, Hu J, Li Y (2023) An improved label propagation algorithm based on community core node and label importance for community detection in sparse network. Applied Intell 53:17935–1795
Laassem B, Idarrou A, Boujlaleb L et al (2022) Label propagation algorithm for community detection based on coulomb’s law. Physica A: Stat Mech Appl 593:126881
Attal J-P, Malek M, Zolghadri M (2021) Overlapping community detection using core label propagation algorithm and belonging functions. Applied Intell 51:8067–8087
Boroujeni RJ, Soleimani S (2022) The role of influential nodes and their influence domain in community detection: An approximate method for maximizing modularity. Exp Syst Appl 202:117452
Salha-Galvan G, Lutzeyer JF, Dasoulas G, Hennequin R, Vazirgiannis M (2022) Modularity-aware graph autoencoders for joint community detection and link prediction. Neural Netw 153:474–495
Zhu W, Chen C, Peng B (2023) Unified robust network embedding framework for community detection via extreme adversarial attacks. Inf Sci 643:119200
Zhu J et al (2021) Community detection in graph: an embedding method. IEEE Trans Netw Sci Eng 9(2):689–702
Tagarelli A, Amelio A, Gullo F (2017) Ensemble-based community detection in multilayer networks. Data Mining and Knowl Disc 31:1506–1543
Amini A, Paez M, Lin L (2022) Hierarchical stochastic block model for community detection in multiplex networks. Bayesian Anal 1(1):1–27
Huang Y, Panahi A, Krim H, Dai L (2020) Community detection and improved detectability in multiplex networks. IEEE Trans Netw Sci Eng 7(3):1697–1709
Interdonato R, Tagarelli A, Ienco D, Sallaberry A, Poncelet P (2017) Local community detection in multilayer networks. Data Mining and Knowl Disc 31:1444–1479
Huang L, Wang C-D, Chao H-Y (2019) Higher-order multi-layer community detection. Proceed AAAI Conf Art Intell 33(01):9945–9946
Psorakis I, Roberts S, Ebden M, Sheldon B (2011) Overlapping community detection using bayesian non-negative matrix factorization. Phys Rev E 83(6):066114
Ye F, Chen C, Zheng Z (2018) Deep autoencoder-like nonnegative matrix factorization for community detection. Proceed 27th ACM Int Conf Inf Knowl Manage 1393–1402
Luo X, Liu Z, Jin L, Zhou Y, Zhou M (2021) Symmetric nonnegative matrix factorization-based community detection models and their convergence analysis. IEEE Trans Neural Netw Learn Syst 33(3):1203–1215
Berahmand K, Mohammadi M, Saberi-Movahed F, Li Y, Xu Y (2022) Graph regularized nonnegative matrix factorization for community detection in attributed networks. IEEE Trans Netw Sci Eng 10(1):372–385
Ma X, Dong D, Wang Q (2018) Community detection in multi-layer networks using joint nonnegative matrix factorization. IEEE Trans Knowl Data Eng 31(2):273–286
Kamuhanda D, Wang M, He K (2020) Sparse nonnegative matrix factorization for multiple-local-community detection. IEEE Trans Comput Social Syst 7(5):1220–1233
Yang L, Zhang L, Pan Z, Hu G, Zhang Y (2018) Community detection based on co-regularized nonnegative matrix tri-factorization in multi-view social networks. 2018 IEEE Int Conf Big Data and Smart Comput (BigComp) 98–105
Liu J, Wang C, Gao J, Han, J (2013) Multi-view clustering via joint nonnegative matrix factorization. Proceed 2013 SIAM Int Conf Data Mining 252–260
Lee D, Seung H S (2000) Algorithms for non-negative matrix factorization. Adv Neural Inf Process Syst 13
Guo Z, Zhang S (2020) Sparse deep nonnegative matrix factorization. Big Data Mining and Anal 3(1):13–28
Luong K, Nayak R, Balasubramaniam T, Bashar MA (2022) Multi-layer manifold learning for deep non-negative matrix factorization-based multi-view clustering. Pattern Recogn 131:108815
Liu H, Wu Z, Li X, Cai D, Huang TS (2011) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299–1311
Greene D, Cunningham, P (2013) Producing a unified graph representation from multiple social network views. Proceed 5th annual ACM Web Sci Conf 118–121
He X, Kan M-Y, Xie P, Chen X (2014) Comment-based multi-view clustering of web 2.0 items. Proceed 23rd Int Conf World Wide Web 771–782
Ma J, Zhang Y, Zhang L (2021) Discriminative subspace matrix factorization for multiview data clustering. Pattern Recogn 111:107676
Acknowledgements
This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LY24F030005, and the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No.2022YW40.
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Qinli Zhou: Methodology, Software, Writing.Wenjie Zhu: Writing, Conceptualization, Supervision, Funding acquisition.Hao Chen: Coding, Experiments, Validation.Bo Peng: Conceptualization.
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Zhou, Q., Zhu, W., Chen, H. et al. Community detection in multiplex networks by deep structure-preserving non-negative matrix factorization. Appl Intell 55, 26 (2025). https://doi.org/10.1007/s10489-024-05870-8
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DOI: https://doi.org/10.1007/s10489-024-05870-8