Improved Deep Embeddings for Inferencing with Multi-Layered Networks

Inferencing with network data necessitates the mapping of its nodes into a vector space, where the relationships are preserved. However, with multi-layered networks, where multiple types of relationships exist for the same set of nodes, it is crucial to exploit the information shared between layers, in addition to the distinct aspects of each layer. In this paper, we propose a novel approach that first obtains node embeddings in all layers jointly via DeepWalk on a \textit{supra} graph, which allows interactions between layers, and then fine-tunes the embeddings to encourage cohesive structure in the latent space. With empirical studies in node classification, link prediction and multi-layered community detection, we show that the proposed approach outperforms existing single- and multi-layered network embedding algorithms on several benchmarks. In addition to effectively scaling to a large number of layers (tested up to $37$), our approach consistently produces highly modular community structure, even when compared to methods that directly optimize for the modularity function.

[1]  O. Bagasra,et al.  Proceedings of the National Academy of Sciences , 1914, Science.

[2]  Steven Skiena,et al.  DeepWalk: online learning of social representations , 2014, KDD.

[3]  Srinivasan Parthasarathy,et al.  Proceedings of the 2010 SIAM International Conference on Data Mining , 2010 .

[4]  Massimiliano Zanin,et al.  Emergence of network features from multiplexity , 2012, Scientific Reports.

[5]  Prakash Ishwar,et al.  Node Embedding via Word Embedding for Network Community Discovery , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[6]  Jieping Ye,et al.  Discriminative K-means for Clustering , 2007, NIPS.

[7]  Alfred O. Hero,et al.  Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms , 2017, IEEE Transactions on Signal and Information Processing over Networks.

[8]  Boleslaw K. Szymanski,et al.  Community Detection via Maximization of Modularity and Its Variants , 2014, IEEE Transactions on Computational Social Systems.

[9]  Pradeep Ravikumar,et al.  Collaborative Filtering with Graph Information: Consistency and Scalable Methods , 2015, NIPS.

[11]  J. C. Schlimmer,et al.  Concept acquisition through representational adjustment , 1987 .

[12]  Ian Davidson,et al.  Proceedings of the 2012 SIAM International Conference on Data Mining , 2012 .

[13]  PentlandAlex,et al.  Reality mining: sensing complex social systems , 2006 .

[14]  Jeffrey Dean,et al.  Distributed Representations of Words and Phrases and their Compositionality , 2013, NIPS.

[15]  Ali Farhadi,et al.  Unsupervised Deep Embedding for Clustering Analysis , 2015, ICML.

[16]  Xiaochun Cao,et al.  Modularity Based Community Detection with Deep Learning , 2016, IJCAI.

[17]  Jure Leskovec,et al.  node2vec: Scalable Feature Learning for Networks , 2016, KDD.

[18]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Michael Breakspear,et al.  Graph analysis of the human connectome: Promise, progress, and pitfalls , 2013, NeuroImage.

[20]  M. Elter,et al.  The prediction of breast cancer biopsy outcomes using two CAD approaches that both emphasize an intelligible decision process. , 2007, Medical physics.

[21]  Huan Liu,et al.  Multi-Layered Network Embedding , 2018, SDM.

[22]  E. Lazega Introduction : Collegial Phenomenon : The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership , 2001 .

[23]  Mingzhe Wang,et al.  LINE: Large-scale Information Network Embedding , 2015, WWW.

[24]  D. Chklovskii,et al.  Wiring optimization can relate neuronal structure and function. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .

[26]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Alex Pentland,et al.  Reality mining: sensing complex social systems , 2006, Personal and Ubiquitous Computing.

[28]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.