Lower order information preserved network embedding based on non-negative matrix decomposition

Abstract Network embedding has been successfully used for a variety of tasks, e.g., node clustering, community detection, link prediction and evolution analysis on complex networks. For a given network, embedding methods are usually designed based on first-order proximity, second-order proximity, community constraints, etc. However, they are incapable of capturing the structural similarity of nodes. The bridge nodes with small proximity and located in different communities, should be similar in embedding space since they have the same surrounding structure. In this paper, these structural features are referred to as lower-order information, which could reveal and modify the structural similarity of nodes in the embedding space. Specifically, we propose to construct the feature matrix with the lower-order information of the network. In order to effectively fuse the structural features of nodes into embedding space, an intuitive, interpretable and feasible method named LONE-NMF is proposed, which adopts the representation learning framework based on non-negative matrix factorization. It can effectively learn the representation vectors of nodes in the network via preserving the proximity and lower-order information. Moreover, an optimization algorithm is designed for LONE-NMF. Extensive experiments based on clustering and link prediction show that the proposed method achieves significant performance improvement comparing with some baselines. Finally, we validate the principle and advantage of LONE-NMF through a case study.

[1]  Ruoming Jin,et al.  Axiomatic ranking of network role similarity , 2011, KDD.

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

[3]  Lise Getoor,et al.  Collective Classification in Network Data , 2008, AI Mag..

[4]  Ludovic Denoyer,et al.  Temporal link prediction by integrating content and structure information , 2011, CIKM '11.

[5]  Ling Chen,et al.  Link prediction based on non-negative matrix factorization , 2017, PloS one.

[6]  Christos Faloutsos,et al.  It's who you know: graph mining using recursive structural features , 2011, KDD.

[7]  David Liben-Nowell,et al.  The link-prediction problem for social networks , 2007 .

[8]  Xueqi Cheng,et al.  A Non-negative Symmetric Encoder-Decoder Approach for Community Detection , 2017, CIKM.

[9]  Yu Wang,et al.  Graph regularized nonnegative matrix factorization for temporal link prediction in dynamic networks , 2018 .

[10]  Fei Wang,et al.  Community discovery using nonnegative matrix factorization , 2011, Data Mining and Knowledge Discovery.

[11]  D. Hunter,et al.  A Tutorial on MM Algorithms , 2004 .

[12]  Diogo M. Camacho,et al.  Next-Generation Machine Learning for Biological Networks , 2018, Cell.

[13]  Zhiyuan Liu,et al.  Fast Network Embedding Enhancement via High Order Proximity Approximation , 2017, IJCAI.

[14]  Chris H. Q. Ding,et al.  On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering , 2005, SDM.

[15]  Ryan A. Rossi,et al.  Role-Based Graph Embeddings , 2020, IEEE Transactions on Knowledge and Data Engineering.

[16]  Ryan A. Rossi,et al.  Role Discovery in Networks , 2014, IEEE Transactions on Knowledge and Data Engineering.

[17]  Xuewei Li,et al.  Semi-supervised Community Detection Framework Based on Non-negative Factorization Using Individual Labels , 2015, ICSI.

[18]  Matjaz Perc,et al.  Inheritance patterns in citation networks reveal scientific memes , 2014, ArXiv.

[19]  Bin Li,et al.  DeepEye: Link prediction in dynamic networks based on non-negative matrix factorization , 2018, Big Data Min. Anal..

[20]  Xing Xie,et al.  High-order Proximity Preserving Information Network Hashing , 2018, KDD.

[21]  Max Welling,et al.  Variational Graph Auto-Encoders , 2016, ArXiv.

[22]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, Knowledge and Information Systems.

[23]  Jian Pei,et al.  Arbitrary-Order Proximity Preserved Network Embedding , 2018, KDD.

[24]  Ivan Herman,et al.  Graph Visualization and Navigation in Information Visualization: A Survey , 2000, IEEE Trans. Vis. Comput. Graph..

[25]  Fanghua Ye,et al.  Deep Autoencoder-like Nonnegative Matrix Factorization for Community Detection , 2018, CIKM.

[26]  Jian Li,et al.  Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec , 2017, WSDM.

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

[28]  Qiongkai Xu,et al.  GraRep: Learning Graph Representations with Global Structural Information , 2015, CIKM.

[29]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[30]  Makarand Hastak,et al.  Social network analysis: Characteristics of online social networks after a disaster , 2018, Int. J. Inf. Manag..

[31]  Jian Pei,et al.  Asymmetric Transitivity Preserving Graph Embedding , 2016, KDD.

[32]  Danai Koutra,et al.  RolX: structural role extraction & mining in large graphs , 2012, KDD.

[33]  Jingyi Wang,et al.  Graph regularization weighted nonnegative matrix factorization for link prediction in weighted complex network , 2019, Neurocomputing.

[34]  Hong Jin,et al.  Graph regularized nonnegative matrix tri-factorization for overlapping community detection , 2019, Physica A: Statistical Mechanics and its Applications.

[35]  Haiyuan Yu,et al.  Detecting overlapping protein complexes in protein-protein interaction networks , 2012, Nature Methods.

[36]  Hongtao Lu,et al.  Adaptive Overlapping Community Detection with Bayesian NonNegative Matrix Factorization , 2017, DASFAA.

[37]  Jian Pei,et al.  Community Preserving Network Embedding , 2017, AAAI.

[38]  Wenwu Zhu,et al.  Structural Deep Network Embedding , 2016, KDD.

[39]  Omer Levy,et al.  Neural Word Embedding as Implicit Matrix Factorization , 2014, NIPS.

[40]  Hongtao Lu,et al.  Community detection in social network with pairwisely constrained symmetric non-negative matrix factorization , 2015, 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM).

[41]  Jian Pei,et al.  A Survey on Network Embedding , 2017, IEEE Transactions on Knowledge and Data Engineering.

[42]  Graham Cormode,et al.  Node Classification in Social Networks , 2011, Social Network Data Analytics.

[43]  Shou-De Lin,et al.  PRUNE: Preserving Proximity and Global Ranking for Network Embedding , 2017, NIPS.