Discovering Communication Pattern Shifts in Large-Scale Networks using Encoder Embedding and Vertex Dynamics

The analysis of large-scale time-series network data, such as social media and email communications, remains a significant challenge for graph analysis methodology. In particular, the scalability of graph analysis is a critical issue hindering further progress in large-scale downstream inference. In this paper, we introduce a novel approach called"temporal encoder embedding"that can efficiently embed large amounts of graph data with linear complexity. We apply this method to an anonymized time-series communication network from a large organization spanning 2019-2020, consisting of over 100 thousand vertices and 80 million edges. Our method embeds the data within 10 seconds on a standard computer and enables the detection of communication pattern shifts for individual vertices, vertex communities, and the overall graph structure. Through supporting theory and synthesis studies, we demonstrate the theoretical soundness of our approach under random graph models and its numerical effectiveness through simulation studies.

[1]  C. Priebe,et al.  Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection , 2023, ArXiv.

[2]  C. Priebe,et al.  Euclidean mirrors and dynamics in network time series , 2022, 2205.06877.

[3]  J. Leskovec,et al.  Combining Graph Convolutional Neural Networks and Label Propagation , 2021, ACM Trans. Inf. Syst..

[4]  C. Priebe,et al.  One-Hot Graph Encoder Embedding , 2021, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Patrick Rubin-Delanchy,et al.  Spectral embedding for dynamic networks with stability guarantees , 2021, NeurIPS.

[6]  Duncan J. Watts,et al.  A Large-Scale Comparative Study of Informal Social Networks in Firms , 2021, Manag. Sci..

[7]  Carey E. Priebe,et al.  Dynamic Silos: Increased Modularity in Intra-organizational Communication Networks during the Covid-19 Pandemic , 2021, 2104.00641.

[8]  Qian Huang,et al.  Combining Label Propagation and Simple Models Out-performs Graph Neural Networks , 2020, ICLR.

[9]  Christoper M. White,et al.  Multiple Network Embedding for Anomaly Detection in Time Series of Graphs. , 2020, 2008.10055.

[10]  Arjun Krishnan,et al.  PecanPy: a fast, efficient and parallelized Python implementation of node2vec , 2020, bioRxiv.

[11]  Carey E. Priebe,et al.  Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace , 2019, J. Mach. Learn. Res..

[12]  Vincent A. Traag,et al.  From Louvain to Leiden: guaranteeing well-connected communities , 2018, Scientific Reports.

[13]  Jie Zhang,et al.  Spectral Network Embedding: A Fast and Scalable Method via Sparsity , 2018, ArXiv.

[14]  Leland McInnes,et al.  UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction , 2018, ArXiv.

[15]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

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

[17]  Steve Harenberg,et al.  Anomaly detection in dynamic networks: a survey , 2015 .

[18]  Danai Koutra,et al.  Graph based anomaly detection and description: a survey , 2014, Data Mining and Knowledge Discovery.

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

[20]  C. Priebe,et al.  Universally consistent vertex classification for latent positions graphs , 2012, 1212.1182.

[21]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[22]  Adam M. Kleinbaum,et al.  Discretion Within Constraint: Homophily and Structure in a Formal Organization , 2012, Organ. Sci..

[23]  Carey E. Priebe,et al.  Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs , 2012, 1207.6745.

[24]  Lars Backstrom,et al.  The Anatomy of the Facebook Social Graph , 2011, ArXiv.

[25]  Ji Zhu,et al.  Consistency of community detection in networks under degree-corrected stochastic block models , 2011, 1110.3854.

[26]  Carey E. Priebe,et al.  A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs , 2011, 1108.2228.

[27]  V A Traag,et al.  Narrow scope for resolution-limit-free community detection. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Bin Yu,et al.  Spectral clustering and the high-dimensional stochastic blockmodel , 2010, 1007.1684.

[30]  Jure Leskovec,et al.  Predicting positive and negative links in online social networks , 2010, WWW '10.

[31]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[32]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[33]  Edward R. Scheinerman,et al.  Random Dot Product Graph Models for Social Networks , 2007, WAW.

[34]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[36]  Jon Kleinberg,et al.  The link prediction problem for social networks , 2003, CIKM '03.

[37]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[38]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Kathryn B. Laskey,et al.  Stochastic blockmodels: First steps , 1983 .

[40]  Philip S. Yu,et al.  A Comprehensive Survey on Graph Neural Networks , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Ilya Sutskever,et al.  Language Models are Unsupervised Multitask Learners , 2019 .

[42]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[43]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure , 1997 .

[44]  A. Krizhevsky.  ImageNet Classification with Deep Convolutional Neural Networks , 2022 .