Multiplex graph matching matched filters

We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the framework of [14] to the multiplex setting, leverages a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels.

[1]  Daniel Cullina,et al.  Exact alignment recovery for correlated Erdos Renyi graphs , 2017, ArXiv.

[2]  Elza Erkip,et al.  Optimal de-anonymization in random graphs with community structure , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[3]  Matteo Magnani,et al.  The ML-Model for Multi-layer Social Networks , 2011, 2011 International Conference on Advances in Social Networks Analysis and Mining.

[4]  Julian R. Ullmann,et al.  An Algorithm for Subgraph Isomorphism , 1976, J. ACM.

[5]  Derek G. Corneil,et al.  The graph isomorphism disease , 1977, J. Graph Theory.

[6]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[7]  Carey E. Priebe,et al.  Matched Filters for Noisy Induced Subgraph Detection , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Noga Alon,et al.  Biomolecular network motif counting and discovery by color coding , 2008, ISMB.

[9]  Jeong-Hoon Lee,et al.  An In-depth Comparison of Subgraph Isomorphism Algorithms in Graph Databases , 2012, Proc. VLDB Endow..

[10]  Daniel L. Sussman,et al.  Matchability of heterogeneous networks pairs. , 2017, Information and inference : a journal of the IMA.

[11]  Daniel Cullina,et al.  Improved Achievability and Converse Bounds for Erdos-Renyi Graph Matching , 2016, SIGMETRICS.

[12]  Matthias Grossglauser,et al.  When can two unlabeled networks be aligned under partial overlap? , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[13]  H. Vincent Poor,et al.  Partial Recovery of Erdðs-Rényi Graph Alignment via k-Core Alignment , 2019, Proc. ACM Meas. Anal. Comput. Syst..

[14]  Mason A. Porter,et al.  Isomorphisms in Multilayer Networks , 2015, IEEE Transactions on Network Science and Engineering.

[15]  Carey E. Priebe,et al.  Statistical Inference on Errorfully Observed Graphs , 2012, 1211.3601.

[16]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[17]  Carey E. Priebe,et al.  Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks , 2018, J. Comput. Graph. Stat..

[18]  Stratis Ioannidis,et al.  A Family of Tractable Graph Distances , 2018, SDM.

[19]  Y. Aflalo,et al.  On convex relaxation of graph isomorphism , 2015, Proceedings of the National Academy of Sciences.

[20]  Matthias Grossglauser,et al.  On the privacy of anonymized networks , 2011, KDD.

[21]  Andrea L. Bertozzi,et al.  Filtering Methods for Subgraph Matching on Multiplex Networks , 2018, 2018 IEEE International Conference on Big Data (Big Data).

[22]  Jiming Liu,et al.  Mining Multiplex Structural Patterns from Complex Networks , 2016, Semantic Web Technologies for Intelligent Engineering Applications.

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

[24]  Carey E. Priebe,et al.  Seeded graph matching , 2012, Pattern Recognit..

[25]  Mario Vento,et al.  A (sub)graph isomorphism algorithm for matching large graphs , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[27]  Jiaming Xu,et al.  Efficient random graph matching via degree profiles , 2018, Probability Theory and Related Fields.

[28]  Walter A. Kosters,et al.  Detecting Motifs in Multiplex Corporate Networks , 2017, COMPLEX NETWORKS.

[29]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

[30]  Hongyuan Zha,et al.  A Short Survey of Recent Advances in Graph Matching , 2016, ICMR.

[31]  Fedor V. Fomin,et al.  Faster algorithms for finding and counting subgraphs , 2009, J. Comput. Syst. Sci..

[32]  Noga Alon,et al.  Color-coding , 1995, JACM.

[33]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[34]  Yunming Ye,et al.  MultiRank: co-ranking for objects and relations in multi-relational data , 2011, KDD.

[35]  Vince Lyzinski,et al.  A joint graph inference case study: the C. elegans chemical and electrical connectomes , 2015, Worm.

[36]  Krishna P. Gummadi,et al.  On the Reliability of Profile Matching Across Large Online Social Networks , 2015, KDD.

[37]  Tselil Schramm,et al.  (Nearly) Efficient Algorithms for the Graph Matching Problem on Correlated Random Graphs , 2018, NeurIPS.

[38]  Yongtang Shi,et al.  Fifty years of graph matching, network alignment and network comparison , 2016, Inf. Sci..

[39]  Prateek Mittal,et al.  Partial Recovery of Erd\H{o}s-R\'{e}nyi Graph Alignment via $k$-Core Alignment , 2018 .

[40]  Mario Vento,et al.  Graph Matching and Learning in Pattern Recognition in the Last 10 Years , 2014, Int. J. Pattern Recognit. Artif. Intell..

[41]  Matthias Grossglauser,et al.  Growing a Graph Matching from a Handful of Seeds , 2015, Proc. VLDB Endow..