FS3: A sampling based method for top-k frequent subgraph mining

Mining labeled subgraph is a popular research task in data mining because of its potential application in many different scientific domains. All the existing methods for this task explicitly or implicitly solve the subgraph isomorphism task which is computationally expensive, so they suffer from the lack of scalability problem when the graphs in the input database are large. In this work, we propose FS3, which is a sampling based method. It mines a small collection of subgraphs that are most frequent in the probabilistic sense. FS3 performs a Markov Chain Monte Carlo (MCMC) sampling over the space of a fixed-size subgraphs such that the potentially frequent subgraphs are sampled more often. Besides, FS3 is equipped with an innovative queue manager. It stores the sampled subgraph in a finite queue over the course of mining in such a manner that the top-k positions in the queue contain the most frequent subgraphs. Our experiments on database of large graphs show that FS3 is efficient, and it obtains subgraphs that are the most frequent amongst the subgraphs of a given size.

[1]  Luc De Raedt,et al.  Don't Be Afraid of Simpler Patterns , 2006, PKDD.

[2]  Kamalakar Karlapalem,et al.  MARGIN: Maximal Frequent Subgraph Mining , 2006, ICDM.

[3]  Eamonn J. Keogh,et al.  Towards parameter-free data mining , 2004, KDD.

[4]  Mohammad Al Hasan,et al.  MUSK: Uniform Sampling of k Maximal Patterns , 2009, SDM.

[5]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[6]  Fernando M. A. Silva,et al.  g-tries: an efficient data structure for discovering network motifs , 2010, SAC '10.

[7]  Jiawei Han,et al.  Mining coherent dense subgraphs across massive biological networks for functional discovery , 2005, ISMB.

[8]  Jiong Yang,et al.  SPIN: mining maximal frequent subgraphs from graph databases , 2004, KDD.

[9]  Ravi Montenegro,et al.  Mathematical Aspects of Mixing Times in Markov Chains , 2006, Found. Trends Theor. Comput. Sci..

[10]  Takashi Washio,et al.  An Apriori-Based Algorithm for Mining Frequent Substructures from Graph Data , 2000, PKDD.

[11]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics) , 1981 .

[12]  Scott A. Sisson,et al.  Reversible Jump MCMC , 2011 .

[13]  Thorsten Meinl,et al.  A Quantitative Comparison of the Subgraph Miners MoFa, gSpan, FFSM, and Gaston , 2005, PKDD.

[14]  Mohammad Al Hasan,et al.  FS3: A sampling based method for top-k frequent subgraph mining , 2014, BigData.

[15]  Mohammad Al Hasan,et al.  Output Space Sampling for Graph Patterns , 2009, Proc. VLDB Endow..

[16]  Wilfred Ng,et al.  Fg-index: towards verification-free query processing on graph databases , 2007, SIGMOD '07.

[17]  Donald F. Towsley,et al.  Efficiently Estimating Motif Statistics of Large Networks , 2013, TKDD.

[18]  George Karypis,et al.  An efficient algorithm for discovering frequent subgraphs , 2004, IEEE Transactions on Knowledge and Data Engineering.

[19]  Philip S. Yu,et al.  Graph indexing: a frequent structure-based approach , 2004, SIGMOD '04.

[20]  Sebastian Wernicke,et al.  Efficient Detection of Network Motifs , 2006, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[21]  Jan Ramon,et al.  Frequent subgraph mining in outerplanar graphs , 2006, KDD '06.

[22]  Joost N. Kok,et al.  The Gaston Tool for Frequent Subgraph Mining , 2005, GraBaTs.

[23]  Jan Ramon,et al.  Efficient frequent connected subgraph mining in graphs of bounded tree-width , 2010, LWA.

[24]  Sahar Asadi,et al.  Kavosh: a new algorithm for finding network motifs , 2009, BMC Bioinformatics.

[25]  Jiawei Han,et al.  gSpan: graph-based substructure pattern mining , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[26]  Wei Wang,et al.  GAIA: graph classification using evolutionary computation , 2010, SIGMOD Conference.

[27]  Jeffrey S. Rosenthal,et al.  Optimal Proposal Distributions and Adaptive MCMC , 2011 .

[28]  John F. Roddick,et al.  FP-GraphMiner-A Fast Frequent Pattern Mining Algorithm for Network Graphs , 2011, J. Graph Algorithms Appl..

[29]  Philip S. Yu,et al.  Mining significant graph patterns by leap search , 2008, SIGMOD Conference.

[30]  Mohammad Al Hasan,et al.  Finding Network Motifs Using MCMC Sampling , 2015, CompleNet.

[31]  Xiaokui Xiao,et al.  Large-scale frequent subgraph mining in MapReduce , 2014, 2014 IEEE 30th International Conference on Data Engineering.

[32]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[33]  Venkatesan Guruswami.  Rapidly Mixing Markov Chains: A Comparison of Techniques (A Survey) , 2016, ArXiv.

[34]  Mohammad Al Hasan,et al.  ORIGAMI: A Novel and Effective Approach for Mining Representative Orthogonal Graph Patterns , 2008, Stat. Anal. Data Min..

[35]  George Karypis,et al.  Frequent substructure-based approaches for classifying chemical compounds , 2003, IEEE Transactions on Knowledge and Data Engineering.

[36]  Lawrence B. Holder,et al.  Substructure Discovery Using Minimum Description Length and Background Knowledge , 1993, J. Artif. Intell. Res..

[37]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[38]  Philip S. Yu,et al.  Near-optimal Supervised Feature Selection among Frequent Subgraphs , 2009, SDM.

[39]  Luc De Raedt,et al.  Frequent Hypergraph Mining , 2006, ILP.

[40]  Uri Alon,et al.  Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs , 2004, Bioinform..

[41]  Mohammad Al Hasan,et al.  An integrated, generic approach to pattern mining: data mining template library , 2008, Data Mining and Knowledge Discovery.

[42]  Mohammad Al Hasan,et al.  An Iterative MapReduce Based Frequent Subgraph Mining Algorithm , 2013, IEEE Transactions on Knowledge and Data Engineering.

[43]  Jiawei Han,et al.  CloseGraph: mining closed frequent graph patterns , 2003, KDD '03.