Lecture07-2-Out-of-Core-Cocain - Out-of-Core Coherent...

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12009/11/19Out-of-Core Coherent Closed Quasi-CliqueMining from Large Dense Graph DatabasesJianyong WangDepartment of Computer Science and TechnologyTsinghua University, Beijing, P.R. ChinaEmail: [email protected]Joint work with Zhiping Zeng, Lizhu Zhou, and George Karypis
22009/11/19Case study 1: an initial solution-Frequent Closed Clique MiningThe CLAN algorithmCLANstands for Frequent closedCLique pAtterNminingCase Study 2: a more complex solution-Frequent Coherent Closed Quasi-Clique MiningThe Cocain algorithmCocainstands forCoherentclosed quasi-clique miningCase Study 3: an out-of-core solution-Out-of-core Coherent Closed Quasi-Clique MiningThe Cocain* algorithmFrequent Coherent Closed Subgraph MiningCase Studies
32009/11/19Part1:Closed Clique Mining
42009/11/19CLAN: An Algorithm for Mining ClosedCliques from Large Dense Graph DatabasesJianyong Wang1, Zhiping Zeng2, Lizhu Zhou3{1jianyong,3dcszlz}@tsinghua.edu.cn2[email protected]Department of Computer Science and TechnologyTsinghua University, Beijing, P.R. ChinaProc. 2006 IEEE Int. Conf. on Data Engineering. (ICDE'06)
52009/11/19OutlineProblem definition and motivation-Problem definition-MotivationThe CLAN solution-Canonical form of a clique-Efficient clique enumerationLow-degree vertex pruningStructural redundancy pruning-Closed clique discoveryClique closure checking schemeNon-closed prefix pruning-Integrated algorithmEmpirical resultsConclusions
62009/11/19Problem Formulation
72009/11/19PreliminariesInput database D: a set of undirected labeled input graphs.Undirected labeled input graph GG={V, E, LV, FV}V: the set of verticesE: the set of edges,LV: the set of vertex labelsCardinality of graph G:|G|= |V|Note: in this work, we do not consider the edge labels.VVEVVLVF:
82009/11/19PreliminariesInduced subgraph:-Aninduced subgraphis a subset of the vertices of a graph togetherwith any edges whose endpoints are both in this subset.Examples:-V(G2)={v1,v2,v3,v4,v5,v6}-E(G2)={(v1,v2),}-Lv(G2)={a, b, c, d, e}-Card(G2)=6u4u3u5Induced Subgraph of G1cdb
92009/11/19PreliminariesClique: a clique C is a fully connected subgraphClique Isomorphism:-A clique C1={V1, L1, F1} isisomorphicto another clique C2={V2, L2, F2} iff|V1|=| V2| and there exists a bijection f: V1V2such thatSubclique and Superclique:-If a clique C is isomorphic to a subgraph of another clique C,C is called asubcliqueof C, while Cis called asupercliqueof C. We use CCor CC(CCbut C≠C) to denotethe subcliqueor proper subclique relationship.))(()(,211vfFvFVv
102009/11/19PreliminariesEmbedding-If a fully connected subgraphhof a graph G is isomorphic to a clique C, we callhanembeddingof C in G.

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Term
Fall
Professor
WangWei
Tags
Graph Theory, Data Mining, Databases, Vertex, coherent, Canonical form, Clique Mining

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