TAILIEUCHUNG - Managing and Mining Graph Data part 41

Managing and Mining Graph Data part 41 is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. . | Mining Graph Patterns 387 Algorithm 21 ORIGAMI D minsup a 0 Input Graph dataset D minimum support minsup a 0 Output a-orthogonal 0-representative set K 1 EM Edge-Map D 2 E1 Find-Frequent-Edges D minsup 3 M o 4 while s itof g_c -oncli true do 5 M RandomtMeximal-Graph D E1 EM minsup 6 M M U M 7 K Orthogonal-Representative-Sets M a 0 8 return K Randomized Maximal Subgraph Mining As the first step ORIGAMl mines a set of maximal subgraphs on which the a-orthogonal 0-representative jrr ajrh pattern sei is generated. This is based on the obscrvatton that the number of maximal frequent subgraphs is much fewer than that of frequent subgraphs and ihe maximal subgraphs provide a synopsis of the frequent ones to some extent. Thus it is reasonable to mine the representative orthogonal pattern set based in the maximal subgraphs rather than the frequent ones. However even mrntng all of maximal subgraphs could be iofeasible in some real world applications. To avoid this problem ORIGAMI ifrst finds a sain ple M of the complote cef of maximal frequent subgraphs M. The goal is to find a set ot maximal subgraphs M which is as diverse as possible. To achieve this goal ORIGAMl avoidc using combinatorial enumeration to mine rnaei mat subgsaph patterns Instead it adopts a random walk approach to rnumerate o cli verse eei of maximrl subgraphs from the positive bordor of euch maxrmal paitemSi The randomized mining algorithm starts with an empty pattern and Iteratively adds a random edge during each extension until a maximai subgraph M is generaSed and no more edges can be added. This proccsf walks a random chain ln the partial order of frequent subgraphs. To extnnd an intermediate pattern S Q M it chooser a random vertex v from which the extension wlU be attempted. Then a random edge e incident on v ii selected tor extemion. if iso such edge is found no extension is possible from the vertex. When no vartices can hive any further extension in S the random walk terminates and S M ii tie .

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