TAILIEUCHUNG - Managing and Mining Graph Data part 20

Managing and Mining Graph Data part 20 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. . | 1772 MANAGING AND MINING GRAPH DATA Frequency Difference Once ittie neper bound of7 misses is obtained it could be used to prune graphs. Let f1 f2 . fn be Use indexing lealures. Given a target graph G and a query graph Q Set u u1 u2 . un T and v v1 v2 . vn T lie their corrctpomline feature vectors where u and Vi aee die frequencies . ihc numhca ol embeddings of feature f in graphs G ami Q. Figure shows Lwo feaiuro vectors u and v. As mentioned eclorCi for any feature set covLCspontiing feaiure vector of e target graph can be obtained from the feature-graph matrix alirecliy wi .houl. scanning the graph database. Figure . Frequency Difference F q. frequency diffcrence of f it sc quesy graph and ihe iiirgcil. graph x i0 if Ui Vi r Ui Vi lvi ui otherwise. Fot the tcai. iLts vectors thown in Figure r u1 v1 0 ihc extra embed-dinfs from the - Lrg eML graaii are not taken into account. The summed frequency dii feyaacc of each feature in G ami Q is as d G Q . F q. 515 aums up ah rhe frequency differences n d G Q r ui Vi . i 1 Suppose ihc c ucrri can be relaxed with k cdons and the upfes bound of allowed feature misies li then estimated eitiirg tlua grcctiy algorithm mentioned before. If d G Q is n atirr ihan that hound. is can he concluded that G doea not con-ialn Q wiibin k edge relaxaHt s For tiios casCi tq is not necessary to perform any comprnson between G ami Q. Since all Lite computations ere dove on the preprocessed information in the indices the filtering -taoi cof s fast. Graph Indexing 1773 Feature Set Selection Though a hie o. i in . using all the features together will not necessarily give the optimai solution in some cases it even deteriorates the performance rather Shan improving it. Given a query graph Q let F i f2 . fm be die sal of icaturcs included in Q and dp the maximal numCev of Icaiuriss missed in F idler Q is aclaxcd cillur rr .

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