Managing and Mining Graph Data part 40 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 tl77 In graph mining it is useful to have sparse weight vectors w such that only a limited number of patterns arc used for- prediction. To this aim we introduce the sparseness So die pre-weight vectors v as Vij 0 if vijI e j 1 . d. Due to ths 1 incar eelstionsHp between vi srcd Wi w becomes spaase as well. Then we can sort vij in ihe dceccnslmg order take the top-fc eSements and set sail ihe other elements to zero. It Is worthwhitie to notice that tins reesidtail of regression up to the i 1 -th lealstres. i-1 rik Vk 2 ajwjXk 3-6 j 1 is equal to die fc-th dement o f ri. It can Ise veti-ist l by substituting the deli nition ctf aj in Eq. 3e5 into Eq. . So tn the non-dedation algorithm the preweight vector v is ohraised as the direciion tisai maximizes the covariance with residues. T tsiis oblcrvalton litsrlilt liu that rccemblance of PLS and boosting algorithms. Graph PLS Branch-and-Bound Search. In ihis paste we discuss how to appty rhe non-ddiaiion PLS atgoridnn tii gt ijrla data. The set of daining graphs is scpscscntcd as G1 y1 . Gn yn . Let P be d-e cei of di patterns then the feature vet tot of each graph G is encoded as a P -dimensional vector xi. Siti e P is a huge number -i is mfeassbie to keep the whole design matrix. So She method sets X as an t m iy matrix lissis atd grows the matrix as the iteration proceeds. In each 1 -110 it obtains the set of patterns p whose pres weight vip is above the . wtried can be wriden as n pi P11 rijxjp e - 3-7 j 1 Then she dcrign matci to it expanded to include newly introduced paderns. The pseudo node of gPLS is described in Algorithm 16. The pat-ern search pmblciu ita is exactly the same as the one solved in gbooSt tlirt ugh a branch-and-hoiind search tn this problem the gain function is defined as s p 11C i GjXjp . The pruntng condition is described s- tiaaii-. Theorem . Define y sgn ri . For any pattern p such that p C p s p e holds if max s p s p e 378 MANAGING .
