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10-celf_annot - CS224W: JureLeskovec,StanfordUniversity...

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CS224W: Social and Information Network Analysis Jure Leskovec Stanford University Jure Leskovec, http://cs224w.stanford.edu
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Most influential set of a d 0.4 size k: set S of k nodes producing largest b f 0.4 0.2 0.2 0.3 0.3 0.3 expected cascade size f(S) if activated e g h 0.4 0.2 0.4 0.3 0.3 0.3 0.2 [Domingos Richardson ‘01] c i 0.4 Optimization problem: ) ( max S f 10/20/2010 2 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu k size of S
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Hill Climbing: f(S i 1 {v}) Start with S 0 ={} For i=1…k Choose node v that max f(S i 1 {v}) a b Let S i = S i 1 {v} Hill climbing produces a solution S where f(S) (1 1/ ) f ti l l (~63%) c d (1 1/e) of optimal value (~63%) [Hemhauser, Fisher, Wolsey ’78, Kempe, Kleinberg, Tardos ‘03] Claim holds for functions f with 2 properties: e f is monotone: if S T then f (S) f (T) and f ({})=0 f is submodular: adding element to a set gives less improvement than adding to one of subsets 10/20/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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