Sparsifcatin if Infmuence Netmwirks Michael Matmhiiudakis 1 , - PowerPoint PPT Presentation

Sparsifcatin if Infmuence Netmwirks Michael Matmhiiudakis 1 , Francesci Binchi 2 , Carlis Castlli 2 , Aris Giinis 2 , Ant Ukkinen 2 1 Universitmy if Tirintmi, Canada 2 Yahii! Research Barcelina, Spain

Intmriductin inline sicial netmwirks facebiik 750m users tmwiter 100m+ users users perfirm actins nice indeed! pistm messages, pictmures, videis read cinnectmed witmh itmher users intmeractm, infmuence each itmher 09:00 09:30 actins pripagatme 2

Priblem which cinnectins are mistm impirtmantm fir tmhe pripagatin if actins? sparsify netmwirk eliminatme large number if cinnectins keep impirtmantm cinnectins sparsifcatin: a datma reductin iperatin netmwirk visualizatin efcientm graph analysis 3

Whatm We Di tmechnical framewirk sparsify netmwirk accirding tmi ibserved actvitmy keep cinnectins tmhatm bestm explain pripagatins iur appriach sicial netmwirk & ibserved pripagatins learn independentm cascade midel (ICM) selectm k cinnectins mistm likely tmi have priduced pripagatins 4

Outmline • intmriductin • setng – sicial netmwirk – pripagatin midel • sparsifcatin – iptmal algiritmhm – greedy algiritmhm: spine • experimentms 5

Sicial Netmwirk A B users – nides B filliws A – arc A→B 6

Pripagatin if Actins users perfirm actins actins pripagatme i ndependentm c ascade m idel pripagatin if an actin unfilds in tmestmeps I liked tmhis greatm infmuence pribabilitmy mivie mivie p(A,B) A B tm tm+1 7

Pripagatin if Actins icm generatmes pripagatins sequence if actvatins likelihiid B D p(A,B) actve actin α C A E nitm actve tm-1 tm tm+1 8

Estmatng Infmuence Pribabilites sicial netmwirk max likelihiid + p(A,B) setm if pripagatins EM – [Saitmi etm.al.] B D p(A,B) actve actin α C A E nitm actve tm-1 tm tm+1 9

Outmline • intmriductin • setng – sicial netmwirk – pripagatin midel • sparsifcatin – iptmal algiritmhm – greedy algiritmhm: spine • experimentms 10

Sparsifcatin sicial netmwirk p(A,B) k arcs setm if mistm likely tmi pripagatins explain all pripagatins B p(A,B) A 11

Sparsifcatin sicial netmwirk p(A,B) k arcs setm if mistm likely tmi pripagatins explain all pripagatins B p(A,B) A 12

Sparsifcatin not tmhe k arcs witmh largestm pribabilites NP-hard and inappriximable difcultm tmi fnd silutin witmh nin-zeri likelihiid 13

Hiw tmi Silve? brutme-firce appriach tmry all subsetms if k arcs? ni break diwn intmi smaller priblems cimbine silutins 14

Optmal Algiritmhm sparsify separatmely inciming arcs if individual nides iptmize cirrespinding likelihiid A B C k A + + k C k B = k dynamic prigramming iptmal silutin hiwever… 15

Spine sp arsifcatin if i nfmuence ne tmwirks greedy algiritmhm efcientm, giid resultms tmwi phases phase 1 tmry tmi ibtmain a nin-zeri-likelihiid silutin k 0 < k arcs phase 2 build in tmip if phase 1 16

Spine – Phase 1 phase 1 ibtmain a nin-zeri-likelihiid silutin selectm greedily arcs tmhatm partcipatme in mistm pripagatins untl all pripagatins are explained B sicial netmwirk A actin α C B D A C tm tm+1 D B actin β A C D 17

Spine – Phase 2 add ine arc atm a tme, tmhe ine tmhatm ifers largestm increase in likelihiid logL submidular # arcs k 0 k appriximatin guarantmee fir phase 2 18

Outmline • intmriductin • setng – sicial netmwirk – pripagatin midel • sparsifcatin – iptmal algiritmhm – greedy algiritmhm: spine • experimentms 19

Experimentms datmasetms meme.yahii.cim actins: pistngs (phitmis), nides: users, arcs: whi filliws whim datma frim 2010 memetmracker.irg actins: mentins if a phrase, nides: bligs & news siurces, arcs: whi links tmi whim datma frim 2009 20

Experimentms sampled datmasetms if diferentm sizes Dataset Actons Arcs Arcs, prob > 0 YMeme-L 26k 1.25M 430k YMeme-M 13k 1.15M 380k YMeme-S 5k 466k 73k MTrack-L 9k 200k 7.8k MTrack-M 120 110k 1.4k MTrack-S 780 78k 768 YMeme meme.yahii.cim MTrack memetmracker.irg 21

Experimentms algiritmhms iptmal (very inefcientm) spine (a few secinds tmi 3.5hrs) by arc pribabilitmy randim 22

Experimentms 23

Midel Selectin using BIC BIC(k) = -2ligL + kligN 24

Applicatin spine as a prepricessing stmep infmuence maximizatin selectm k nides tmi maximize spread if actin [Kempe, Kleinberg, Tardis, 03] NP-hard, greedy appriximatin perfirm in sparsifed netmwirk instmead large beneftm in efciency, litle liss in qualitmy 25

Applicatin 26

Public Cide and Datma htp://www.cs.tmirintmi.edu/~matmhiiu/spine/ 27

The End Questins? 28

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