Milad Eftekhar , Yashar Ganjali, Nick Koudas
Introduction β’ Identifying the π most influential individuals is a well- studied problem. β’ We generalize this problem to identify the π most influential groups . β’ Application: β’ Companies often target groups of people β’ E.g. by billboards, TV commercials, newspaper ads, etc. 2
Group targeting β’ Groups Billboard β’ Advantages β’ Improved performance β’ Natural targets for advertising β’ An economical choice 3
Fine-Grained Diffusion (FGD) β’ Determine how advertising to a group translates into individual adopters. β’ Run individual diffusion process on these adopters. 4
FGD Modeling β’ Graph π»β² : add a node for each group, add edges between a node corresponding to a group π π and its members with weight π₯ π that depends on β’ Advertising budget, size of group, the escalation factor, and the budget needed to convince an individual 5
FGD Modeling (Contβd) β’ Escalation Factor πΎ : how many more initial adaptors we can get by group targeting rather than individual targeting. Individual Targeting Group Targeting Advertising budget Advertising budget $1000 $1000 Cost of convincing an individual Billboard $100 Audience = 10000 Cost = $1000 individuals 20 initial adopters 10 initial adopters πΎ = 20 10 = 2 6
FGD Modeling (Contβd) β’ Escalation Factor πΎ β’ Based on the problem structure, the size and shape of the network, the initial advertising method, etc. β’ Individual advertising: πΎ = 1 β’ Billboard advertising: πΎ = 200 β’ Online advertising: πΎ = 400 7
Problem statement β’ Goal : Find the π most influential groups (blue group- nodes) Top-2 Top-2 influential influential groups groups β’ NP-hard under FGD model 8
topfgd algorithm β’ Diffusion in FGD is monotone and submodular β’ topfgd: a greedy algorithm provides a (1-1/e) approximation factor. β’ In each iteration, add the group resulting to the maximum marginal increase in the final influence. β’ Time: π ( π Γ π Γ| πΉ πππ |Γ π ) 9
Coarse-Graind Diffusion (CGD) β’ FGD is not practical for large social networks β’ Idea: incorporate information about individuals without running explicitly on the level of individuals β’ A graph to model inter-group influences Group 1 10
CGD Modeling β’ Differences with βIndividual Diffusionβ models β’ No binary decisions β’ Progress fraction for each group β’ Two types of diffusion β’ Inter-group diffusion Progress fraction = 0.6 β’ Intra-group diffusion β’ Submodularity? 11
CGD Diffusion Model β’ Each newly activated fraction of a group can activate its neighboring groups β’ As a result of an activation attempt from A to B, some activation attempts also occur between members of B β’ Continue for several iterations to converge 0 0 0.04 β 0.05 Group 1 Group 1 0 0 β 0.04 0 0.2 0.2 0 0 β 0.2 12
topcgd algorithm β’ Goal : Find the π most influential groups β’ NP-hard under CGD model β’ Diffusion in CGD is monotone and submodular β’ topcgd: a greedy algorithm provides a (1-1/e) approximation factor. β’ Time: π( πΉ πππ + ππ ππ’ + π ) β’ π’ is the number of iterations to converge (~10) 13
Experimental setup β’ Datasets: β’ DBLP: 800K nodes, 6.3M edges, 3200 groups β’ Comparison β’ Spend same advertising budget on all algorithms β’ Measure the final influence (the number of convinced individuals) β’ Run Individual Diffusion process on the initial convinced individuals 14
Results β’ DBLP-1980: 8000 nodes, 69 groups β’ Compare topid vs. topfgd vs. topcgd β’ Final influence: topfgd and topcgd outperform topid for πΎ > 3 β’ Time: topid (30 days), topfgd (an hour), topcgd (0.2 sec) topfgd topcgd topid 6000 final influence 5000 4000 3000 2000 1000 0 0 10 20 30 40 50 60 70 80 90 100 Ξ² 15
Results (Contβd) β’ DBLP: topcgd vs. Baselines β’ rnd, small, big, degree β’ Time of topcgd : 100 minutes β’ topfgd and topid not practical topcgd degree big rnd small 70000 60000 final influence 50000 40000 30000 20000 10000 0 10 30 50 70 90 Ξ² 16
Conclusion and Future Works β’ Focus on groups rather than individuals β’ Wider diffusion β’ Improved performance β’ More less influential individuals vs. less more influential individuals β’ Although CGD aggregates the information about individuals (hence improved performance), it results to final influence comparable to FGD. β’ We are interested in a generalized model where β’ Groups are allowed to receive different budgets β’ The cost of advertising to each group is predetermined 17
Thanks! (Questions?) 18
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