influence maximization · chen w., wang c,, and wang y. scalable influence maximization for...
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Matthew Richardson and Pedro Domingos: Mining the network value of customers. KDD 2001 http://doi.acm.org/10.1145/502512.502525 Matthew Richardson and Pedro Domingos: Mining knowledge-sharing sites for viral marketing. KDD 2002 http://doi.acm.org/10.1145/775047.775057
simplified model here, does not
include product attributes 𝒀 ={𝑌1, … , 𝑌𝑘}.
Computation of revenue includes
marketing cost, discount, and uses
naïve Bayes model, etc. to simplify the
computation.
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David Kempe, Jon Kleinberg, and Eva Tardos: Maximizing the spread of influence through a social network. KDD 2003 http://doi.acm.org/10.1145/956750.956769
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Damon Centola and Michael Macy: Complex Contagions and the Weakness of Long Ties. American Journal of Sociology 2007 http://www.jstor.org/stable/10.1086/521848
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from 𝑓 𝑆 ∪ 𝑇 + 𝑓 𝑆 ∩ 𝑇 ≤ 𝑓 𝑆 +𝑓 𝑇 to prove 𝑓 𝑆 ∪ 𝑣 − 𝑓 𝑆 ≥𝑓 𝑇 ∪ 𝑣 − 𝑓(𝑇),
just consider two sets 𝑆 ∪ 𝑣 and T, and apply the first formula
For the opposite direction, Let 𝑇\S = {𝑢1, 𝑢2, … , 𝑢𝑘}, Let 𝑇𝑗 =
{𝑢1, 𝑢2, … , 𝑢𝑗}, let 𝐴𝑗 = (𝑆 ∩ 𝑇) ∪ 𝑇𝑗,
and let 𝐵𝑗 = 𝑆 ∪ 𝑇𝑗 we have
𝑓 𝐴𝑗 ∪ 𝑢𝑗+1 − 𝑓 𝐴𝑗 ≥
𝑓 𝐵𝑗 ∪ 𝑢𝑗+1 − 𝑓 𝐵𝑗 , 𝑗 =
0,1,2, … , 𝑗 − 1.
Summing up all these equations, we have
𝑓 𝑇 − 𝑓 𝑆 ∩ 𝑇 ≥ 𝑓 𝑆 ∪ 𝑇 − 𝑓 𝑆 .
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Also referred as greedy hill-climbing algorithm, greedy approximation algorithm.
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G. L. Nemhauser, L. A. Wolsey and M. L. Fisher: An analysis of approximations for maximizing submodular set functions. Mathematical Programming 1978 http://dx.doi.org/10.1007/BF01588971
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Based on equivalent live-edge graphs • Find a random edge selection
process, such that each edge is either live or blocked, and all live edges form a random live-edge graph.
• Show that a diffusion model is equivalent to the reachability in random live-edge graphs: Given any seed set S, the distribution of active node sets after the diffusion process with seed set S ends is the same as the distribution of node set reachable from S in a random live-edge graph.
• Applicable to both IC and LT model.
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Elchanan Mossel, Sébastien Roch: On
the submodularity of influence in
social networks. STOC’2007. 128-134
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Use this slide in lieu of the next three if running out of time.
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