Lecture 4 Influence Maximization Ding-Zhu Du University of
Texas at Dallas
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Outline Kate Middleton effect Submodular Function Max
Independent Cascade 2
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The trend effect that Kate, Duchess of Cambridge has on others,
from cosmetic surgery for brides, to sales of coral-colored jeans.
Kate Middleton effect Kate Middleton effect 3
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According to Newsweek, "The Kate Effect may be worth 1 billion
to the UK fashion industry." Tony DiMasso, L. K. Bennetts US
president, stated in 2012, "...when she does wear something, it
always seems to go on a waiting list." Hike in Sales of Special
Products 4
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Influential persons often have many friends. Kate is one of the
persons that have many friends in this social network. For more
Kates, its not as easy as you might think! How to Find Kate? 5
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Given a digraph and k>0, Find k seeds (Kates) to maximize
the number of influenced persons. Influence Maximization 6
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7 Theorem Proof
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Outline Kate Middleton effect Submodular Function Max
Independent Cascade 8
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What is a submodular function? Consider a function f on all
subsets of a set E. f is submodular if
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Max Coverage Given a collection C of subsets of a set E, find a
subcollection C of C, with |C|63%) of the number of nodes that any
size-k set could activate.
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Proof of Submodularity 32
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Decision Version of InfMax in IC 34 Theorem Corollary Is it in
NP?
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35 Theorem (Chen et al., 2010) Proof
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Disadvantage Lack of efficiency. Computing m (S) is # P-hard
under both IC and LT models. Selecting a new vertex u that provides
the largest marginal gain m (S+u) - m (S), which can only be
approximated by Monte-Carlo simulations (10,000 trials). Assume a
weighted social graph as input. How to learn influence
probabilities from history?
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Monte-Carlo Method 38 Buffon's needle
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Research done by our group in UTD 39
Slide 40
Zaixin Lu, Wei Zhang, Weili Wu, Bin Fu, Ding- Zhu Du:
Approximation and Inapproximation for the Influence Maximization
Problem in Social Networks under Deterministic Linear Threshold
Model. ICDCS Workshops 2011: 160-165ICDCS Workshops 2011 40
Slide 41
Zaixin Lu, Lidan Fan, Weili Wu, Bhavani Thuraisingham and Kai
Yang, Efficient influence spread estimation for influence
maximization under the linear threshold model, Computational Social
Networks, 1 (2014) 41
Slide 42
Wen Xu, Zaixin Lu, Weili Wu, Zhiming Chen: A novel approach to
online social influence maximization. Social Netw. Analys. Mining
4(1) (2014) 42
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Editor-in-Chief: Ding-Zhu Du My T. Thai Computational Social
Networks 43 A New Springer Journal Welcome to Submit Papers
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Yuqing Zhu, Zaixin Lu, Yuanjun Bi, Weili Wu, Yiwei Jiang,
Deying Li: Influence and Profit: Two Sides of the Coin. ICDM 2013:
1301-1306 44
Slide 45
Lidan Fan, Zaixin Lu, Weili Wu, Yuanjun Bi, Ailian Wang: A New
Model for Product Adoption over Social Networks. COCOON 2013:
737-746COCOON 2013 45
Slide 46
Songsong Li, Yuqing Zhu, Deying Li, Donghyun Kim, Huan Ma,
Hejiao Huang: Influence maximization in social networks with user
attitude modification. ICC 2014: 3913-3918ICC 2014 46
