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Influence Propagation in Graphs and ...

Lee, Eun Jee.

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Influence Propagation in Graphs and Applications to Network Analysis.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Influence Propagation in Graphs and Applications to Network Analysis./
作者:	Lee, Eun Jee.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:	108 p.
附註:	Source: Dissertations Abstracts International, Volume: 80-04, Section: B.
Contained By:	Dissertations Abstracts International80-04B.
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10829636
ISBN:	9780438535275

Influence Propagation in Graphs and Applications to Network Analysis.
Lee, Eun Jee.

Influence Propagation in Graphs and Applications to Network Analysis. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 108 p.

Source: Dissertations Abstracts International, Volume: 80-04, Section: B.

Thesis (Ph.D.)--Princeton University, 2018.

This item must not be sold to any third party vendors.

The phenomenon of influence propagation is concerned with how influence spreads in a network from a set of seeds. One of the most widely adopted models that describe such propagation phenomena is the independent cascade model, where influence propagates from the seed-nodes along the edges with independent probabilities. This thesis focuses on influence propagation in the independent cascade model and studies its applications to various problems concerned with graphs and networks. A fundamental problem in influence propagation is to measure the size of the influence spread, and perhaps, the most basic measure is the influence, the expected number of nodes that a seed set can influence in the independent cascade model. Unfortunately, this is #P hard to compute. Thus, many estimators on the influence were proposed. In this thesis, we propose deterministic bounds on the influence. We develop mainly two types of bounds: (i) using the spectral norm of a modified Hazard matrix to handle sensitive edges and (ii) exploiting r-nonbacktracking walks and Fortuin-Kasteleyn-Ginibre (FKG) type inequalities to compute bounds via message passing algorithms. We then study influence maximization problem, which aims to select the k nodes in a network that maximize the influence when the propagation starts from these k nodes. In this thesis, we investigate this problem in boundary cases and provide solutions to tree networks. Finally, this thesis introduces the mutual influence (MI), a measure of how similarly influential two nodes in a network are. We establish properties of the MI and investigate its application to clustering. We propose two clustering methods based on MI: (i) we use MI as a similarity metric for spectral clustering, and (ii) we use MI to identify cluster leaders that are individually influential but not influential on each other.

ISBN: 9780438535275Subjects--Topical Terms:

1669109
Applied Mathematics.

Influence Propagation in Graphs and Applications to Network Analysis.
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520 $a The phenomenon of influence propagation is concerned with how influence spreads in a network from a set of seeds. One of the most widely adopted models that describe such propagation phenomena is the independent cascade model, where influence propagates from the seed-nodes along the edges with independent probabilities. This thesis focuses on influence propagation in the independent cascade model and studies its applications to various problems concerned with graphs and networks. A fundamental problem in influence propagation is to measure the size of the influence spread, and perhaps, the most basic measure is the influence, the expected number of nodes that a seed set can influence in the independent cascade model. Unfortunately, this is #P hard to compute. Thus, many estimators on the influence were proposed. In this thesis, we propose deterministic bounds on the influence. We develop mainly two types of bounds: (i) using the spectral norm of a modified Hazard matrix to handle sensitive edges and (ii) exploiting r-nonbacktracking walks and Fortuin-Kasteleyn-Ginibre (FKG) type inequalities to compute bounds via message passing algorithms. We then study influence maximization problem, which aims to select the k nodes in a network that maximize the influence when the propagation starts from these k nodes. In this thesis, we investigate this problem in boundary cases and provide solutions to tree networks. Finally, this thesis introduces the mutual influence (MI), a measure of how similarly influential two nodes in a network are. We establish properties of the MI and investigate its application to clustering. We propose two clustering methods based on MI: (i) we use MI as a similarity metric for spectral clustering, and (ii) we use MI to identify cluster leaders that are individually influential but not influential on each other.
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