Influence-Based Community Detection Lecture 6-4 Influence-Based Community Detection Ding-Zhu Du University of Texas at Dallas First, I want to thank you for you presence. ********In this presentation I will try to introduce The social network which is a theoretical structure to study relationships between individuals, groups, organizations, or even entire societies.  It is related to a wide range of disciplines. These disciplines include, but are not limited to information science, biology, economics, geography, communication studies, and so on.. The study of social networks begins with the late eighteenth century, two sociologists (Émile [ei'mi:l] Durkheim and Ferdinand ['fɝdənænd] Fer迪南de Tönnies) foreshadowed the idea of social networks in their theories and research of social groups. Nowadays, we study social networks using network analysis to identify social communities, pick influential person, and design good software. lidong.wu@utdallas.edu

Model-Based Detection Community Detection Accurate or not? Formulation (Model) Solve formulated problem

Influence-based Model

Idea People in a same community share common interests in - clothes, music, beliefs, movies, food, etc. Influence each other strongly. People in a same community share common interests in the same brand of clothes, same kind of music, movies, food, etc. They influence each other strongly. Therefore, within three steps, the influence is strong. When companies focus first on meeting the needs of the people they serve, they don’t have to spend big money to attract new customers. And when they stay close to their communities they don’t need market research to tell them what people want. innovation

Definition

5 2 3 4 1

5 2 3 4 1

Model

Lemma 1 Proof

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Lemma 2

Proof basis

induction

Induction (continue)

Induction (continue)

Theorem 1

Theorem 2 Proof is given later.

General Theory

Theorem

Example 1: A Connection-based Model

Lemma Proof

Theorem 1 Theorem 2

Example 2: Global Influence “influence in large part is the ability to reach a crucial man through the right channels, and the more the channels in reserve the better.“ --- Pool and Kochen (1978)

Global Influence Global Influence allows paths with cycles!!

Analogy of Connection-based and Influence-based Models Edge weight w(I,j) is the probability of node j receiving influence from node i.

Influence-based Modularity

References

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