Confluence: Conformity Influence in Large Social Networks

Introduction:

Conformity is a type of social influence involving a change in opinion or behavior in order to fit with a group. There is a model called Confluence Model to formalize the effects and quantification of the conformity into a probabilistic model. Confluence Model is also a scaled up for large social networks. Many studies of psychology,economics showed departure from one group to another, influencing behavior of one group over the other. There are bulk of studies on social influence analysis. Most of the works focused on the qualitative studies.

Problem Definitions:

Let G=(V,E) denote the social network,where V is a set of |V|=N users and E is a subset of V*V where E is the set of relationships between users. A user behavior is denote as (a,vi,t) to represent user vi performed action a which belongs to A at time t. Input of the problem consists of two components, i.e an attribute augmented network G=(V,E,C,X) and action history A. X denotes an N*d attribute matrix with an element xij indicating jth attribute of user vi. And C is N*m matrix to represent group's memberships.

The goal of the model is to study how a user's behavior conforms to her peer friends and the groups that she belongs to.

Individual Conformity:

Mathematically speaking individual conformity is

Peer Conformity:

Peer Conformity is defined to represent how likely the user v's behavior is influenced by one particular friend.

And the peer conformity is

Group Conformity:

Problem is to formalize finding a model parameter that satisfies

and to predict future actions in the social network.

Confluence Model Framework:

Conformity-aware Factor Graph Model:

Factor graph provides a method to factorize the global probability as a product of "local" functions,each of which depends on a subset of the variables in the graph. Three types of conformity (individual conformity factor,peer conformity, and group conformity) factors combined and we get a log-likelihood objective function.

Feature Definition:

4 features are helpful to predict the task.

Opinion Leader: Whether the user posting is an opinion leader or not.

Structure Hole: Whether the user is a structural hole spinner.

Social Ties: a binary feature is defined as whether a tie between two users is strong or weak tie.

Social Balance: a binary feature is defined for each of the triad structure.

Evaluation:

The paper presenting the model have tested their model using the datasets of Flickr, Gowalla, Weibo, Co-Author and they get 0.7383,0.9644, 0.7572,0.9579 accuracy in the respective datasets.

References:

To get the detailed model and the scaled up version,please refer to the following paper:

http://keg.cs.tsinghua.edu.cn/jietang/publications/KDD13-Tang-et-al-Conformity-Influence.pdf

[SIGKDD'13]