A new preferential model with homophily for recommender systems

TL;DR

This paper introduces a novel social network model combining rich-get-richer and homophily effects, demonstrating power-law degree distributions and providing statistical inference methods, with validation on simulated and real data.

Contribution

It proposes a new evolving social network model integrating homophily and rich-get-richer phenomena, with theoretical analysis and practical validation.

Findings

The KPA model exhibits power-law degree distributions for each group.

The CLT for MLE of parameters is established.

Model validation through simulated and real data examples.

Abstract

"Rich-get-richer" and "homophily" are two important phenomena in evolving social networks. "Rich-get-richer" means people with higher followings are more likely to attract new fans, and "homophily" means people prefer to bond with others of the same social group or who have some other attribute in common. To formalize the phenomena simultaneously in the context of an evolving social network, we consider a K-groups preferential attachment (KPA) network model, which is helpful for the social networks recommender system. The main contribution of this paper is to propose a new evolving social network model with the mechanisms of rich-get-richer and homophily. We show that the KPA model exhibits a power-law degree distribution for each group and prove the central limit theorem (CLT) for the maximum likelihood estimation (MLE) of the parameters in the KPA model. We illustrate our results through simulated data and explore the usage of this model with real data examples.