A Popularity Scaled Latent Space Model for Large-Scale Directed Social Network

41 Pages Posted: 16 May 2018 Last revised: 20 May 2018

See all articles by Xiangyu Chang

Xiangyu Chang

Xi'an Jiaotong University (XJTU) - School of Management

Danyang Huang

Peking University

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: May 2, 2018

Abstract

Large-scale directed social network data often involve degree heterogeneity, reciprocity, and transitivity properties. A sensible network generating model should take these features into consideration. To this end, we propose a popularity scaled latent space model for the large-scale directed network structure formulation. It assumes for each node a position in a hypothetically assumed latent space. Then, the nodes close (far away) to each other should have larger (less) probability to be connected. As a consequence, the reciprocity and transitivity properties can be analytically derived. In addition to that, we assume for each node a popularity parameter. Those nodes with larger (smaller) popularity are more (less) likely to be followed by other nodes. By assuming different distributions for popularity parameters, different types of degree heterogeneity can be modeled. Furthermore, based on the proposed model, a comprehensive probabilistic index is constructed for link prediction. Its finite sample performance is demonstrated by extensive simulation studies and a Sina Weibo (a Twitter-type social network in China) dataset. The performances are competitive.

Keywords: Latent Space Model, Link Prediction, Large-Scale Social

Suggested Citation

Chang, Xiangyu and Huang, Danyang and Wang, Hansheng, A Popularity Scaled Latent Space Model for Large-Scale Directed Social Network (May 2, 2018). Available at SSRN: https://ssrn.com/abstract=3172160 or http://dx.doi.org/10.2139/ssrn.3172160

Xiangyu Chang

Xi'an Jiaotong University (XJTU) - School of Management ( email )

28,Xianning West Road
Xi'an, Shaanxi 710049
China

Danyang Huang

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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