Citation: Xie, L.; Huang, H.; Du, Q. A
Hierarchical Generative Embedding
Model for Influence Maximization in
Attributed Social Networks. Appl. Sci.
2022, 12, 1321. https://doi.org/
10.3390/app12031321
Academic Editors: Nikos D. Lagaros
and Vagelis Plevris
Received: 24 November 2021
Accepted: 20 January 2022
Published: 26 January 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
A Hierarchical Generative Embedding Model for Influence
Maximization in Attributed Social Networks
Luodi Xie
1
, Huimin Huang
2,
* and Qing Du
3
1
School of Computer Science, Sun Yat-sen University, Guangzhou 510275, China; xield@mail2.sysu.edu.cn
2
School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou 325035, China
3
School of Software, South China University of Technology, Guangzhou 510641, China; duqing@scut.edu.cn
* Correspondence: huanghm45@gmail.com
Abstract:
Nowadays, we use social networks such as Twitter, Facebook, WeChat and Weibo as
means to communicate with each other. Social networks have become so indispensable in our
everyday life that we cannot imagine what daily life would be like without social networks. Through
social networks, we can access friends’ opinions and behaviors easily and are influenced by them
in turn. Thus, an effective algorithm to find the top-K influential nodes (the problem of influence
maximization) in the social network is critical for various downstream tasks such as viral marketing,
anticipating natural hazards, reducing gang violence, public opinion supervision, etc. Solving the
problem of influence maximization in real-world propagation scenarios often involves estimating
influence strength (influence probability between two nodes), which cannot be observed directly.
To estimate influence strength, conventional approaches propose various humanly devised rules to
extract features of user interactions, the effectiveness of which heavily depends on domain expert
knowledge. Besides, they are often applicable for special scenarios or specific diffusion models.
Consequently, they are difficult to generalize into different scenarios and diffusion models. Inspired
by the powerful ability of neural networks in the field of representation learning, we designed a
hierarchical generative embedding model (HGE) to map nodes into latent space automatically. Then,
with the learned latent representation of each node, we proposed a HGE-GA algorithm to predict
influence strength and compute the top-K influential nodes. Extensive experiments on real-world
attributed networks demonstrate the outstanding superiority of the proposed HGE model and HGE-
GA algorithm compared with the state-of-the-art methods, verifying the effectiveness of the proposed
model and algorithm.
Keywords: influence maximization; influence strength; network embedding; social networks
1. Introduction
Fueled by the spectacular growth of the internet and Internet of Things, plenty of
social networks such as Facebook, Twitter and WeChat have sprung up, changed the
mode of interaction between people, and accelerated the development of viral marketing.
Originally from the idea of word-of-mouth advertising, viral marketing takes advantage of
trust among close social circles of friends, colleagues or families to promote a new product,
i.e., when a friend relationship affects a user making decisions on item selection [
1
,
2
].
Motivated by applications to early viral marketing, a new study area of influence diffusion
has thrived. Therein, the problem of influence maximization is to select a fixed size set of
seed nodes in a network to maximize the influence spread according to a specially designed
influence diffusion model. Figure 1 gives a toy example of social influence. The nodes
v
1
,
v
2
,
v
3
in black are the seed nodes which are initially active, and the nodes in gray color
are newly activated by the seed nodes. In terms of viral marketing, for example, if user
v
1
,
v
2
,
v
3
bought a product, their friends in a given social network will likely buy this product
because of the friend-to-friend influence.
Appl. Sci. 2022, 12, 1321. https://doi.org/10.3390/app12031321 https://www.mdpi.com/journal/applsci
