Understanding Influence Maximization via Higher-Order Decomposition

TL;DR

This paper introduces a higher-order analysis framework for influence maximization in social networks using Sobol indices, leading to an improved seed selection algorithm that accounts for complex seed interactions.

Contribution

It presents a novel higher-order decomposition approach for influence spread analysis and proposes the SIM algorithm to enhance influence maximization by considering seed interactions.

Findings

SIM outperforms existing algorithms in effectiveness

The higher-order analysis accurately identifies key seed interactions

Experiments on synthetic and real-world graphs validate the approach

Abstract

Given its vast application on online social networks, Influence Maximization (IM) has garnered considerable attention over the last couple of decades. Due to the intricacy of IM, most current research concentrates on estimating the first-order contribution of the nodes to select a seed set, disregarding the higher-order interplay between different seeds. Consequently, the actual influence spread frequently deviates from expectations, and it remains unclear how the seed set quantitatively contributes to this deviation. To address this deficiency, this work dissects the influence exerted on individual seeds and their higher-order interactions utilizing the Sobol index, a variance-based sensitivity analysis. To adapt to IM contexts, seed selection is phrased as binary variables and split into distributions of varying orders. Based on our analysis with various Sobol indices, an IM algorithm dubbed SIM is proposed to improve the performance of current IM algorithms by over-selecting nodes followed by strategic pruning. A case study is carried out to demonstrate that the explanation of the impact effect can dependably identify the key higher-order interactions among seeds. SIM is empirically proved to be superior in effectiveness and competitive in efficiency by experiments on synthetic and real-world graphs.