[Paper Review] Revisiting Non-Progressive Influence Models: Scalable Influence Maximization

Golshan Golnari, T Amir Asiaee+2 more|arXiv (Cornell University)|Dec 18, 2014

Complex Network Analysis Techniques20 references3 citations

TL;DR

This paper introduces the Heat Conduction (HC) model, a novel non-progressive influence model that captures reversible user behavior in social networks, unifying and extending existing models like Voter and non-progressive LT. It proposes C2Greedy, a scalable, greedy algorithm with closed-form computations for influence spread and seed selection, achieving near-optimal influence maximization in large networks with provable guarantees and superior performance over state-of-the-art methods.

ABSTRACT

While influence maximization in social networks has been studied extensively in computer science community for the last decade the focus has been on the progressive influence models, such as independent cascade (IC) and Linear threshold (LT) models, which cannot capture the reversibility of choices. In this paper, we present the Heat Conduction (HC) model which is a non-progressive influence model with real-world interpretations. We show that HC unifies, generalizes, and extends the existing nonprogressive models, such as the Voter model [1] and non-progressive LT [2]. We then prove that selecting the optimal seed set of influential nodes is NP-hard for HC but by establishing the submodularity of influence spread, we can tackle the influence maximization problem with a scalable and provably near-optimal greedy algorithm. We are the first to present a scalable solution for influence maximization under nonprogressive LT model, as a special case of the HC model. In sharp contrast to the other greedy influence maximization methods, our fast and efficient C2GREEDY algorithm benefits from two analytically computable steps: closed-form computation for finding the influence spread as well as the greedy seed selection. Through extensive experiments on several large real and synthetic networks, we show that C2GREEDY outperforms the state-of-the-art methods, in terms of both influence spread and scalability.

Motivation & Objective

• To address the lack of scalable solutions for influence maximization under non-progressive models, which better reflect real-world reversible behaviors like switching service providers or research topics.
• To develop a unified, interpretable influence model that captures both social and non-social influences, such as media effects and user inertia.
• To prove that influence maximization under the HC model is NP-hard, necessitating efficient approximation algorithms.
• To design a scalable algorithm that avoids Monte Carlo simulations and enables fast computation on large networks.
• To validate the method on real-world networks, including a novel non-progressive cascade dataset on research topic adoption.

Proposed method

• Proposes the Heat Conduction (HC) model as a non-progressive influence model that generalizes Voter and non-progressive LT models, incorporating both social and non-social influences.
• Establishes submodularity of influence spread under HC, enabling the use of greedy approximation algorithms with theoretical performance guarantees.
• Derives a closed-form analytical expression for influence spread computation, eliminating the need for expensive Monte Carlo simulations.
• Develops a closed-form greedy selection rule for identifying the next best seed node, enabling O(1) per-node evaluation without simulation.
• Introduces the C2Greedy algorithm, which combines closed-form influence spread and seed selection to achieve high scalability and efficiency.
• Employs Markov chain theory and probability analysis to derive exact, analytically tractable solutions for influence dynamics under infinite time horizon.

Experimental results

Research questions

• RQ1 Can a non-progressive influence model be designed that captures real-world reversible behaviors such as switching between service providers or research topics?
• RQ2 Is influence maximization under the proposed Heat Conduction model NP-hard, and if so, can it be solved efficiently with provable approximation guarantees?
• RQ3 Can closed-form analytical solutions be derived for both influence spread and greedy seed selection under non-progressive models, eliminating reliance on Monte Carlo simulations?
• RQ4 How does the performance of the proposed C2Greedy algorithm compare to state-of-the-art methods in terms of influence spread and scalability on large real and synthetic networks?
• RQ5 Does the HC model better explain coexistence of multiple product adoptions compared to consensus-driven models like the Voter model?

Key findings

• C2Greedy achieves influence spread significantly higher than state-of-the-art methods on real and synthetic networks, including the MLWFW network of 10,604 authors and 168,918 edges.
• The algorithm completes influence maximization in minutes on networks with hundreds of thousands of nodes and nearly a million edges, demonstrating high scalability.
• C2Greedy outperforms not only standard baselines but also the 'most cited author' heuristic, which is a well-known method in academic influence settings.
• The most influential nodes under progressive models (e.g., IC, LT) do not necessarily remain influential under non-progressive models, highlighting the need for dedicated algorithms.
• The HC model successfully captures non-progressive cascades, such as research topic adoption in academia, where users switch between topics over time.
• The study presents the first publicly available real non-progressive cascade dataset based on citation networks, enabling future research in this domain.