Finding influential users for different time bounds in social networks using multi-objective optimization

Online social networks play an important role in marketing services. Influence maximization is a major challenge, in which the goal is to find the most influential users in a social network. Increasing the number of influenced users at the end of a diffusion process while decreasing the time of diffusion are two main objectives of the influence maximization problem. The goal of this paper is to find multiple sets of influential users such that each of them is the best set to spread influence for a specific time bound. Considering two conflicting objectives, increasing influence and decreasing diffusion time, we employ the NSGA-II algorithm which is a powerful algorithm in multi-objective optimization to find different seed sets with high influence at different diffusion times. Since social networks are large, computing influence and diffusion time of all chromosomes in each iteration will be challenging and computationally expensive. Therefore, we propose two methods which can estimate the expected influence and diffusion time of a seed set in an efficient manner. Providing the set of all potentially optimal solutions helps a decision maker evaluate the trade-offs between the two objectives, i.e., the number of influenced users and diffusion time. In addition, we develop an approach for selecting seed sets, which have optimal influence for specific time bounds, from the resulting Pareto front of the NSGA-II. Finally, we show that applying our algorithm to real social networks outperforms existing algorithms for the influence maximization problem. The results show a good compromise between the two objectives and the final seed sets result in high influence for different time bounds

A Multi-Transformation Evolutionary Framework for Influence Maximization in Social Networks

Influence maximization is a crucial issue for mining the deep information of social networks, which aims to select a seed set from the network to maximize the number of influenced nodes. To evaluate the influence spread of a seed set efficiently, existing studies have proposed transformations with lower computational costs to replace the expensive Monte Carlo simulation process. These alternate transformations, based on network prior knowledge, induce different search behaviors with similar characteristics to various perspectives. Specifically, it is difficult for users to determine a suitable transformation a priori. This article proposes a multi-transformation evolutionary framework for influence maximization (MTEFIM) with convergence guarantees to exploit the potential similarities and unique advantages of alternate transformations and to avoid users manually determining the most suitable one. In MTEFIM, multiple transformations are optimized simultaneously as multiple tasks. Each transformation is assigned an evolutionary solver. Three major components of MTEFIM are conducted via: 1) estimating the potential relationship across transformations based on the degree of overlap across individuals of different populations, 2) transferring individuals across populations adaptively according to the inter-transformation relationship, and 3) selecting the final output seed set containing all the transformation's knowledge. The effectiveness of MTEFIM is validated on both benchmarks and real-world social networks. The experimental results show that MTEFIM can efficiently utilize the potentially transferable knowledge across multiple transformations to achieve highly competitive performance compared to several popular IM-specific methods. The implementation of MTEFIM can be accessed at https://github.com/xiaofangxd/MTEFIM.Comment: This work has been submitted to the IEEE Computational Intelligence Magazine for publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Large-scale multi-objective influence maximisation with network downscaling

Finding the most influential nodes in a network is a computationally hard problem with several possible applications in various kinds of network-based problems. While several methods have been proposed for tackling the influence maximisation (IM) problem, their runtime typically scales poorly when the network size increases. Here, we propose an original method, based on network downscaling, that allows a multi-objective evolutionary algorithm (MOEA) to solve the IM problem on a reduced scale network, while preserving the relevant properties of the original network. The downscaled solution is then upscaled to the original network, using a mechanism based on centrality metrics such as PageRank. Our results on eight large networks (including two with $\sim$50k nodes) demonstrate the effectiveness of the proposed method with a more than 10-fold runtime gain compared to the time needed on the original network, and an up to $82\%$ time reduction compared to CELF

Compressing networks with super nodes

Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network to be partitioned into a smaller network of 'super nodes', each super node comprising one or more nodes in the original network. To define the seeds of our super nodes, we apply the 'CoreHD' ranking from dismantling and decycling. We test our approach through the analysis of two common methods for community detection: modularity maximization with the Louvain algorithm and maximum likelihood optimization for fitting a stochastic block model. Our results highlight that applying community detection to the compressed network of super nodes is significantly faster while successfully producing partitions that are more aligned with the local network connectivity, more stable across multiple (stochastic) runs within and between community detection algorithms, and overlap well with the results obtained using the full network