Influence maximization in multilayer networks based on adaptive coupling degree

Influence Maximization(IM) aims to identify highly influential nodes to maximize influence spread in a network. Previous research on the IM problem has mainly concentrated on single-layer networks, disregarding the comprehension of the coupling structure that is inherent in multilayer networks. To solve the IM problem in multilayer networks, we first propose an independent cascade model (MIC) in a multilayer network where propagation occurs simultaneously across different layers. Consequently, a heuristic algorithm, i.e., Adaptive Coupling Degree (ACD), which selects seed nodes with high spread influence and a low degree of overlap of influence, is proposed to identify seed nodes for IM in a multilayer network. By conducting experiments based on MIC, we have demonstrated that our proposed method is superior to the baselines in terms of influence spread and time cost in 6 synthetic and 4 real-world multilayer networks

Recommender Systems

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports

MCDAN: a Multi-scale Context-enhanced Dynamic Attention Network for Diffusion Prediction

Information diffusion prediction aims at predicting the target users in the information diffusion path on social networks. Prior works mainly focus on the observed structure or sequence of cascades, trying to predict to whom this cascade will be infected passively. In this study, we argue that user intent understanding is also a key part of information diffusion prediction. We thereby propose a novel Multi-scale Context-enhanced Dynamic Attention Network (MCDAN) to predict which user will most likely join the observed current cascades. Specifically, to consider the global interactive relationship among users, we take full advantage of user friendships and global cascading relationships, which are extracted from the social network and historical cascades, respectively. To refine the model's ability to understand the user's preference for the current cascade, we propose a multi-scale sequential hypergraph attention module to capture the dynamic preference of users at different time scales. Moreover, we design a contextual attention enhancement module to strengthen the interaction of user representations within the current cascade. Finally, to engage the user's own susceptibility, we construct a susceptibility label for each user based on user susceptibility analysis and use the rank of this label for auxiliary prediction. We conduct experiments over four widely used datasets and show that MCDAN significantly overperforms the state-of-the-art models. The average improvements are up to 10.61% in terms of Hits@100 and 9.71% in terms of MAP@100, respectively

Constructing hypergraphs from temporal data

A wide range of systems across the social and natural sciences produce temporal data consisting of interaction events among nodes in disjoint sets. Online shopping, for example, generates purchasing events of the form (user, product, time of purchase), and mutualistic interactions in plant-pollinator systems generate pollination events of the form (insect, plant, time of pollination). These data sets can be meaningfully modeled as temporal hypergraph snapshots in which multiple nodes within one set (i.e. online shoppers) share a hyperedge if they interacted with a common node in the opposite set (i.e. purchased the same product) within a given time window, allowing for the application of a range of hypergraph analysis techniques. However, it is often unclear how to choose the number and duration of these temporal snapshots, which have a strong influence on the final hypergraph representations. Here we propose a principled, efficient, nonparametric solution to this longstanding problem by extracting temporal hypergraph snapshots that optimally capture structural regularities in temporal event data according to the minimum description length principle. We demonstrate our methods on real and synthetic datasets, finding that they can recover planted artificial hypergraph structure in the presence of considerable noise and reveal meaningful activity fluctuations in human mobility data

Quantum and Classical Multilevel Algorithms for (Hyper)Graphs

Combinatorial optimization problems on (hyper)graphs are ubiquitous in science and industry. Because many of these problems are NP-hard, development of sophisticated heuristics is of utmost importance for practical problems. In recent years, the emergence of Noisy Intermediate-Scale Quantum (NISQ) computers has opened up the opportunity to dramaticaly speedup combinatorial optimization. However, the adoption of NISQ devices is impeded by their severe limitations, both in terms of the number of qubits, as well as in their quality. NISQ devices are widely expected to have no more than hundreds to thousands of qubits with very limited error-correction, imposing a strict limit on the size and the structure of the problems that can be tackled directly. A natural solution to this issue is hybrid quantum-classical algorithms that combine a NISQ device with a classical machine with the goal of capturing “the best of both worlds”. Being motivated by lack of high quality optimization solvers for hypergraph partitioning, in this thesis, we begin by discussing classical multilevel approaches for this problem. We present a novel relaxation-based vertex similarity measure termed algebraic distance for hypergraphs and the coarsening schemes based on it. Extending the multilevel method to include quantum optimization routines, we present Quantum Local Search (QLS) – a hybrid iterative improvement approach that is inspired by the classical local search approaches. Next, we introduce the Multilevel Quantum Local Search (ML-QLS) that incorporates the quantum-enhanced iterative improvement scheme introduced in QLS within the multilevel framework, as well as several techniques to further understand and improve the effectiveness of Quantum Approximate Optimization Algorithm used throughout our work

Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications

Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the notion of $k$-cores, which proved useful with numerous applications for pairwise graphs, to hypergraphs. However, the previous extensions are based on an unrealistic assumption that hyperedges are fragile, i.e., a high-order relation becomes obsolete as soon as a single member leaves it. In this work, we propose a new substructure model, called ($k$, $t$)-hypercore, based on the assumption that high-order relations remain as long as at least $t$ fraction of the members remain. Specifically, it is defined as the maximal subhypergraph where (1) every node has degree at least $k$ in it and (2) at least $t$ fraction of the nodes remain in every hyperedge. We first prove that, given $t$ (or $k$), finding the ($k$, $t$)-hypercore for every possible $k$ (or $t$) can be computed in time linear w.r.t the sum of the sizes of hyperedges. Then, we demonstrate that real-world hypergraphs from the same domain share similar ($k$, $t$)-hypercore structures, which capture different perspectives depending on $t$. Lastly, we show the successful applications of our model in identifying influential nodes, dense substructures, and vulnerability in hypergraphs.Comment: 24 pages, 14 figure