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Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network alignment is sparse due to the exponentially growing solution space and lack of high-order discrepancy measures. To fill this gap, we propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. To handle the large solution space, multiple networks are decomposed into smaller aligned clusters via the fused Gromov-Wasserstein (FGW) barycenter. To depict high-order relationships across multiple networks, the FGW distance is generalized to the multi-marginal setting, based on which networks can be aligned jointly. A fast proximal point method is further developed with guaranteed convergence to a local optimum. Extensive experiments and analysis show that our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability.

 

Despite the prevalence of hypergraphs in a variety of high-impact applications, there are relatively few works on hypergraph representation learning, most of which primarily focus on hyperlink prediction, and are often restricted to the transductive learning setting. Among others, a major hurdle for effective hypergraph representation learning lies in the label scarcity of nodes and/or hyperedges. To address this issue, this paper presents an end-to-end, bi-level pre-training strategy with Graph Neural Networks for hypergraphs. The proposed framework named HyperGRL bears three distinctive advantages. First, it is mainly designed in the self-supervised fashion which has broad applicability, and meanwhile it is also capable of ingesting the labeling information when available. Second, at the heart of the proposed HyperGRL are two carefully designed pretexts, one on the node level and the other on the hyperedge level, which enable us to encode both the local and the global context in a mutually complementary way. Third, the proposed framework can work in both transductive and inductive settings. When applying the two proposed pretexts in tandem, it can accelerate the adaptation of the knowledge from the pre-trained model to downstream applications in the transductive setting, thanks to the bi-level nature of the proposed method. Extensive experiments demonstrate that: (1) HyperGRL achieves up to 5.69% improvements in hyperedge classification, and (2) improves pre-training efficiency by up to 42.80% on average 

Bundle recommendation is an emerging research direction in the recommender system with the focus on recommending customized bundles of items for users. Although Graph Neural Networks (GNNs) have been applied to this problem and achieved superior performance, existing methods underexplore the graph-level GNN methods, which exhibit great potential in traditional recommender system. Furthermore, they usually lack the transferability from one domain with sufficient supervision to another domain which might suffer from the label scarcity issue. In this work, we propose a subgraph-based Graph Neural Network model, SuGeR, for bundle recommendation to handle these limitations. SuGeR generates heterogeneous subgraphs around the user-bundle pairs and then maps those subgraphs to the users' preference predictions via neural relational graph propagation. Experimental results show that SUGER significantly outperforms the state-of-the-art baselines in the basic and the transfer bundle recommendation tasks by up to 77.17% by NDCG@40. The source code is available at: https://github.com/Zhang-Zhenning/SUGER. 

Knowledge graph reasoning plays a pivotal role in many real-world applications, such as network alignment, computational fact-checking, recommendation, and many more. Among these applications, knowledge graph completion (KGC) and multi-hop question answering over knowledge graph (Multi-hop KGQA) are two representative reasoning tasks. In the vast majority of the existing works, the two tasks are considered separately with different models or algorithms. However, we envision that KGC and Multi-hop KGQA are closely related to each other. Therefore, the two tasks will benefit from each other if they are approached adequately. In this work, we propose a neural model named BiNet to jointly handle KGC and multi-hop KGQA, and formulate it as a multi-task learning problem. Specifically, our proposed model leverages a shared embedding space and an answer scoring module, which allows the two tasks to automatically share latent features and learn the interactions between natural language question decoder and answer scoring module. Compared to the existing methods, the proposed BiNet model addresses both multi-hop KGQA and KGC tasks simultaneously with superior performance. Experiment results show that BiNet outperforms state-of-the-art methods on a wide range of KGQA and KGC benchmark datasets. 

The past decades have witnessed the prosperity of graph mining, with a multitude of sophisticated models and algorithms designed for various mining tasks, such as ranking, classification, clustering and anomaly detection. Generally speaking, the vast majority of the existing works aim to answer the following question, that is, given a graph, what is the best way to mine it? In this paper, we introduce the graph sanitation problem, to an- swer an orthogonal question. That is, given a mining task and an initial graph, what is the best way to improve the initially provided graph? By learning a better graph as part of the input of the mining model, it is expected to benefit graph mining in a variety of settings, ranging from denoising, imputation to defense. We formulate the graph sanitation problem as a bilevel optimization problem, and fur- ther instantiate it by semi-supervised node classification, together with an effective solver named GaSoliNe. Extensive experimental results demonstrate that the proposed method is (1) broadly appli- cable with respect to various graph neural network models and flexible graph modification strategies, (2) effective in improving the node classification accuracy on both the original and contaminated graphs in various perturbation scenarios. In particular, it brings up to 25% performance improvement over the existing robust graph neural network methods. 

How can we identify the same or similar users from a collection of social network platforms (e.g., Facebook, Twitter, LinkedIn, etc.)? Which restaurant shall we recommend to a given user at the right time at the right location? Given a disease, which genes and drugs are most relevant? Multi-way association, which identifies strongly correlated node sets from multiple input networks, is the key to answering these questions. Despite its importance, very few multi-way association methods exist due to its high complexity. In this paper, we formulate multi-way association as a convex optimization problem, whose optimal solution can be obtained by a Sylvester tensor equation. Furthermore, we propose two fast algorithms to solve the Sylvester tensor equation, with a linear time and space complexity. We further provide theoretic analysis in terms of the sensitivity of the Sylvester tensor equation solution. Empirical evaluations demonstrate the efficacy of the proposed method. 

Networks (i.e., graphs) are often collected from multiple sources and platforms, such as social networks extracted from multiple online platforms, team-specific collaboration networks within an organization, and inter-dependent infrastructure networks, etc. Such networks from different sources form the multi-networks, which can exhibit the unique patterns that are invisible if we mine the individual network separately. However, compared with single-network mining, multi-network mining is still under-explored due to its unique challenges. First ( multi-network models ), networks under different circumstances can be modeled into a variety of models. How to properly build multi-network models from the complex data? Second ( multi-network mining algorithms ), it is often nontrivial to either extend single-network mining algorithms to multi-networks or design new algorithms. How to develop effective and efficient mining algorithms on multi-networks? The objectives of this tutorial are to: (1) comprehensively review the existing multi-network models, (2) elaborate the techniques in multi-network mining with a special focus on recent advances, and (3) elucidate open challenges and future research directions. We believe this tutorial could be beneficial to various application domains, and attract researchers and practitioners from data mining as well as other interdisciplinary fields. 

Logical queries constitute an important subset of questions posed in knowledge graph question answering systems. Yet, effectively answering logical queries on large knowledge graphs remains a highly challenging problem. Traditional subgraph matching based methods might suffer from the noise and incompleteness of the underlying knowledge graph, often with a prolonged online response time. Recently, an alternative type of method has emerged whose key idea is to embed knowledge graph entities and the query in an embedding space so that the embedding of answer entities is close to that of the query. Compared with subgraph matching based methods, it can better handle the noisy or missing information in knowledge graph, with a faster online response. Promising as it might be, several fundamental limitations still exist, including the linear transformation assumption for modeling relations and the inability to answer complex queries with multiple variable nodes. In this paper, we propose an embedding based method (NewLook) to address these limitations. Our proposed method offers three major advantages. First (Applicability), it supports four types of logical operations and can answer queries with multiple variable nodes. Second (Effectiveness), the proposed NewLook goes beyond the linear transformation assumption, and thus consistently outperforms the existing methods. Third (Efficiency), compared with subgraph matching based methods, NewLook is at least 3 times faster in answering the queries; compared with the existing embed-ding based methods, NewLook bears a comparable or even faster online response and offline training time.