Graphs and hypergraphs provide powerful abstractions for modeling interactions among a set of entities of interest and have been attracting a growing interest in the literature thanks to many successful applications in several fields. In particular, they are rapidly expanding in domains such as chemistry and biology, especially in the areas of drug discovery and molecule generation. One of the areas witnessing the fasted growth is the chemical reactions field, where chemical reactions can be naturally encoded as directed hyperedges of a hypergraph. In this paper, we address the chemical reaction classification problem by introducing the notation of a Directed Line Graph (DGL) associated with a given directed hypergraph. On top of it, we build the Directed Line Graph Network (DLGNet), the first spectral-based Graph Neural Network (GNN) expressly designed to operate on a hypergraph via its DLG transformation. The foundation of DLGNet is a novel Hermitian matrix, the Directed Line Graph Laplacian, which compactly encodes the directionality of the interactions taking place within the directed hyperedges of the hypergraph thanks to the DLG representation. The Directed Line Graph Laplacian enjoys many desirable properties, including admitting an eigenvalue decomposition and being positive semidefinite, which make it well-suited for its adoption within a spectral-based GNN. Through extensive experiments on chemical reaction datasets, we show that DGLNet significantly outperforms the existing approaches, achieving on a collection of real-world datasets an average relative-percentage-difference improvement of 33.01%, with a maximum improvement of 37.71%.
Hyperlink prediction aims to predict interactions among multiple entries, constituting a practical yet challenging problem in the literature. While a handful of solutions have been proposed, they generally operate on the entire hypergraph. A practical subgraph-based solution not only enables better identification of localized characteristics of the central hyperedge but also alleviates scalability concerns. In this study, we present SSF, an innovative hyperlink prediction methodology based on Subgraph Structural Features. The rationale behind SSF is that hyperedges and non-hyperedges exhibit distinct local patterns, which can be unveiled through the assimilation of subgraph structural features. To this end, we utilize well-established structural heuristics such as walks and loops as the fundamental building blocks. We commence by extracting a subgraph encompassing each focal hyperedge, subsequently integrating an edge weakening scheme to facilitate feature extraction from the initial subgraph and its variations. The extracted feature vector is interpretable, and the designed edge weakening scheme empowers SSF with an adaptive capability to handle hypergraphs with varying densities. Lastly, a multilayer perceptron classifier is trained for prediction. Experiment results on ten real-world hypergraph networks demonstrate the effectiveness of the proposed approach.
Road network is a critical infrastructure powering many applications including transportation, mobility and logistics in real life. To leverage the input of a road network across these different applications, it is necessary to learn the representations of the roads in the form of vectors, which is named \emph{road network representation learning} (RNRL). While several models have been proposed for RNRL, they capture the pairwise relationships/connections among roads only (i.e., as a simple graph), and fail to capture among roads the high-order relationships (e.g., those roads that jointly form a local region usually have similar features such as speed limit) and long-range relationships (e.g., some roads that are far apart may have similar semantics such as being roads in residential areas). Motivated by this, we propose to construct a \emph{hypergraph}, where each hyperedge corresponds to a set of multiple roads forming a region. The constructed hypergraph would naturally capture the high-order relationships among roads with hyperedges. We then allow information propagation via both the edges in the simple graph and the hyperedges in the hypergraph in a graph neural network context. The graph reconstruction and hypergraph reconstruction tasks are conventional ones and can capture structural information. The hyperedge classification task can capture long-range relationships between pairs of roads that belong to hyperedges with the same label. We call the resulting model \emph{HyperRoad}. We further extend HyperRoad to problem settings when additional inputs of road attributes and/or trajectories that are generated on the roads are available.
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, 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 HyperGene bears three distinctive advantages. First, it is capable of ingesting the labeling information when available, but more importantly, it is mainly designed in the self-supervised fashion which significantly broadens its applicability. Second, at the heart of the proposed HyperGene 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. The extensive experimental results demonstrate that: (1) HyperGene achieves up to 5.69% improvements in hyperedge classification, and (2) improves pre-training efficiency by up to 42.80% on average.
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise interactions. In such cases, the relationships in the data are better represented as hyperedges (set of entities) of a non-uniform hypergraph. While there have been works on principled methods for learning representations of nodes of a hypergraph, these approaches are limited in their applicability to tasks on non-uniform hypergraphs (hyperedges with different cardinalities). In this work, we exploit the incidence structure to develop a hypergraph neural network to learn provably expressive representations of variable sized hyperedges which preserve local-isomorphism in the line graph of the hypergraph, while also being invariant to permutations of its constituent vertices. Specifically, for a given vertex set, we propose frameworks for (1) hyperedge classification and (2) variable sized expansion of partially observed hyperedges which captures the higher order interactions among vertices and hyperedges. We evaluate performance on multiple real-world hypergraph datasets and demonstrate consistent, significant improvement in accuracy, over state-of-the-art models.
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly in the hypergraph context, despite a large body of prior work that has shown the utility of deep learning over graphs and sets. Building upon these recent advances, we propose \textit{Deep Hyperedges} (DHE), a modular framework that jointly uses contextual and permutation-invariant vertex membership properties of hyperedges in hypergraphs to perform classification and regression in transductive and inductive learning settings. In our experiments, we use a novel random walk procedure and show that our model achieves and, in most cases, surpasses state-of-the-art performance on benchmark datasets. Additionally, we study our framework's performance on a variety of diverse, non-standard hypergraph datasets and propose several avenues of future work to further enhance DHE.