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Hypergraph Representation of Diagrams in Diagram Editors

AAAI Conferences

When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are well-known concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relations between components. Using such an internal model requires a method for translating diagrams into their hypergraph model. Such a graphical scanning method is proposed in this paper. The scanner makes use of a specification of the diagram language. Since the scanner also considers how diagram components are embedded into their context, it is applicable to a wide range of diagram languages and their hypergraph models.


Hypergraph Clustering: A Modularity Maximization Approach

arXiv.org Machine Learning

Clustering on hypergraphs has been garnering increased attention with potential applications in network analysis, VLSI design and computer vision, among others. In this work, we generalize the framework of modularity maximization for clustering on hypergraphs. To this end, we introduce a hypergraph null model, analogous to the configuration model on undirected graphs, and a node-degree preserving reduction to work with this model. This is used to define a modularity function that can be maximized using the popular and fast Louvain algorithm. We additionally propose a refinement over this clustering, by reweighting cut hyperedges in an iterative fashion. The efficacy and efficiency of our methods are demonstrated on several real-world datasets.


Deep Hyperedges: a Framework for Transductive and Inductive Learning on Hypergraphs

arXiv.org Machine Learning

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.


Hyper-SAGNN: a self-attention based graph neural network for hypergraphs

arXiv.org Machine Learning

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.


Molecular Hypergraph Grammar with its Application to Molecular Optimization

arXiv.org Machine Learning

This paper is concerned with a molecular optimization framework using variational autoencoders (VAEs). In this paradigm, VAE allows us to convert a molecular graph into/from its latent continuous vector, and therefore, the molecular optimization problem can be solved by continuous optimization techniques. One of the longstanding issues in this area is that it is difficult to always generate valid molecules. The very recent work called the junction tree variational autoencoder (JT-VAE) successfully solved this issue by generating a molecule fragment-by-fragment. While it achieves the state-of-the-art performance, it requires several neural networks to be trained, which predict which atoms are used to connect fragments and stereochemistry of each bond. In this paper, we present a molecular hypergraph grammar variational autoencoder (MHG-VAE), which uses a single VAE to address the issue. Our idea is to develop a novel graph grammar for molecular graphs called molecular hypergraph grammar (MHG), which can specify the connections between fragments and the stereochemistry on behalf of neural networks. This capability allows us to address the issue using only a single VAE. We empirically demonstrate the effectiveness of MHG-VAE over existing methods.