Related papers: Hypergraph Neural Sheaf Diffusion: A Symmetric Sim…

Inspired by recent findings that generative diffusion models learn semantically meaningful representations, we use them to discover the intrinsic hierarchical structure in biomedical 3D images using unsupervised segmentation. We show that…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…

Heterogeneous graphs, comprising diverse node and edge types connected through varied relations, are ubiquitous in real-world applications. Message-passing heterogeneous graph neural networks (HGNNs) have emerged as a powerful model class…

Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

We introduce Hyperdimensional Graph Learner (HDGL), a novel method for node classification and link prediction in graphs. HDGL maps node features into a very high-dimensional space (\textit{hyperdimensional} or HD space for short) using the…

Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…

The information diffusion performance of GCN and its variant models is limited by the adjacency matrix, which can lower their performance. Therefore, we introduce a new framework for graph convolutional networks called Hybrid…

Convolutional neural networks (CNN) have made significant advances in hyperspectral image (HSI) classification. However, standard convolutional kernel neglects the intrinsic connections between data points, resulting in poor region…

Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel…

Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency…

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…

Graph convolutional networks learn effective node embeddings that have proven to be useful in achieving high-accuracy prediction results in semi-supervised learning tasks, such as node classification. However, these networks suffer from the…

We propose Multi-Level Local SGD, a distributed gradient method for learning a smooth, non-convex objective in a heterogeneous multi-level network. Our network model consists of a set of disjoint sub-networks, with a single hub and multiple…

Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…

Simplicial complexes have recently been in the limelight of higher-order network analysis, where a minority of simplices play crucial roles in structures and functions due to network heterogeneity. We find a significant inconsistency…

Hyperspectral Image (HSI) classification is an important issue in remote sensing field with extensive applications in earth science. In recent years, a large number of deep learning-based HSI classification methods have been proposed.…

Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. Most existing methods are only based on the original intrinsic or…