Related papers: Graph Persistence goes Spectral
This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs…
Vectorization methods for \emph{Persistent Homology} (PH), such as the \emph{Persistence Image} (PI), encode persistence diagrams into finite dimensional vector spaces while preserving stability. In parallel, the \emph{Persistent Laplacian}…
Characterizing the structural properties of neural networks is crucial yet poorly understood, and there are no well-established similarity measures between networks. In this work, we observe that neural networks can be represented as…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant…
While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…
Graph neural networks (GNNs) have shown advantages in graph-based analysis tasks. However, most existing methods have the homogeneity assumption and show poor performance on heterophilic graphs, where the linked nodes have dissimilar…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where…
We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's…
Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address…
Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
Graph Neural Networks (GNNs) face fundamental limitations in expressivity and capturing structural heterogeneity. Standard message-passing architectures are constrained by the 1-dimensional Weisfeiler-Leman (1-WL) test, unable to…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
Representation learning on graphs has emerged as a powerful mechanism to automate feature vector generation for downstream machine learning tasks. The advances in representation on graphs have centered on both homogeneous and heterogeneous…
Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…
Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation,…