Related papers: Graph Persistence goes Spectral
An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…
Graph theory is emerging as a new source of tools for time series analysis. One promising method is to transform a signal into its visibility graph, a representation which captures many interesting aspects of the signal. Here we introduce…
Spectral Graph Neural Networks (SGNNs) have achieved remarkable performance in tasks such as node classification due to their ability to learn flexible filters. Typically, these filters are learned under the supervision of downstream tasks,…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Spectral graph contrastive learning often constructs low- and high-frequency views to capture complementary graph signals, but these views are commonly combined by graph-level or node-agnostic fusion rules. We show that graph-level fusion…
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of…
The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…
Geometric deep learning has made great strides towards generalizing the design of structure-aware neural networks from traditional domains to non-Euclidean ones, giving rise to graph neural networks (GNN) that can be applied to…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning over structured data, including text-attributed graphs (TAGs), which are common in domains such as citation networks, social platforms, and knowledge graphs. GNNs are…
Community structure is an important property that captures inhomogeneities common in large networks, and modularity is one of the most widely used metrics for such community structure. In this paper, we introduce a principled methodology,…
In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Though graph representation learning (GRL) has made significant progress, it is still a challenge to extract and embed the rich topological structure and feature information in an adequate way. Most existing methods focus on local structure…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the…
The integration of Spiking Neural Networks (SNNs) and Graph Neural Networks (GNNs) is gradually attracting attention due to the low power consumption and high efficiency in processing the non-Euclidean data represented by graphs. However,…