相关论文: Two Channel Filter Banks on Arbitrary Graphs with …

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…

We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of…

A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…

Graph neural networks (GNNs) have emerged as a promising solution to deal with unstructured data, outperforming traditional deep learning architectures. However, most of the current GNN models are designed to work with a single graph, which…

Fraud detection on graph data can be viewed as a demanding task that requires distinguishing between different types of nodes. Because graph neural networks (GNNs) are naturally suited for processing information encoded in graph form…

Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since…

Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints,…

In recent years, improvements in various image acquisition techniques gave rise to the need for adaptive processing methods, aimed particularly for large datasets corrupted by noise and deformations. In this work, we consider datasets of…

Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…

A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper $L_{2}$-boundedness for locally stationary random graph signals; (ii) $L_{2}$-isometry for \textit{i.i.d.} random graph…

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…

Polynomial graph filters have been widely used as guiding principles in the design of Graph Neural Networks (GNNs). Recently, the adaptive learning of the polynomial graph filters has demonstrated promising performance for modeling graph…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…

Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of…

Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…

We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…

In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…

Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the…