相关论文: Accelerated graph-based spectral polynomial filter…

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric…

In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix,…

In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed…

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…

It has been shown that the effectiveness of graph convolutional network (GCN) for recommendation is attributed to the spectral graph filtering. Most GCN-based methods consist of a graph filter or followed by a low-rank mapping optimized…

We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and…

This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…

Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered…

In this survey paper, we analyze image based graph neural networks and propose a three-step classification approach. We first convert the image into superpixels using the Quickshift algorithm so as to reduce 30% of the input data. The…

Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed in high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model,…

The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often performed in practice by tuning filter parameters, such as by increasing the width of the…

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…

Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper…

The feedforward selective fixed-filter method selects the most suitable pre-trained control filter based on the spectral features of the detected reference signal, effectively avoiding slow convergence in conventional adaptive algorithms.…

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for…

Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised learning on graph-based datasets. For sparse graphs, linear and polynomial filter functions have yielded impressive results. For large non-sparse…

Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…

Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to…

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…

Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high…