Related papers: SVD-based ugmt-gft on directed product graphs

In this paper, we introduce a new, spectral notion of approximation between directed graphs, which we call singular value (SV) approximation. SV-approximation is stronger than previous notions of spectral approximation considered in the…

Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…

In recent years, substantial progress has been made on Graph Convolutional Networks (GCNs). However, the computing of GCN usually requires a large memory space for keeping the entire graph. In consequence, GCN is not flexible enough,…

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…

Classical spectral graph theory and graph signal processing rely on a symmetry principle: undirected graphs induce symmetric (self-adjoint) adjacency/Laplacian operators, yielding orthogonal eigenbases and energy-preserving Fourier…

In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…

Recently, an approach to graph signal processing based on graphons was proposed. Here we show how such a graphon-driven approach to the Fourier transform can be used on graphs sampled from a stochastic block model (SBM). In particular, we…

Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…

The three standard products (the Cartesian, the direct and the strong product) of undirected graphs have been wellinvestigated, unique prime factor decomposition (PFD) are known and polynomial time algorithms have been established for…

The analysis of the brain surface modeled as a graph mesh is a challenging task. Conventional deep learning approaches often rely on data lying in the Euclidean space. As an extension to irregular graphs, convolution operations are defined…

Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…

We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we…

Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although…

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…

In recent years, graph prompt learning/tuning has garnered increasing attention in adapting pre-trained models for graph representation learning. As a kind of universal graph prompt learning method, Graph Prompt Feature (GPF) has achieved…

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…

Graph Neural Networks (GNNs) have shown excellent performance on graphs that exhibit strong homophily with respect to the node labels i.e. connected nodes have same labels. However, they perform poorly on heterophilic graphs. Recent…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented…