相关论文: Graph Fourier transform based on singular value de…

In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…

This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the $L^1$-norm of the fractional…

Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation…

The fundamentals of Fourier Transform are presented, with analytical solutions derived for Continuous Fourier Transform (CFT) of truncated signals, to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFT were…

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…

We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition. The Transformer has access to…

Eigenvectors of the Laplacian of a cycle graph exhibit the sinusoidal characteristics of the standard DFT basis, and signals defined on such graphs are amenable to linear shift invariant (LSI) operations. In this paper we propose to reduce…

A generalized Nonlinear Fourier Transform (GNFT), which includes eigenvalues of higher multiplicity, is considered for information transmission over fiber optic channels. Numerical algorithms are developed to compute the direct and inverse…

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…

Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains.…

To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation,…

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of…

Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…

The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…

In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…

The singular values of convolutional mappings encode interesting spectral properties, which can be used, e.g., to improve generalization and robustness of convolutional neural networks as well as to facilitate model compression. However,…

Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a…

We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral…

Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…