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Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important…

Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph…

In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In these decades, some useful formulas for the Fourier transform…

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…

This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal…

Graph Transformers (GTs) have significantly advanced the field of graph representation learning by overcoming the limitations of message-passing graph neural networks (GNNs) and demonstrating promising performance and expressive power.…

Feature transformation plays a critical role in enhancing machine learning model performance by optimizing data representations. Recent state-of-the-art approaches address this task as a continuous embedding optimization problem, converting…

Graph neural networks (GNNs) have achieved remarkable success in various domains, yet they often struggle with domain adaptation due to significant structural distribution shifts and insufficient exploration of transferable patterns. One of…

Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph…

Fourier-transform spectroscopy (FTS) has been widely used as a standard analytical technique over the past half-century. FTS is a simple and robust autocorrelation-based technique that is compatible with both temporally coherent and…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

With recent advancements in graph neural networks (GNNs), spectral GNNs have received increasing popularity by virtue of their ability to retrieve graph signals in the spectral domain. These models feature uniqueness in efficient…

Visual object tracking is a challenging computer vision task with numerous real-world applications. Here we propose a simple but efficient Spectral Filter Tracking (SFT)method. To characterize rotational and translation invariance of…

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 Comparative Learning (GCL) is a self-supervised method that combines the advantages of Graph Convolutional Networks (GCNs) and comparative learning, making it promising for learning node representations. However, the GCN encoders used…

Graph Transformer (GT), as a special type of Graph Neural Networks (GNNs), utilizes multi-head attention to facilitate high-order message passing. However, this also imposes several limitations in node classification applications: 1) nodes…

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…

Transformers have achieved remarkable success in time series modeling, yet their internal mechanisms remain opaque. This work demystifies the Transformer encoder by establishing its fundamental equivalence to a Graph Convolutional Network…

The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…