Related papers: A Digraph Fourier Transform With Spread Frequency …
Graph neural networks (GNNs) achieve strong performance on graph learning tasks, but training on large-scale networks remains computationally challenging. Transferability results show that GNNs with fixed weights can generalize from smaller…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…
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…
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…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We study the problem of generating graph signals from unknown distributions defined over given graphs, relevant to domains such as recommender systems or sensor networks. Our approach builds on generative diffusion models, which are well…
This work introduces the multidimensional Graph Fourier Transformation Neural Network (GFTNN) for long-term trajectory predictions on highways. Similar to Graph Neural Networks (GNNs), the GFTNN is a novel network architecture that operates…
DFT is the numerical implementation of Fourier transform (FT), and it has many forms. Ordinary DFT (ODFT) and symmetric DFT (SDFT) are the two main forms of DFT. The most widely used DFT is ODFT, and the phase spectrum of this form is…
Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to…
Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from…
We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
Spread-spectrum systems are presented, which are based on Finite Field Fourier Transforms. Orthogonal spreading sequences defined over a finite field are derived. New digital multiplex schemes based on such spread-spectrum systems are also…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…
Graph Neural Networks (GNNs) have excelled in handling graph-structured data, attracting significant research interest. However, two primary challenges have emerged: interference between topology and attributes distorting node…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
Let $D(G)$ and $D^Q(G)= Diag(Tr) + D(G)$ be the distance matrix and distance signless Laplacian matrix of a simple strongly connected digraph $G$, respectively, where $Diag(Tr)=\textrm{diag}(D_1,D_2,$ $\ldots,D_n)$ be the diagonal matrix…
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…