Related papers: Graph Fourier Transform with Negative Edges for De…
Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring…
Subgraph pattern detection aims to uncover complex interaction structures in graphs. However, state-of-the-art graph neural network (GNN)-based solutions assume centralized access to the entire graph. When graphs are instead distributed…
The Helmholtzian matrix of a graph $G=(V(G),E(G))$ is a graph-theoretic analogue of the vector Laplacian (or Helmholtz operator) [S. Li, L. Lu, J.F. Wang, A graph discretization of vector Laplacian, 379 (2026) 446--460]. Motivated by the…
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum…
We study homomorphism problems of signed graphs from a computational point of view. A signed graph $(G,\Sigma)$ is a graph $G$ where each edge is given a sign, positive or negative; $\Sigma\subseteq E(G)$ denotes the set of negative edges.…
We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…
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…
Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…
Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision…
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…
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…
Recently, transformers have shown promising performance in learning graph representations. However, there are still some challenges when applying transformers to real-world scenarios due to the fact that deep transformers are hard to train…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…
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…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…
We introduce a novel masked graph autoencoder (MGAE) framework to perform effective learning on graph structure data. Taking insights from self-supervised learning, we randomly mask a large proportion of edges and try to reconstruct these…
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…