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We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT is a multiresolution transform, formed by combining spatially localized block transforms. We assume the points are…
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…
Graph neural network (GNN)-based fault diagnosis (FD) has received increasing attention in recent years, due to the fact that data coming from several application domains can be advantageously represented as graphs. Indeed, this particular…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
Graph Transformers (GTs) have demonstrated their advantages across a wide range of tasks. However, the self-attention mechanism in GTs overlooks the graph's inductive biases, particularly biases related to structure, which are crucial for…
This paper presents the rigorous mathematical construction and foundational properties of the Divergence-Free Radiant Transform (DFRT), a spectral transform specifically designed for divergence-free vector fields, with applications in…
Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed…
We present the Graph Forward-Forward (GFF) algorithm, an extension of the Forward-Forward procedure to graphs, able to handle features distributed over a graph's nodes. This allows training graph neural networks with forward passes only,…
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…
Applications of graph transformation (GT) systems often require control structures that can be used to direct GT processes. Most existing GT tools follow a stateful computational model, where a single graph is repeatedly modified "in-place"…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…
The Graph Fourier Transform (GFT) has recently demonstrated promising results in speech enhancement. However, existing GFT-based speech enhancement approaches often employ fixed graph topologies to build the graph Fourier basis, whose the…
Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…