Related papers: SVD-based ugmt-gft on directed product graphs
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
Graph representation learning (GRL) methods, such as graph neural networks and graph transformer models, have been successfully used to analyze graph-structured data, mainly focusing on node classification and link prediction tasks.…
We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…
In this paper, we redefine the Graph Fourier Transform (GFT) under the DSP$_\mathrm{G}$ framework. We consider the Jordan eigenvectors of the directed Laplacian as graph harmonics and the corresponding eigenvalues as the graph frequencies.…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…