Related papers: Shift-invariant spaces on finite undirected 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,…
The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in…
In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic…
Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…
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…
We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
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…
We extend Fourier analysis to curved spaces by defining a Generalized Fourier Transform (GFT) on any Riemannian manifold $\Sigma$ via spectral decomposition. Under minimal requirements that the transform is an isometric isomorphism and has…
Signal analysis on graphs relies heavily on the graph Fourier transform, which is defined as the projection of a signal onto an eigenbasis of the associated shift operator. Large graphs of similar structure may be represented by a graphon.…
Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…
Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial…
Graphs are fundamental tools for modeling pairwise interactions in complex systems. However, many real-world systems involve multi-way interactions that cannot be fully captured by standard graphs. Hypergraphs, which generalize graphs by…
This paper introduces a novel deconvolution algorithm, shift-invariant multi-linearity (SIML), which significantly enhances the analysis of data from a comprehensive two-dimensional gas chromatograph coupled to a mass spectrometric detector…
We present a graph-theoretic model for dynamical systems $(X,\sigma)$ given by a surjective local homeomorphism $\sigma$ on a totally disconnected compact metrizable space $X$. In order to make the dynamics appear explicitly in the graph,…
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.…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
We address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the unknown network. Using the…
This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles. Special attention is paid to the notion of…