Related papers: Perfect Reconstruction Two-Channel Wavelet Filter-…
Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of…
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…
In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points.…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
Graph neural networks are gaining attention in fifth-generation (5G) core network digital twins, which are data-driven complex systems with numerous components. Analyzing these data can be challenging due to rare failure types, leading to…
Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious…
Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from…
A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH-property): a graph admitting a perfect matching is said to…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
Finding equitable partitions is closely related to the extraction of graph symmetries and of interest in a variety of applications context such as node role detection, cluster synchronization, consensus dynamics, and network control…
Considering the problem of nonlinear and non-gaussian filtering of the graph signal, in this paper, a robust square root unscented Kalman filter based on graph signal processing is proposed. The algorithm uses a graph topology to generate…
Deep generative models, since their inception, have become increasingly more capable of generating novel and perceptually realistic signals (e.g., images and sound waves). With the emergence of deep models for graph structured data, natural…
Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints,…
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…
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass…