Related papers: Graph signal interpolation with Positive Definite …
The natural kinship between classical theories of interpolation and approximation is well explored. In contrast to this, the interrelation between interpolation and approximation is subtle and this duality is relatively obscure in the…
We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their…
The effective representation, precessing, analysis, and visualization of large-scale structured data over graphs are gaining a lot of attention. So far most of the literature has focused on real-valued signals. However, signals are often…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of…
The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The…
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical…
Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral…
Fraud detection on graph data can be viewed as a demanding task that requires distinguishing between different types of nodes. Because graph neural networks (GNNs) are naturally suited for processing information encoded in graph form…
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density…
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…
One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal…
We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral…
Graph-structured data are ubiquitous. However, graphs encode diverse types of information and thus play different roles in data representation. In this paper, we distinguish the \textit{representational} and the \textit{correlational} roles…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of…