Related papers: Graph signal interpolation with Positive Definite …

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…

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph…

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…

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…

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely…

Recently, the optimization of polynomial filters within Spectral Graph Neural Networks (GNNs) has emerged as a prominent research focus. Existing spectral GNNs mainly emphasize polynomial properties in filter design, introducing…

Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

We present a combinatorial characterization of the Bethe entropy function of a factor graph, such a characterization being in contrast to the original, analytical, definition of this function. We achieve this combinatorial characterization…

Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…

In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…

We consider the task of representing signals supported on graph bundles, which are generalizations of product graphs that allow for "twists" in the product structure. Leveraging the localized product structure of a graph bundle, we…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…

A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3), 2015, pp. 435-446]. From the view point of operator theory…

In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…

We define vertex-colourings for edge-partitioned digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define generalized chromatic functions, which merge the chromatic…

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…