Related papers: Consistent sampling of Paley-Wiener functions on g…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
Inductive Recommender Systems are capable of recommending for new users and with new items thus avoiding the need to retrain after new data reaches the system. However, these methods are still trained on all the data available, requiring…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
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…
One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling…
We consider the problem of estimating graph limits, known as graphons, from observations of sequences of sparse finite graphs. In this paper we show a simple method that can shed light on a subset of sparse graphs. The method involves…
In the present paper, complete designs of graphs are considered. The notion of (regular) sampling is introduced and analyzed in detail, showing that the trivial necessary condition for its existence is actually sufficient. Some examples are…
Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
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…
Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful feature representations from network data. However, on large-scale graphs convolutions incur in high computational cost, leading to…
Greb\'ik and Rocha [Fractional Isomorphism of Graphons, Combinatorica 42, pp 365-404 (2022)] extended the well studied notion of fractional isomorphism of graphs to graphons. We prove that fractionally isomorphic graphons can be…
Multiple sampling-based methods have been developed for approximating and accelerating node embedding aggregation in graph convolutional networks (GCNs) training. Among them, a layer-wise approach recursively performs importance sampling to…
The de Branges spaces of entire functions generalise the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of…
This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for…
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
In this paper we present a criteria to obtain interpolations formulas in terms of the sequence $\left(\{T_n(f)(Nm)\}\}_{m\in\mathbb{Z}}\right)_{n=1}^N$, where $f$ are functions whose Fourier transform is supported in $[-1/2,1/2]$, and $T_n$…
We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…