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Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity…

Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…

Community detection is a central problem in graph analysis, with applications ranging from network science to graph signal processing. In recent years, Graph Neural Networks (GNNs) have emerged as effective tools for learning…

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…

In this paper the Partition of Unity Method (PUM) is efficiently performed using Radial Basis Functions (RBFs) as local approximants. In particular, we present a new space-partitioning data structure extremely useful in applications because…

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

We consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting…

Graph Neural networks (GNNs) have recently become a powerful technique for many graph-related tasks including graph classification. Current GNN models apply different graph pooling methods that reduce the number of nodes and edges to learn…

Graph pooling is a family of operations which take graphs as input and produce shrinked graphs as output. Modern graph pooling methods are trainable and, in general inserted in Graph Neural Networks (GNNs) architectures as graph shrinking…

In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on…

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…

In this work, we propose an approach to perform non-uniform image interpolation based on a Gaussian Mixture Model. Traditional image interpolation methods, like nearest neighbor, bilinear, Hamming, Lanczos, etc. assume that the coordinates…

In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…

Message passing mechanism contributes to the success of GNNs in various applications, but also brings the oversquashing problem. Recent works combat oversquashing by improving the graph spectrums with rewiring techniques, disrupting the…

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…

The Partition of Unity (PU) method, performed with local Radial Basis Function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good…

We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in $2D$. Function extension plays a fundamental role…

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…

We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for…