Related papers: Variational limits of k-NN graph based functionals…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
The k-Terminal Cut problem, also known as the Multiway Cut problem, is defined on an edge-weighted graph with $k$ distinct vertices called "terminals." The goal is to remove a minimum weight collection of edges from the graph such that…
$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially…
We propose an adaptive graph coarsening method to jointly learn graph neural network (GNN) parameters and merge nodes via K-means clustering during training. As real-world graphs grow larger, processing them directly becomes increasingly…
Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation -- potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
In the domain of point cloud analysis, despite the significant capabilities of Graph Neural Networks (GNNs) in managing complex 3D datasets, existing approaches encounter challenges like high computational costs and scalability issues with…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Numerous theories of failure have been postulated and implemented in various commercial programs for composite materials. Even the best theories have had limited success in predicting damage and failure in validation exercises. In view of…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Point cloud completion is a vital task focused on reconstructing complete point clouds and addressing the incompleteness caused by occlusion and limited sensor resolution. Traditional methods relying on fixed local region partitioning, such…
This paper addresses the problem of compression of 3D point cloud sequences that are characterized by moving 3D positions and color attributes. As temporally successive point cloud frames are similar, motion estimation is key to effective…
Graph Neural Networks (GNNs) have demonstrated impressive performance across diverse graph-based tasks by leveraging message passing to capture complex node relationships. However, on large-scale real-world graphs, GNNs face two major…
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling…
The fused lasso, also known as total-variation denoising, is a locally-adaptive function estimator over a regular grid of design points. In this paper, we extend the fused lasso to settings in which the points do not occur on a regular…
Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…
Graph neural networks (GNNs) model representations from networked data and allow for decentralized inference through localized communications. Existing GNN architectures often assume ideal communications and ignore potential channel…