Related papers: Graphon estimation via nearest neighbor algorithm …
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
We consider estimating the edge-probability matrix of a network generated from a graphon model when the full network is not observed---only some overlapping subgraphs are. We extend the neighbourhood smoothing (NBS) algorithm of Zhang et…
In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly,…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…
Approximate nearest neighbor search (ANNS) in high-dimensional spaces is a pivotal challenge in the field of machine learning. In recent years, graph-based methods have emerged as the superior approach to ANNS, establishing a new state of…
We study low-rank estimation of an unknown sparse graphon from sampled network data under operator-norm loss, motivated by targeted interventions in graphon games. Starting from the observed adjacency matrix, we construct low-rank…
We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of…
Graph Neural Networks (GNNs) have proven to be powerful in many graph-based applications. However, they fail to generalize well under heterophilic setups, where neighbor nodes have different labels. To address this challenge, we employ a…
Graph search is one of the most successful algorithmic trends in near neighbor search. Several of the most popular and empirically successful algorithms are, at their core, a simple walk along a pruned near neighbor graph. Such algorithms…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which…
We propose a denoising method for multimodal graph signals by an alternating minimization scheme that sequentially solves signal restoration and graph learning problems. Many complex-structured data, i.e., those on sensor networks, can…
Relative Nearest Neighbor Descent (RNN-Descent) is a state-of-the-art algorithm for constructing sparse approximate nearest neighbor (ANN) graphs by combining the iterative refinement of NN-Descent with the edge-pruning rules of the…
$k$ 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 consider the problem of classifying a map using a team of communicating robots. It is assumed that all robots have localized visual sensing capabilities and can exchange their information with neighboring robots. Using a graph…