Related papers: Variational limits of k-NN graph based functionals…

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…

We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to…

The paper investigates the approximation of the symmetric Total Variation functional on graphs. Such an approximation is given in terms of a discrete and symmetric finite difference model defined on point clouds obtained by randomly…

This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…

In this paper, we aim at improving the computational efficiency of graph convolutional networks (GCNs) for learning on point clouds. The basic graph convolution that is typically composed of a $K$-nearest neighbor (KNN) search and a…

We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…

We propose simple yet effective improvements in point representations and local neighborhood graph construction within the general framework of graph neural networks (GNNs) for 3D point cloud processing. As a first contribution, we propose…

The present article proposes a graph-based approach to customer segmentation, combining the RFM analysis with the classical optimization max-$k$-cut problem. We consider each customer as a vertex of a weighted graph, and the edge weights…

Acquired 3D point cloud data, whether from active sensors directly or from stereo-matching algorithms indirectly, typically contain non-negligible noise. To address the point cloud denoising problem, we propose a fast graph-based local…

In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data…

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…

We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…

In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities. Allowing weighted edges in the graph, the kernelized graph affinity provides a more general type of $k$NN…

Data streams are often defined as large amounts of data flowing continuously at high speed. Moreover, these data are likely subject to changes in data distribution, known as concept drift. Given all the reasons mentioned above, learning…

In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…

The $k$-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct $k$-NN graphs remains a challenge, especially for…