Related papers: Probabilistic Voronoi Diagrams for Probabilistic M…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…
In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…
Prediction of human motions is key for safe navigation of autonomous robots among humans. In cluttered environments, several motion hypotheses may exist for a pedestrian, due to its interactions with the environment and other pedestrians.…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…
We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset $P$ in $\mathbb{R}^d$ is chosen arbitrarily from an unknown subspace of low…
Approximate k-Nearest Neighbour (ANN) methods are often used for mining information and aiding machine learning on large scale high-dimensional datasets. ANN methods typically differ in the index structure used for accelerating searches,…
Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…
The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters,…
Approximate nearest neighbor (ANN) search in high-dimensional metric spaces is a fundamental problem with many applications. Over the past decade, proximity graph (PG)-based indexes have demonstrated superior empirical performance over…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Efficient and reliable generation of global path plans are necessary for safe execution and deployment of autonomous systems. In order to generate planning graphs which adequately resolve the topology of a given environment, many…
Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…
Approximate nearest neighbor (ANN) search in high dimensions is an integral part of several computer vision systems and gains importance in deep learning with explicit memory representations. Since PQT, FAISS, and SONG started to leverage…
Topological maps are more suitable than metric maps for robotic exploration tasks. However, real-time updating of accurate and detail-rich environmental topological maps remains a challenge. This paper presents a topological map updating…
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data…
While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi…
Probabilistic k-nearest neighbour (PKNN) classification has been introduced to improve the performance of original k-nearest neighbour (KNN) classification algorithm by explicitly modelling uncertainty in the classification of each feature…
Approximate Nearest Neighbor (ANN) search is a fundamental technique for (e.g.,) the deployment of recommender systems. Recent studies bring proximity graph-based methods into practitioners' attention -- proximity graph-based methods…
This paper introduces the innovative Power Muirhead Mean K-Nearest Neighbors (PMM-KNN) algorithm, a novel data classification approach that combines the K-Nearest Neighbors method with the adaptive Power Muirhead Mean operator. The proposed…