Related papers: Approximate Nearest Neighbor Search in High Dimens…
Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with…
Given a training set $P \subset \mathbb{R}^d$, the nearest-neighbor classifier assigns any query point $q \in \mathbb{R}^d$ to the class of its closest point in $P$. To answer these classification queries, some training points are more…
Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…
Let $\mathcal{D}$ be a set of straight-line segments in the plane, potentially crossing, and let $c$ be a positive integer. We denote by $P$ the union of the endpoints of the straight-line segments of $\mathcal{D}$ and of the intersection…
Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…
The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining…
A k nearest neighbor (kNN) query on road networks retrieves the k closest points of interest (POIs) by their network distances from a given location. Today, in the era of ubiquitous mobile computing, this is a highly pertinent query. While…
Reverse k nearest neighbor (RkNN) queries are fundamental in spatial databases, location-based analytics, and recommendation systems. Existing state-of-the-art techniques rely on spatial pruning supported by R-trees and their variants.…
We compare the performance of three nearest neighbor search algorithms: the Orchard, ball tree, and VP-tree algorithms. These algorithms are commonly used for nearest-neighbor searches and are known for their efficiency in large datasets.…
We propose $\kappa$-approximate nearest neighbor (ANN) data structures for $n$ polygonal curves under the Fr\'{e}chet distance in $\mathbb{R}^d$, where $\kappa \in \{1+\varepsilon,3+\varepsilon\}$ and $d \geq 2$. We assume that every input…
Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We take a first step towards a rigorous asymptotic analysis of graph-based approaches for finding (approximate) nearest neighbors in high-dimensional spaces, by analyzing the complexity of (randomized) greedy walks on the approximate near…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
Nearest neighbour search over dense vector collections has important applications in information retrieval, retrieval augmented generation (RAG), and content ranking. Performing efficient search over large vector collections is a well…
We study the Nearest Neighbor Search (NNS) problem in a high-dimensional setting where data lies in a low-dimensional subspace and is corrupted by Gaussian noise. Specifically, we consider a semi-random model in which $n$ points from an…