Related papers: Approximate k-flat Nearest Neighbor Search
$\renewcommand{\Re}{\mathbb{R}}$Recent work showed how to construct nearest-neighbor graphs of linear size, on a given set $P$ of $n$ points in $\Re^d$, such that one can answer approximate nearest-neighbor queries in logarithmic time in…
High-dimensional approximate $K$ nearest neighbor search (AKNN) is a fundamental task for various applications, including information retrieval. Most existing algorithms for AKNN can be decomposed into two main components, i.e., candidate…
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.…
K-nearest neighbor classification algorithm is one of the most basic algorithms in machine learning, which determines the sample's category by the similarity between samples. In this paper, we propose a quantum K-nearest neighbor…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
Approximate Nearest Neighbors (ANN) search is a crucial task in several applications like recommender systems and information retrieval. Current state-of-the-art ANN libraries, although being performance-oriented, often lack modularity and…
Given a set of $n$ points in the plane, and a parameter $k$, we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing $k$ points. We present the first near quadratic time algorithm for this…
Approximate nearest neighbor (ANN) search is a fundamental problem in areas such as data management,information retrieval and machine learning. Recently, Li et al. proposed a learned approach named AdaptNN to support adaptive ANN query…
Learned dense representations are a popular family of techniques for encoding queries and documents using high-dimensional embeddings, which enable retrieval by performing approximate k nearest-neighbors search (A-kNN). A popular technique…
We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTASs) to several well-known problems in Computational Geometry, such as $k$-center clustering and farthest nearest neighbor.…
We are given a directed graph $G = (V,E)$ with $n$ vertices and $m$ edges, with positive weights on the edges, and a parameter $k >0$. We show how to compute, for every vertex $v \in V$, its $k$ nearest-neighbors. The algorithm runs in $O(…
The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has…
Fast k-Nearest Neighbor search over real-valued vector spaces (KNN) is an important algorithmic task for information retrieval and recommendation systems. We present a method for using reduced precision to represent vectors through…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they…
Approximate Nearest Neighbor Search (ANNS) is the task of finding the database vector that is closest to a given query vector. Graph-based ANNS is the family of methods with the best balance of accuracy and speed for million-scale datasets.…
This study proposes an efficient exact k-flexible aggregate nearest neighbor (k-FANN) search algorithm in road networks using the M-tree. The state-of-the-art IER-kNN algorithm used the R-tree and pruned off unnecessary nodes based on the…
Approximate Nearest Neighbor (ANN) search in high-dimensional Euclidean spaces is a fundamental problem with a wide range of applications. However, there is currently no ANN method that performs well in both indexing and query answering…
In the polytope membership problem, a convex polytope $K$ in $R^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given a query point $q \in R^d$, it is possible to determine efficiently whether $q \in K$.…
Big data mining is well known to be an important task for data science, because it can provide useful observations and new knowledge hidden in given large datasets. Proximity-based data analysis is particularly utilized in many real-life…