Related papers: Approximate Nearest Neighbor Search in High Dimens…
When we have two data sets and want to find the nearest neighbour of each point in the first dataset among points in the second one, we need the all nearest neighbour operator. This is an operator in spatial databases that has many…
Large-scale approximate nearest neighbor search (ANN) has been gaining attention along with the latest machine learning researches employing ANNs. If the data is too large to fit in memory, it is necessary to search for the most similar…
We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…
LSH (locality sensitive hashing) had emerged as a powerful technique in nearest-neighbor search in high dimensions [IM98, HIM12]. Given a point set $P$ in a metric space, and given parameters $r$ and $\varepsilon > 0$, the task is to…
Modern neural network technologies, including large language models, have achieved remarkable success in various applied artificial intelligence applications, however, they face a range of fundamental limitations. Among them are…
Range-aggregate query is an important type of queries with numerous applications. It aims to obtain some structural information (defined by an aggregate function $F(\cdot)$) of the points (from a point set $P$) inside a given query range…
The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed…
Retrieving the most similar objects in a large-scale database for a given query is a fundamental building block in many application domains, ranging from web searches, visual, cross media, and document retrievals. State-of-the-art…
Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations…
KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
The property of almost every point being a Lebesgue point has proven to be crucial for the consistency of several classification algorithms based on nearest neighbors. We characterize Lebesgue points in terms of a 1-Nearest Neighbor…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
The {\em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality, defined as the minimum over all bijections between the point sets of the maximum distance between any pair of points put…
This paper proposes a new algorithm for reducing Approximate Nearest Neighbor problem to Approximate Near Neighbor problem. The advantage of this algorithm is that it achieves O(log n) query time. As a reduction problem, the uery time…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…
Prior methods for retrieval of nearest neighbors in high dimensions are fast and approximate--providing probabilistic guarantees of returning the correct answer--or slow and exact performing an exhaustive search. We present Certified…
We study the $r$-near neighbors reporting problem ($r$-NN), i.e., reporting \emph{all} points in a high-dimensional point set $S$ that lie within a radius $r$ of a given query point $q$. Our approach builds upon on the locality-sensitive…
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…