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Approximate nearest neighbor (ANN) search in high-dimensional spaces is a foundational component of many modern retrieval and recommendation systems. Currently, almost all algorithms follow an $\epsilon$-Recall-Bounded principle when…
The problem of landmark recognition has achieved excellent results in small-scale datasets. When dealing with large-scale retrieval, issues that were irrelevant with small amount of data, quickly become fundamental for an efficient…
Let $P$ be a set of $n$ colored points. We develop efficient data structures that store $P$ and can answer chromatic $k$-nearest neighbor ($k$-NN) queries. Such a query consists of a query point $q$ and a number $k$, and asks for the color…
We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…
Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis…
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
For a given dataset $\mathcal{D}$ and structured label $f$, the goal of Filtered Approximate Nearest Neighbor Search (FANNS) algorithms is to find top-$k$ points closest to a query that satisfy label constraints, while ensuring both recall…
With their wide field of view and high duty cycle, water-Cherenkov-based observatories are integral to studying the very high-energy gamma-ray sky. For gamma-ray observations, precise event reconstruction and highly effective background…
To denoise a reference patch, the Non-Local-Means denoising filter processes a set of neighbor patches. Few Nearest Neighbors (NN) are used to limit the computational burden of the algorithm. Here here we show analytically that the NN…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate…
k nearest neighbor join (kNN join), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operation widely adopted by many data mining applications. As a combination of the k nearest…
Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time…
Recent studies have shown that Dense Retrieval (DR) techniques can significantly improve the performance of first-stage retrieval in IR systems. Despite its empirical effectiveness, the application of DR is still limited. In contrast to…
We revisit the moving k nearest neighbor (MkNN) query, which computes one's k nearest neighbor set and maintains it while at move. Existing MkNN algorithms are mostly safe region based, which lack efficiency due to either computing small…
Approximate k-Nearest Neighbor (AKNN) search is widely used in vector databases. When vectors carry additional attributes (e.g., labels or numerical values), filtered AKNN search retrieves the nearest vectors to a query vector under…
In this paper, we present an overview of Nearest neighbor (NN) methods, which are frequently employed for solving classification problems using supervised learning. The article concisely introduces the theoretical background, algorithmic,…
Large-scale visual localization systems continue to rely on 3D point clouds built from image collections using structure-from-motion. While the 3D points in these models are represented using local image features, directly matching a query…
We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a…