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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…

Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…

Gadget3 is nowadays one of the most frequently used high performing parallel codes for cosmological hydrodynamical simulations. Recent analyses have shown t\ hat the Neighbour Search process of Gadget3 is one of the most time-consuming…

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

Neighbor search is of fundamental important to many engineering and science fields such as physics simulation and computer graphics. This paper proposes to formulate neighbor search as a ray tracing problem and leverage the dedicated ray…

Approximate Nearest neighbor search (ANNS) is fundamental and essential operation in applications from many domains, such as databases, machine learning, multimedia, and computer vision. Although many algorithms have been continuously…

Nearest neighbor search is fundamental to a wide range of applications. Since the exact nearest neighbor search suffers from the "curse of dimensionality", approximate approaches, such as Locality-Sensitive Hashing (LSH), are widely used to…

The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an $n$-point dataset $X$ lying in a metric space $\mathcal{M}$, so that given a query point $q \in \mathcal{M}$, one can quickly return a point of…

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…

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

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…

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…

DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, a bottleneck of the algorithm is in the worst case, the run time complexity is $O(n^2)$. To address this limitation, we propose a new…

K-nearest neighbor search is one of the fundamental tasks in various applications and the hierarchical navigable small world (HNSW) has recently drawn attention in large-scale cloud services, as it easily scales up the database while…

Automated searches for strong gravitational lensing in optical imaging survey datasets often employ machine learning and deep learning approaches. These techniques require more example systems to train the algorithms than have presently…

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor…

We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…

We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…

We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved…

Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…