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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 Approximate Nearest Neighbor (ANN) search often suffers from performance degradation in high-dimensional spaces due to the Euclidean-Geodesic mismatch, where greedy routing diverges from the underlying data manifold. To address…
We study the Approximate Nearest Neighbor (ANN) problem under a powerful adaptive adversary that controls both the dataset and a sequence of $Q$ queries. Primarily, for the high-dimensional regime of $d = \omega(\sqrt{Q})$, we introduce a…
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.…
Approximate nearest neighbour (ANN) search is one of the most important problems in computer science fields such as data mining or computer vision. In this paper, we focus on ANN for high-dimensional binary vectors and we propose a simple…
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…
The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…
The $c$-approximate Near Neighbor problem in high dimensional spaces has been mainly addressed by Locality Sensitive Hashing (LSH), which offers polynomial dependence on the dimension, query time sublinear in the size of the dataset, and…
In the advent of big data era, interactive visualization of large data sets consisting of M*10^5+ high-dimensional feature vectors of length N (N ~ 10^3+), is an indispensable tool for data exploratory analysis. The state-of-the-art data…
Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how…
In most practical applications of image retrieval, high-dimensional feature vectors are required, but current multi-dimensional indexing structures lose their efficiency with growth of dimensions. Our goal is to propose a divisive…
Approximate Nearest Neighbor Search with arbitrary filtering predicates (AFANNS) is essential for modern data applications, yet existing methods often incur substantial storage and computational costs. In this work, we introduce the Maximal…
Density-based clustering aims to find groups of similar objects (i.e., clusters) in a given dataset. Applications include, e.g., process mining and anomaly detection. It comes with two user parameters ({\epsilon}, MinPts) that determine the…
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the…
K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificial intelligence software with applications in robotics, and autonomous vehicles. These wide-ranging applications utilize KNN either directly for simple classification or…
ANNS for embedded vector representations of texts is commonly used in information retrieval, with two important information representations being sparse and dense vectors. While it has been shown that combining these representations…
Nearest neighbor search plays a fundamental role in many disciplines such as multimedia information retrieval, data-mining, and machine learning. The graph-based search approaches show superior performance over other types of approaches in…
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…
The $k$-nearest neighbor graph (KNNG) on high-dimensional data is a data structure widely used in many applications such as similarity search, dimension reduction and clustering. Due to its increasing popularity, several methods under the…
Modern deep learning models capture the semantics of complex data by transforming them into high-dimensional embedding vectors. Emerging applications, such as retrieval-augmented generation, use approximate nearest neighbor (ANN) search in…