Related papers: Quantum Sketches, Hashing, and Approximate Nearest…
Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
Similarity searches are a critical task in data mining. As data sets grow larger, exact nearest neighbor searches quickly become unfeasible, leading to the adoption of approximate nearest neighbor (ANN) searches. ANN has been studied for…
Approximate Nearest Neighbor (ANN) search has become fundamental to modern AI infrastructure, powering recommendation systems, search engines, and large language models across industry leaders from Google to OpenAI. Hierarchical Navigable…
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…
Let $X$ be a set of $n$ points of norm at most $1$ in the Euclidean space $R^k$, and suppose $\varepsilon>0$. An $\varepsilon$-distance sketch for $X$ is a data structure that, given any two points of $X$ enables one to recover the square…
Kernel Density Estimation (KDE) is a nonparametric method for estimating the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor…
CountSketch and Feature Hashing (the "hashing trick") are popular randomized dimensionality reduction methods that support recovery of $\ell_2$-heavy hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and approximate inner…
This paper introduces "Multi-Level Spherical LSH": parameter-free, a multi-level, data-dependant Locality Sensitive Hashing data structure for solving the Approximate Near Neighbors Problem (ANN). This data structure uses a modified version…
Approximate near-neighbors search (\textsc{ANNS}) is a long-studied problem in computational geometry. %that has received considerable attention by researchers in the community. In this paper, we revisit the problem and propose the first…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error…
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the…
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…
We propose a generic feature compression method for Approximate Nearest Neighbor Search (ANNS) problems, which speeds up existing ANNS methods in a plug-and-play manner. Specifically, based on transformer, we propose a new network structure…
We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
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…
Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…
The explosive growth in big data has attracted much attention in designing efficient indexing and search methods recently. In many critical applications such as large-scale search and pattern matching, finding the nearest neighbors to a…