Related papers: Entropy based Nearest Neighbor Search in High Dime…

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…

Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of…

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…

We present a novel hashing strategy for approximate furthest neighbor search that selects projection bases using the data distribution. This strategy leads to an algorithm, which we call DrusillaHash, that is able to outperform existing…

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…

For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…

For a metric space $(X, d)$, a family $\mathcal{H}$ of locality sensitive hash functions is called $(r, cr, p_1, p_2)$ sensitive if a randomly chosen function $h\in \mathcal{H}$ has probability at least $p_1$ (at most $p_2$) to map any $a,…

An important question that arises in the study of high dimensional vector representations learned from data is: given a set $\mathcal{D}$ of vectors and a query $q$, estimate the number of points within a specified distance threshold of…

Nearest Neighbor Search (NNS) is a central task in knowledge representation, learning, and reasoning. There is vast literature on efficient algorithms for constructing data structures and performing exact and approximate NNS. This paper…

Locality-sensitive hashing (LSH), introduced by Indyk and Motwani in STOC '98, has been an extremely influential framework for nearest neighbor search in high-dimensional data sets. While theoretical work has focused on the approximate…

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can be quantized into binary codes to give an efficient…

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…

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…

The multichannel rendezvous problem is a fundamental problem for neighbor discovery in many IoT applications. The existing works in the literature focus mostly on improving the worst-case performance, and the average-case performance is…

In this paper, we show a construction of locality-sensitive hash functions without false negatives, i.e., which ensure collision for every pair of points within a given radius $R$ in $d$ dimensional space equipped with $l_p$ norm when $p…

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…

Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…

This work suggests faster and space-efficient index construction algorithms for LSH for Euclidean distance (\textit{a.k.a.}~\ELSH) and cosine similarity (\textit{a.k.a.}~\SRP). The index construction step of these LSHs relies on grouping…