Related papers: Approximate Nearest Neighbor Search in High Dimens…
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…
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…
This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects. In contrast with most existing approaches, we can only access the ``hidden'' space in which…
Reverse nearest neighbor queries are defined as follows: Given an input point-set P, and a query point q, find all the points p in P whose nearest point in P U {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor…
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 introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of $n$ points $P=\{ x_1,\ldots, x_n\}$ in high-dimensions,…
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 present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain $P$ with $n$ vertices. Our goal is to store a dynamic set of $m$ point sites…
Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases,…
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…
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…
Most natural language processing tasks can be formulated as the approximated nearest neighbor search problem, such as word analogy, document similarity, machine translation. Take the question-answering task as an example, given a question…
Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
Near neighbor search (NNS) is a powerful abstraction for data access; however, data indexing is troublesome even for approximate indexes. For intrinsically high-dimensional data, high-quality fast searches demand either indexes with…
In the nearest neighbor problem, we are given a set $S$ of point sites that we want to store such that we can find the nearest neighbor of a (new) query point efficiently. In the dynamic version of the problem, the goal is to design a data…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. There are several variants of the similarity search problem, and one of the most relevant is the $r$-near neighbor ($r$-NN) problem:…
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…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…