Related papers: Hypercube LSH for approximate near neighbors
We propose a novel approach to charged particle tracking at high intensity particle colliders based on Approximate Nearest Neighbors search. With hundreds of thousands of measurements per collision to be reconstructed e.g. at the High…
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:…
The indexing algorithms for the high-dimensional nearest neighbor search (NNS) with the best worst-case guarantees are based on the randomized Locality Sensitive Hashing (LSH), and its derivatives. In practice, many heuristic approaches…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
Consider the geometric range space $(X, \mathcal{H}_d)$ where $X \subset \mathbb{R}^d$ and $\mathcal{H}_d$ is the set of ranges defined by $d$-dimensional halfspaces. In this setting we consider that $X$ is the disjoint union of a red and…
Given a metric space $(X,d_X)$, $c\ge 1$, $r>0$, and $p,q\in [0,1]$, a distribution over mappings $\h:X\to \mathbb N$ is called a $(r,cr,p,q)$-sensitive hash family if any two points in $X$ at distance at most $r$ are mapped by $\h$ to the…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
The Haugazeau method was originally designed to compute the best approximation from an intersection of closed convex sets in Hilbert spaces using the projection operators onto the individual sets iteratively. We propose an abstract…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
This Engineering Note addresses the challenge of estimating the probability of collision for tethered spacecraft during close encounters with other space objects. Standard probability of collision methods, based on spherical hard-body…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…
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…
The concept of \emph{almost orthogonal vectors}, i.e.\ vectors whose cosine similarity is close to $0$, relates to topics both in pure mathematics and in coding theory under the guises of spherical packing and spherical codes. In recent…
The discovery potential of the LHC is investigated for the minimal anomaly-mediated supersymmetry breaking (mAMSB) scenario, using the ATLAS fast detector simulator, including track reconstruction and particle identification. Generic…
Nearest-neighbor query processing is a fundamental operation for many image retrieval applications. Often, images are stored and represented by high-dimensional vectors that are generated by feature-extraction algorithms. Since tree-based…
We propose a novel strategy for disentangling proton collisions at hadron colliders such as the LHC that considerably improves over the current state of the art. Employing a metric inspired by optimal transport problems as the cost function…
In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets…
Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…
We present a simple but powerful reinterpretation of kernelized locality-sensitive hashing (KLSH), a general and popular method developed in the vision community for performing approximate nearest-neighbor searches in an arbitrary…