Related papers: All nearest neighbor calculation based on Delaunay…
Due to the increased rate of information in the present era, local identification of similar and related data points by using neighborhood construction algorithms is highly significant for processing information in various sciences.…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
Fast and reliable K-Nearest Neighbor Graph algorithms are more important than ever due to their widespread use in many data processing techniques. This paper presents a runtime optimized C implementation of the heuristic "NN-Descent"…
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…
We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a $p$-dimensional feature space. By conducting the Delaunay triangulation algorithm…
We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\|\cdot\|$,…
High-dimensional approximate $K$ nearest neighbor search (AKNN) is a fundamental task for various applications, including information retrieval. Most existing algorithms for AKNN can be decomposed into two main components, i.e., candidate…
Let $\mathcal{D}$ be a set of straight-line segments in the plane, potentially crossing, and let $c$ be a positive integer. We denote by $P$ the union of the endpoints of the straight-line segments of $\mathcal{D}$ and of the intersection…
A recent series of papers by Andoni, Naor, Nikolov, Razenshteyn, and Waingarten (STOC 2018, FOCS 2018) has given approximate near neighbour search (NNS) data structures for a wide class of distance metrics, including all norms. In…
Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours…
When data is of an extraordinarily large size or physically stored in different locations, the distributed nearest neighbor (NN) classifier is an attractive tool for classification. We propose a novel distributed adaptive NN classifier for…
Approximate nearest neighbor search (ANNS) in high-dimensional vector spaces has a wide range of real-world applications. Numerous methods have been proposed to handle ANNS efficiently, while graph-based indexes have gained prominence due…
Neighborhood graphs are gaining popularity as a concise data representation in machine learning. However, naive graph construction by pairwise distance calculation takes $O(n^2)$ runtime for $n$ data points and this is prohibitively slow…
In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the…
In this paper, we study top-$k$ aggregate (or group) nearest neighbor queries using the weighted SUM operator under the $L_1$ metric in the plane. Given a set $P$ of $n$ points, for any query consisting of a set $Q$ of $m$ weighted points…
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…
Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms…
We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network in which the agents communicate with their neighbors and perform local computation. In the proposed algorithm, each agent can…