Related papers: A Note on Approximate Nearest Neighbor Methods
The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions---$\epsilon$-approximations and…
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…
The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has…
The nearest-neighbor rule is a well-known classification technique that, given a training set P of labeled points, classifies any unlabeled query point with the label of its closest point in P. The nearest-neighbor condensation problem aims…
Nearest neighbors (NN) are traditionally used to compute final decisions, e.g., in Support Vector Machines or k-NN classifiers, and to provide users with explanations for the model's decision. In this paper, we show a novel utility of…
Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between 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 study the problem of approximate near neighbor (ANN) search and show the following results: - An improved framework for solving the ANN problem using locality-sensitive hashing, reducing the number of evaluations of locality-sensitive…
Demands for minimum parameter setup in machine learning models are desirable to avoid time-consuming optimization processes. The $k$-Nearest Neighbors is one of the most effective and straightforward models employed in numerous problems.…
In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…
This paper analyzes k nearest neighbor classification with training data anonymized using anatomy. Anatomy preserves all data values, but introduces uncertainty in the mapping between identifying and sensitive values. We first study the…
In pattern recognition or machine learning, it is a very fundamental task to find nearest neighbors of a given point. All the methods for the task work basically by comparing the given point to all the points in the data set. That is why…
Nearest neighbor search is a basic computational tool used extensively in almost research domains of computer science specially when dealing with large amount of data. However, the use of nearest neighbor search is restricted for the…
Suppose $V$ is an $n$-element set where for each $x \in V$, the elements of $V \setminus \{x\}$ are ranked by their similarity to $x$. The $K$-nearest neighbor graph is a directed graph including an arc from each $x$ to the $K$ points of $V…
The problem of nearest neighbor condensing has enjoyed a long history of study, both in its theoretical and practical aspects. In this paper, we introduce the problem of weighted distance nearest neighbor condensing, where one assigns…
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…
In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the…
We present a randomized distributed approximation algorithm for the metric uncapacitated facility location problem. The algorithm is executed on a bipartite graph in the Congest model yielding a (1.861 + epsilon) approximation factor, where…