Given a set S of n d-dimensional points, the k-nearest neighbors (KNN) is the problem of quickly finding k points in S that are nearest to a query point q. The k-nearest neighbors problem has applications in machine learning for classifications and regression and and also in searching. The secure version of KNN where either q or S are encrypted, has applications such as providing services over ...

Nearest neighbor searching is a fundamental computational problem. A set of n data points is given in real d-dimensional space, and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported efficiently. Because data sets can be quite large, we are primarily interested in data structures that use only O...

This paper provides the first solution to the kinetic reverse k-nearest neighbor (RkNN) problem in R, which is defined as follows: Given a set P of n moving points in arbitrary but fixed dimension d, an integer k, and a query point q / ∈ P at any time t, report all the points p ∈ P for which q is one of the k-nearest neighbors of p.

The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points accumulated by CNN. The bound originates in a bound on the number of times the ...

A k-nearest neighbor (kNN) query determines the k nearest points, using distance metrics, from a given location. An all k-nearest neighbor (AkNN) query constitutes a variation of a kNN query and retrieves the k nearest points for each point inside a database. Their main usage resonates in spatial databases and they consist the backbone of many location-based applications and not only. In this w...

Finding nearest neighbors in large multi-dimensional data has always been one of the research interests in data mining field. In this paper, we present our continuous research on similarity search problems. Previously we have worked on exploring the meaning of K nearest neighbors from a new perspective in PanKNN [20]. It redefines the distances between data points and a given query point Q, eff...

In discrete k-center and k-median clustering, we are given a set of points P in a metric space M , and the task is to output a set C ⊆ P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center, the cost is the furthest a point has to travel to its nearest center, whereas for k-median, the cost is the sum of all point to nearest center distances. In the fault-t...