APPROXIMATE WEIGHTED FARTHEST NEIGHBORS AND MINIMUM DILATION STARS

Approximate Weighted Farthest Neighbors and Minimum Dilation Stars

We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest neighbors, we show how to find (1+ ε)-approximate farthest neighbors in time O(logn) per query in D-dimensional Euclidean space for any constants D and ε. A...

Computing Farthest Neighbors on a Convex Polytope

Let be a set of points in convex position in . The farthest-point Voronoi diagram of partitions into convex cells. We consider the intersection of the diagram with the boundary of the convex hull of . We give an algorithm that computes an implicit representation of in expected time. More precisely, we compute the combinatorial structure of , the coordinates of its vertices, and the equation of ...

On Top-$k$ Weighted SUM Aggregate Nearest and Farthest Neighbors in the $L_1$ Plane

In this paper, we present algorithms for the top-k nearest neighbor searching where the input points are exact and the query point is uncertain under the L1 metric in the plane. The uncertain query point is represented by a discrete probability distribution function, and the goal is to efficiently return the top-k expected nearest neighbors, which have the smallest expected distances to the que...

Farthest Neighbors and Center Points in the Presen

Feature Selection for Clustering by Exploring Nearest and Farthest Neighbors

Feature selection has been explored extensively for use in several real-world applications. In this paper, we propose a new method to select a salient subset of features from unlabeled data, and the selected features are then adaptively used to identify natural clusters in the cluster analysis. Unlike previous methods that select salient features for clustering, our method does not require a pr...