Computing farthest neighbors on a convex polytope

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 ...

Gibbs/Metropolis algorithms on a convex polytope

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyltype inequalities. The top eig...

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...

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...