The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause segregation or association, which are two major types of spatial patterns between the classes. These patterns can be studied using a nearest neighbour contingency table (NNCT) which is constructed using the frequencies of nearest neighbour types. Three new multivariate ...

Binary codes can be used to speed up nearest neighbor search tasks in large scale data sets as they are efficient for both storage and retrieval. In this paper, we propose a robust auto-encoder model that preserves the geometric relationships of high-dimensional data sets in Hamming space. This is done by considering a noise-removing function in a region surrounding the manifold where the train...

Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete geometry in Euclidean space where closed sets are uniquely generated by their extreme points. But, many of the geometries arising in computer science, e.g. the world wide we...

Recently, Bradley and Mangasarian [1] studied the problem of finding the nearest plane to m given points in Rn in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n× n symmetric positive semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0 ≤ q ≤ n− 1.

A phylogenetic tree is a rooted tree with unbounded degree such that each leaf node is uniquely labelled from 1 to n. The descendent subtree of of a phylogenetic tree T is the subtree composed by all edges and nodes of T descending from a vertex. Given a set of phylogenetic trees, we present linear time algorithms for finding all leaf-agree descendent subtrees as well as all isomorphic descende...

Using the most recent updated physics, calibrated solar models have been computed with the new thermonuclear reaction rates of NACRE, the recently available European compilation. Comparisons with models computed with the reaction rates of Caughlan & Fowler (1988) and of Adelberger et al. (1998) are made for global structure, expected neutrinos fluxes, chemical composition and sound speed profil...

Hausdorff metrics are used in geometric settings for measuring the distance between sets of points. They have been used extensively in areas such as computer vision, pattern recognition and computational chemistry. While computing the distance between a single pair of sets under the Hausdorff metric has been well studied, no results were known for the Nearest Neighbor problem under Hausdorff me...