If X is a Banach space then the Banach space c(X) of all X-valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C(X) \ V has a nearest point in V .

Capacitated p-median problem (CPMP) is a well-known facility-location problem, in which p capacitated facility points are selected to satisfy n demand points in such a way that the total assigned demand to each facility does not exceed its capacity. Minimizing the total sum of distances between each demand point and its nearest facility point is the objective of the problem. Developing an effic...

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...

Given a set S of points in a metric space with distance function D, the nearest-neighbor searching problem is to build a data structure for S so that for an input query point q, the point s ∈ S that minimizes D(s, q) can be found quickly. We survey approaches to this problem, and its relation to concepts of metric space dimension. Several measures of dimension can be estimated using nearest-nei...

The use of “nearest-neighbor” sampling has a long history. It involves measuring the distance from a random point in an area to the nearest object. That history involves never quite solving the problem, many examinations of special cases that never occur, adjustments that were ad-hoc, and a great deal of uninformative algebra. In forestry we have attempted to use the “nearest-tree” method for e...

In nearest neighbor searching we are given a set of n data points in real d-dimensional space, <d, 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 interested in data structures that use optimal O(dn) storage. In this paper we consi...

The three-state Potts model with antiferromagnetic nearest-neighbor (n.n.) and ferromagnetic next-nearest-neighbor (n.n.n) interaction is investigated within a mean-field theory. We find that the phase-diagram contains two kind of ordered phases, so-called BSS phase and PSS phase, separated by a discontinuous phase transition line. Order-disorder transition is continuous for the weak n.n.n. int...

Nonsmooth analysis of a broad class of functions taking the form F (x) = mini fi(x), where each fi is a convex function. One element of this class of functions is the distance function, which measures the distance between a point and the nearest point on the nearest obstacle. Many motion planning algorithms are based on the distance function, and thus rigorous analysis of the distance function ...

Face recognition is a very challenging issue and has attracted much attention over the past decades. This paper makes a new attempt to face recognition based on 3D point clouds by constructing 3D eigenfaces. First, a 3D mesh model is built to represent the face shape provided by the point cloud. Then, the principle component analysis (PCA) is used to construct the 3D eigenfaces, which describe ...

Finding point correspondences between two views is generally based on the matching of local photometric descriptors. A subsequent geometric constraint ensures that the set of matching points is consistent with a realistic camera motion. Starting from a paper by Moisan and Stival, we propose an a contrario model for matching interest points based on descriptor similarity and geometric constraint...