Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...

A novel clustering algorithm CSHARP is presented for the purpose of finding clusters of arbitrary shapes and arbitrary densities in high dimensional feature spaces. It can be considered as a variation of the Shared Nearest Neighbor algorithm (SNN), in which each sample data point votes for the points in its k-nearest neighborhood. Sets of points sharing a common mutual nearest neighbor are cons...

In nearest neighbor searching we are given a set of n data points in real d-dimensional space, R, 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. Given the limitation of...

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

User preference queries are very important in spatial databases. With the help of these queries, one can found best location among points saved in database. In many situation users evaluate quality of a location with its distance from its nearest neighbor among a special set of points. There has been less attention about evaluating a location with its distance to nearest neighbors in spatial us...

A database is populated with a set of points represented by n-tuples of real numbers. A query consists of a point q (not necessarily in the database) and an integer k, asking for the k "nearest" database points to the query point. The exact output for the query consists of the k nearest points, but if the database is large and a quick response is required, a good approximate output is sought. A...

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we c...