When objects are represented by curves in a plane, highly useful information is conveyed by significant points. In this paper, we compare the use of different mobile windows to extract dominant points of handwritten characters. The error rate and classification time using an edit distance based nearest neighbour search algorithm are compared for two different cases: string and tree representation.

We propose a separating-hyperplane algorithm for finding a nearest pair of points in two polytopes, where each polytope is expressed as the convex hull of given points in a Euclidian space. The proposed algorithm is an extension of the authors dual algorithm for finding t.he minimum-norm point in a polytope.

Let n points be placed independently in d−dimensional space according to the standard d−dimensional normal distribution. Let dn be the longest edge length for the nearest neighbor graph on these points. We show that lim n→∞ √ log n dn log log n = d √ 2 , d ≥ 2, a.s.

Subspace clustering developed from the group of cluster objects in all subspaces of a dataset. When clustering high dimensional objects, the accuracy and efficiency of traditional clustering algorithms are very poor, because data objects may belong to diverse clusters in different subspaces comprised of different combinations of dimensions. To overcome the above issue, we are going to implement...

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a l...

An offline handwritten signature classification approach is presented. The signature is parameterized using the radius values for contour points in the polar coordinates space. In order to determine the optimum outline for the classification task, nearest and faraway points were took into account. HMM and SVMLight model are analyzed in this work. Selecting faraway points offers better results, ...

Algorithms based on Nested Generalized Exemplar (NGE) theory 10] classify new data points by computing their distance to the nearest \generalized exemplar" (i.e. an axis-parallel multidimensional rectangle). An improved version of NGE, called BNGE, was previously shown to perform comparably to the Nearest Neighbor algorithm. Advantages of the NGE approach include compact representation of the t...

In this paper, we provide a simple approximation for the distance from an arbitrary location to the kth nearest point. Distance is measured as the Euclidean and the rectilinear distances on a continuous plane. The approximation demonstrates that the kth nearest distance is proportional to the square root of k and inversely proportional to the square root of the density of points. The accuracy o...

Many spectral estimation methods for irregularly sampled data tend to be heavily biased at higher frequencies or fail to produce a spectrum that is positive for all frequencies. A time series spectral estimator is introduced that applies the principles of a new automatic equidistant missing data algorithm to unevenly spaced data. This time series estimator approximates the irregular data by a n...

We propose a new approach for outlier detection, based on a new ranking measure that focuses on the question of whether a point is “important” for its nearest neighbors; using our notations low cumulative rank implies the point is central. For instance, a point centrally located in a cluster has relatively low cumulative sum of ranks because it is among the nearest neighbors of its own nearest ...