The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

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 ...

Hausdorr 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 Hausdorr metric has been well studied, no results were known for the Nearest Neighbor problem under Hausdorr metr...

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 two sets of points on a line, we want to translate one of them so that their Hausdorr distance (the maximum of the distances from a point in any of the sets to the nearest point in the other set) is as small as possible. We present an optimal O(n logn) algorithm for this problem.

The identification of universal properties from minimally processed data sets is one goal machine learning techniques applied to statistical physics. Here, we study how the minimum number variables needed accurately describe important features a set - intrinsic dimension ($I_d$) behaves in vicinity phase transitions. We employ state-of-the-art nearest neighbors-based $I_d$-estimators compute $I...

The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. It is proved that NSS is strongly consistent under certain assumptions. For completeness, NSS is evaluated through experiments on various sim...

We show that every in nite dimensional Banach space has a closed and bounded convex set that is not remotal. This settles a problem raised by Sababheh and Khalil in [8].