Topological extensions are closely related to nearness structures of various kinds. For example, the Smirnov compactification of a proximity space X is a compact Hausdorff space Y which contains X as a dense subspace and for which it is true that a pair of subsets of X is near if, and only if, their closures in Y meet. Lodato generalized this result to weaker conditions for the proximity and th...

In this paper, we study low-rank matrix nearness problems, with a focus on learning lowrank positive semidefinite (kernel) matrices for machine learning applications. We propose efficient algorithms that scale linearly in the number of data points and quadratically in the rank of the input matrix. Existing algorithms for learning kernel matrices often scale poorly, with running times that are c...

Aligned corpora are often-used resources in CLIR systems. The three qualities of translation corpora that most dramatically affect the performance of a corpus-based CLIR system are: (1) topical nearness to the translated queries, (2) the quality of the alignments, and (3) the size of the corpus. In this paper, the effects of these factors are studied and evaluated. Topics of two different domai...

In this paper, we introduce a near set approach to image analysis. Near sets result from generalization of rough set theory. One set X is near another set Y to the extent that the description of at least one of the objects in X matches the description of at least one of the objects in Y. Near set Evaluation And Recognition (NEAR) system is used to measure the degree of resemblance between facia...

We show that the properties of being injective, surjective, continuous, strongly surjective, stably solvable, carry over to weakly-near maps. We also prove a data dependence theorem for equations of the form A(x) = z, where A is weakly-near to some bijective map.

The objective of this article is to bridge the gap between two important research directions: (1) nearest neighbor search, which is a fundamental computational tool for large data analysis; and (2) complex network analysis, which deals with large real graphs but is generally studied via graph theoretic analysis or spectral analysis. In this article, we have studied the nearest neighbor search p...