Given a square matrix with noisy dissimilarity measures between pairs of data samples, the metric nearness model computes best approximation from set valid distance metrics. Despite its wide applications in machine learning and processing tasks, faces non-trivial computational requirements seeking solution due to large number constraints associated feasible region. Our work designed practical a...

J. Dobrakovová and the author in [7] introduced the relation of nearness in Banach space. In this paper we will go on investigating the nearness relation in a linear space with a countable vector base, focusing the results to topological properties of such relations.

The present paper investigates approximation spaces in the context of topological structures which axiomatise the notion of nearness. Starting with the framework of information quanta which distinguishes two levels of information structures, namely property systems (the first level) and information quantum relational systems (the second level), we shall introduce the notion of Pawlak’s property...

Let S be a closed convex set of matrices and C be a given matrix. The matrix nearness problem considered in this paper is to find a matrix X in the set S at which max {|xij − cij |} reaches its minimum value. In order to solve the matrix nearness problem, the problem is reformulated to a min-max problem firstly, then the relationship between the min-max problem and a monotone linear variational...

An important step in the solution of a matrix nearness problem that arises in certain machine learning 3 applications is finding the zero of f(α) = z exp(logX + αzz )z − b. The matrix valued exponential and logarithm 4 in f(α) arises from the use of the von Neumann matrix divergence tr(X logX − X log Y − X + Y ) to measure the 5 nearness between the positive definite matrices X and Y . A key st...

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...

Ubaid-Allah Sindhi is among those very few political thinkers and activists of the twentieth-century India who were initially associated with the traditional theological seminaries but their political vision was marked by liberalism and openmindedness. He established a non-communal political party— Mahabharat Sarvrajia Party in 1924 in order to translate his political ideals into practice. The ...