Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding a...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. We found conditions under which T (M) is almost Kählerian, locally conformal Kählerian or Kählerian or wh...

Many authors have introduced the concept of fuzzy metric spaces in different ways.In this paper, we get a special structure for some separable fuzzy metric and M-fuzzy metric spaces, where the metric space has been introduced by George and Veermani.

The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra g without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module a in a canonical way. I...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

This article proposes a novel ship detection method for high-resolution SAR images. Our goal is to look at this question from a information geometry point of view. The method consists of two steps: construction of revised metric and Riemann structure, and extraction of targets. For the first step of the process, a revised metric is introduced on Gamma 2-manifold. We construct a special Riemanni...

An exact solution has an axial symmetry is obtained in the teleparallel theory of grav-itation. The associated metric has the structure function G(ξ) = 1 − ξ 2 − 2mAξ 3. The cubic nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad that its associated metric has the structure function in a factorisable form. This new form has the ...

The local equivalence problem for sub-Riemannian structures on threemanifolds is solved. In the course of the solution, it is shown how to attach a canonical Riemannian metric and connection to the given sub-Riemannian metric and it is shown how all of the differential invariants of the sub-Riemannian structure can be calculated. The relation between the completeness of the sub-Riemannian metri...

This paper aims at the description of the metric structure of music in terms of a processive or temporal approach. While many models in the metric domain assume a relatively consistent metric structure throughout the piece, the experience of listening to a complex piece of music often differs from that assumption. The processive approach applied in this paper is interpreted as the unfolding of ...