Self-organizing maps have been adopted in many fields as the data visualization method of choice. The unified distance matrix is the de facto standard for evaluating and interpreting self-organizing maps. In large, high-dimensional problems clusters can be difficult to identify in the plain unified distance matrix. Here we introduce an enhanced version of the unified distance matrix in which cl...

We consider distance matrices of certain graphs and of points chosen in a rectangular grid. Formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained. Results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved. If D is the distance matrix of a tree, then we obtain certain results for a perturbat...

Elaeagnus angustifolia L. is a Eurasian tree that has become naturalized and has various ecological, medicinal and economical uses. In this study, a combination of morphological traits and RAPD markers were used to study the presence or absence of an association between genetic variation and morphological features among five populations of E. angustifolia collected from the East Azarbaijan of I...

In this study, we propose a three-stage weighted sum method for identifying the group ranks of alternatives. In the first stage, a rank matrix, similar to the cross-efficiency matrix, is obtained by computing the individual rank position of each alternative based on importance weights. In the second stage, a secondary goal is defined to limit the vector of weights since the vector of weights ob...

Keywords: Google problem Power Method Stochastic matrices Global rate of convergence Gradient methods Strong convexity a b s t r a c t In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence ...

Euclidean distance matrix completion problem aims at reconstructing the low dimensional geometry structure of nodes given only a few pairwise distances between nodes [1]. This problem arises in many applications including networks and machine learning where much information of points is laking. For instance, in sensor networks, due to the constraints of energy and communication radius, sensor n...