Multidimensional asymptotic spectral analysis and applications

Bloch Wave Homogenization and Spectral Asymptotic Analysis

We consider a second-order elliptic equation in a bounded periodic heterogeneous medium and study the asymptotic behavior of its spectrum, as the structure period goes to zero. We use a new method of Eloch wave homogenization which, unlike the classical homogenization method, characterizes a renormalized limit of the spectrum, namely sequences of eigenvalues of the order of the square of. the m...

Asymptotic Distribution of Divergence Measure with Applications

Multidimensional Network Analysis: Models, Analytics, Applications

Multidimensional networks (also known as multilayer, multiplex, or multislice) are receiving increased attention from computer scientists, physicists, mathematicians, and other scientists, thanks also to many application scenarios and increased availability of data for analytics. Social sciences are interested in the multidimensional aspects of the connections between individuals, not only by l...

Applications of Convex Analysis to Multidimensional Scaling

A. In this paper we discuss the convergence of an algorithm for metric and nonmetric multidimensional scaling that is very similar to the C-matrix algorithm of Guttman. The paper improves some earlier results in two respects. In the first place the analysis is extended to cover general Minkovski metrics, in the second place a more elementary proof of convergence based on results of Rober...

Spectral multidimensional scaling.

An important tool in information analysis is dimensionality reduction. There are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks. The efficiency of dimension reduction tools is measured in terms of memory and computational complexity, which are usually a function of the number of the given data ...