Natural methods of unsupervised topological alignment
Mikhail S. Arbatskii, Maksim V. Kukushkin, Dmitriy E. Balandin, Alexey V. Churov
TL;DR
A comparison analysis of the methods of the topological alignment is represented and harmonious generalizations of the graph Laplacian and kernel based methods are obtained with the central idea to find a natural structure coupling data sets of various nature.
Abstract
In the paper, we represent a comparison analysis of the methods of the topological alignment and extract the main mathematical principles forming the base of the concept. The main narrative is devoted to the so-called coupled methods dealing with the data sets of various nature. As a main theoretical result, we obtain harmonious generalizations of the graph Laplacian and kernel based methods with the central idea to find a natural structure coupling data sets of various nature. Finally, we discuss prospective applications and consider far reaching generalizations related to the hypercomplex numbers and Clifford algebras.