Natural methods of unsupervised topological alignment
Functional Analysis
2025-10-31 v1
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.
Cite
@article{arxiv.2510.26631,
title = {Natural methods of unsupervised topological alignment},
author = {Mikhail S. Arbatskii and Maksim V. Kukushkin and Dmitriy E. Balandin and Alexey V. Churov},
journal= {arXiv preprint arXiv:2510.26631},
year = {2025}
}