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arXiv · 2510.26631

Natural methods of unsupervised topological alignment

Mikhail S. Arbatskii·Maksim V. Kukushkin·Dmitriy E. Balandin·Alexey V. Churov
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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.

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Mikhail S. Arbatskii, Maksim V. Kukushkin, Dmitriy E. Balandin, Alexey V. Churov. 2025-10-30. Natural methods of unsupervised topological alignment. https://arxiv.org/abs/2510.26631

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