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| Главный автор: | |
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| Формат: | Recurso digital |
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| Опубликовано: |
Zenodo
2025
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| Предметы: | |
| Online-ссылка: | https://doi.org/10.5281/zenodo.17426170 |
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Оглавление:
- This paper explores the application of geometric and topological invariants for the characterization of complex multivariate datasets. In an era of increasing data dimensionality and complexity, traditional statistical methods often fail to capture the intrinsic structure of the data. We posit that tools from algebraic topology and differential geometry, such as persistent homology, Betti numbers, Euler characteristic, and discrete Ricci curvature, provide a robust framework for extracting meaningful, scale-invariant features. This work reviews the theoretical foundations of these invariants, discusses their computational implementation, and outlines a methodology for integrating them into data analysis pipelines. We argue that these methods, grounded in the manifold hypothesis, offer a powerful lens to uncover latent structures, clusters, and periodic patterns that are inaccessible to conventional techniques. By translating data point clouds into geometric and topological summaries, these invariants facilitate a more profound and qualitative understanding of the underlying generative processes, enhancing tasks like classification, anomaly detection, and visualization in high-dimensional spaces.