Nonlinear Dimensionality Reduction with Diffusion Maps in Practice
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908793340690432 |
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| author | Beier, Sönke Pirker-Díaz, Paula Pagenkopf, Friedrich Wiesner, Karoline |
| author_facet | Beier, Sönke Pirker-Díaz, Paula Pagenkopf, Friedrich Wiesner, Karoline |
| contents | Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Dimensionality Reduction with Diffusion Maps in Practice Beier, Sönke Pirker-Díaz, Paula Pagenkopf, Friedrich Wiesner, Karoline Machine Learning Applications Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones. |
| title | Nonlinear Dimensionality Reduction with Diffusion Maps in Practice |
| topic | Machine Learning Applications |
| url | https://arxiv.org/abs/2601.20428 |