Quantum Harmonic Analysis and the Structure in Data: Augmentation
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916966633046016 |
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| author | Doerfler, Monika Luef, Franz McNulty, Henry |
| author_facet | Doerfler, Monika Luef, Franz McNulty, Henry |
| contents | In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to augmented data sets lie in the modulation space $M^1(\mathbb{R}^d)$, guaranteeing smoothness and continuity. Numerical examples on synthetic and audio data confirm the theoretical findings. While interesting in itself, the results suggest that manifold learning and feature extraction algorithms can benefit from systematic and informed augmentation principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Harmonic Analysis and the Structure in Data: Augmentation Doerfler, Monika Luef, Franz McNulty, Henry Functional Analysis Machine Learning Numerical Analysis In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to augmented data sets lie in the modulation space $M^1(\mathbb{R}^d)$, guaranteeing smoothness and continuity. Numerical examples on synthetic and audio data confirm the theoretical findings. While interesting in itself, the results suggest that manifold learning and feature extraction algorithms can benefit from systematic and informed augmentation principles. |
| title | Quantum Harmonic Analysis and the Structure in Data: Augmentation |
| topic | Functional Analysis Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2509.19474 |