Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911158168977408 |
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| author | Beylier, Charlotte Joharinad, Parvaneh Jost, Jürgen Torbati, Nahid |
| author_facet | Beylier, Charlotte Joharinad, Parvaneh Jost, Jürgen Torbati, Nahid |
| contents | Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension Beylier, Charlotte Joharinad, Parvaneh Jost, Jürgen Torbati, Nahid Computer Vision and Pattern Recognition Discrete Mathematics Machine Learning 51K05 (primary) 57-08, 53Z50, 55U10 (secondary) G.2.2 Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques. |
| title | Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension |
| topic | Computer Vision and Pattern Recognition Discrete Mathematics Machine Learning 51K05 (primary) 57-08, 53Z50, 55U10 (secondary) G.2.2 |
| url | https://arxiv.org/abs/2509.13385 |