Efficiently Approximating Spread Dimension with High Confidence
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913481686515712 |
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| author | Dunne, Kevin |
| author_facet | Dunne, Kevin |
| contents | The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. In previous work, we developed the theoretical basis for applications of spread dimension as an intrinsic dimension estimator. In this paper we introduce the pseudo spread dimension which is an efficient approximation of spread dimension, and we derive a formula for the standard error associated with this approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficiently Approximating Spread Dimension with High Confidence Dunne, Kevin Metric Geometry Populations and Evolution The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. In previous work, we developed the theoretical basis for applications of spread dimension as an intrinsic dimension estimator. In this paper we introduce the pseudo spread dimension which is an efficient approximation of spread dimension, and we derive a formula for the standard error associated with this approximation. |
| title | Efficiently Approximating Spread Dimension with High Confidence |
| topic | Metric Geometry Populations and Evolution |
| url | https://arxiv.org/abs/2408.14590 |