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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.03574 |
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| _version_ | 1866910512855384064 |
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| author | Arias-Castro, Ery Coda, Elizabeth |
| author_facet | Arias-Castro, Ery Coda, Elizabeth |
| contents | In this paper, we take an axiomatic approach to defining a population hierarchical clustering for piecewise constant densities, and in a similar manner to Lebesgue integration, extend this definition to more general densities. When the density satisfies some mild conditions, e.g., when it has connected support, is continuous, and vanishes only at infinity, or when the connected components of the density satisfy these conditions, our axiomatic definition results in Hartigan's definition of cluster tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Axiomatic Definition of Hierarchical Clustering Arias-Castro, Ery Coda, Elizabeth Machine Learning Statistics Theory In this paper, we take an axiomatic approach to defining a population hierarchical clustering for piecewise constant densities, and in a similar manner to Lebesgue integration, extend this definition to more general densities. When the density satisfies some mild conditions, e.g., when it has connected support, is continuous, and vanishes only at infinity, or when the connected components of the density satisfy these conditions, our axiomatic definition results in Hartigan's definition of cluster tree. |
| title | An Axiomatic Definition of Hierarchical Clustering |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2407.03574 |