$β$-integrated local depth and corresponding partitioned local depth representation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918067254067200 |
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| author | Wang, Siyi Leblanc, Alexandre McNicholas, Paul D. |
| author_facet | Wang, Siyi Leblanc, Alexandre McNicholas, Paul D. |
| contents | A novel local depth definition, $β$-integrated local depth ($β$-ILD), is proposed as a generalization of the local depth introduced by Paindaveine and Van Bever \cite{paindaveine2013depth}, designed to quantify the local centrality of data points. $β$-ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for $β$-ILD is introduced, leading to the construction of a matrix that quantifies the contribution of one point to another's local depth, providing a new interpretable measure of local centrality. These concepts are applied to classification and outlier detection tasks, demonstrating significant improvements in the performance of depth-based algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $β$-integrated local depth and corresponding partitioned local depth representation Wang, Siyi Leblanc, Alexandre McNicholas, Paul D. Statistics Theory Methodology A novel local depth definition, $β$-integrated local depth ($β$-ILD), is proposed as a generalization of the local depth introduced by Paindaveine and Van Bever \cite{paindaveine2013depth}, designed to quantify the local centrality of data points. $β$-ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for $β$-ILD is introduced, leading to the construction of a matrix that quantifies the contribution of one point to another's local depth, providing a new interpretable measure of local centrality. These concepts are applied to classification and outlier detection tasks, demonstrating significant improvements in the performance of depth-based algorithms. |
| title | $β$-integrated local depth and corresponding partitioned local depth representation |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2506.14108 |