# β-integrated local depth and corresponding partitioned local depth representation

arXiv: https://arxiv.org/abs/2506.14108 · HTML: https://mlsanity.com/paper/2506.14108/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Automatic depth-based local center clustering via β-integrated local depth and adaptive grouping](https://mlsanity.com/paper/2609.26748/) (2026)

## Abstract (arXiv)

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 citepaindaveine2013depth, 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.