$\beta$-integrated local depth and corresponding partitioned local depth representation
Statistics Theory
2025-06-24 v2 Methodology
Statistics Theory
Abstract
A novel local depth definition, -integrated local depth (-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. -ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for -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.
Cite
@article{arxiv.2506.14108,
title = {$\beta$-integrated local depth and corresponding partitioned local depth representation},
author = {Siyi Wang and Alexandre Leblanc and Paul D. McNicholas},
journal= {arXiv preprint arXiv:2506.14108},
year = {2025}
}