$\beta$-integrated local depth and corresponding partitioned local depth representation

TL;DR

This paper introduces a new local depth measure called $eta$-ILD that generalizes existing methods, offering robustness and interpretability, and improves classification and outlier detection performance.

Contribution

The paper proposes the $eta$-integrated local depth as a novel, robust local depth measure and introduces a partitioned representation for enhanced interpretability and application.

Findings

$eta$-ILD is robust and versatile across locality levels.

Partitioned local depth matrix improves interpretability.

Enhanced performance in classification and outlier detection.

Abstract

A novel local depth definition, $\beta$-integrated local depth ($\beta$-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. $\beta$-ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for $\beta$-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.