Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Wang, Siyi, Leblanc, Alexandre, McNicholas, Paul D.
Institutions: McMaster University, University of Manitoba
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6967060086
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