β-integrated local depth and corresponding partitioned local depth representation

2025/06/17 by Wang, Siyi, Leblanc, Alexandre, McNicholas, Paul D.
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2506.14108

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 \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.

Citations

• Depth-Based Local Center Clustering: A Framework for Handling Different Clustering Scenarios
• Anomaly detection using data depth: multivariate case
• Choosing among notions of multivariate depth statistics
• Depth and depth-based classification with R-package ddalpha
• Fast nonparametric classification based on data depth
• Convergence of depths and depth-trimmed regions
• DD-Classifier: Nonparametric Classification Procedure Based onDD-Plot
• Exactly computing bivariate projection depth contours and median

Cited by

• Depth-Based Local Center Clustering: A Framework for Handling Different Clustering Scenarios

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