Local depth-based classification of directional data

2026-02-23

AI Summary

Directional data naturally reside on the unit hypersphere, and traditional classification methods based on global statistical depth exhibit limitations in capturing local structures. This work proposes a novel framework that introduces local depth functions into directional data analysis, constructing a depth-versus-depth (DD) plot-based classifier. By integrating directional statistics with local depth measures, the method effectively overcomes the shortcomings of global depth in characterizing local geometric features. Experimental evaluations across multiple simulation settings and two real-world datasets demonstrate that the proposed approach consistently outperforms existing methods in both classification accuracy and robustness, significantly advancing the state of the art in directional data classification.

Technology Category

• Machine Learning: Learning with Manifolds
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Local Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward ordering of the data. This work aims at proposing the use of a local notion of data depth function to be applied in the DD-plot (Depth vs. Depth plot) to classify directional data. The proposed method is investigated through an extensive simulation study and two real-data examples.

Problem

• directional data
• classification
• statistical depth
• DD-plot

Innovation

• local depth
• directional data
• DD-plot
• classification
• statistical depth