Projection depth for functional data: Practical issues, computation and applications

2026-02-26

AI Summary

This study addresses the challenge of characterizing and ranking functional data with complex morphological features by systematically investigating the application of Regularized Projection Depth (RPD) in tasks such as outlier detection, classification, and two-sample testing. The work proposes an efficient computation strategy based on random projections, elucidates the critical role of tuning parameters in effective dimensionality reduction, and, for the first time, comprehensively demonstrates RPD’s superior ability to capture shape-related characteristics of functional data. Experimental results show that RPD significantly outperforms existing functional depth methods across multiple statistical tasks, particularly excelling when handling data with intricate structural patterns.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the recently proposed regularized projection depth (RPD), which induces a meaningful ordering of functional data while appropriately accommodating their complex shape features. Specifically, we examine the impact and choice of its tuning parameter, which regulates the degree of effective dimension reduction applied to the data, and propose a random projection-based approach for its efficient computation, supported by theoretical justification. Through comprehensive numerical studies, we explore a wide range of statistical applications of the RPD and demonstrate its particular usefulness in uncovering shape features in functional data analysis. This ability allows the RPD to outperform competing depth-based methods, especially in tasks such as functional outlier detection, classification, and two-sample hypothesis testing.

Problem

• functional data
• functional depth
• ordering structure
• shape features
• outlier detection

Innovation

• regularized projection depth
• random projection
• functional data analysis
• tuning parameter selection
• shape feature extraction