Robust domain selection for functional data via interval-wise testing and effect size mapping

2025-06-04

AI Summary

This study addresses the domain selection problem in functional data analysis, aiming to robustly identify subintervals within the function’s domain that significantly discriminate among multiple groups’ location parameters—particularly for quantitative ultrasound (QUS) signals contaminated by outliers and missing segments. We propose a novel framework integrating interval-wise hypothesis testing with functional M-estimation to enable robust inference of location differences across multiple groups. Additionally, we introduce a multiscale effect-size heatmap that facilitates clinically interpretable visualization of dynamic functional patterns and supports subdomain discrimination. Experiments on both simulated and real QUS data demonstrate that our method substantially improves robustness against outliers and segmentwise missingness, achieves higher domain localization accuracy than existing approaches, and yields heatmaps that assist clinicians in efficiently selecting biologically meaningful marker intervals.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Among inferential problems in functional data analysis, domain selection is one of the practical interests aiming to identify sub-interval(s) of the domain where desired functional features are displayed. Motivated by applications in quantitative ultrasound signal analysis, we propose the robust domain selection method, particularly aiming to discover a subset of the domain presenting distinct behaviors on location parameters among different groups. By extending the interval testing approach, we propose to take into account multiple aspects of functional features simultaneously to detect the practically interpretable domain. To further handle potential outliers and missing segments on collected functional trajectories, we perform interval testing with a test statistic based on functional M-estimators for the inference. In addition, we introduce the effect size heatmap by calculating robustified effect sizes from the lowest to the largest scales over the domain to reflect dynamic functional behaviors among groups so that clinicians get a comprehensive understanding and select practically meaningful sub-interval(s). The performance of the proposed method is demonstrated through simulation studies and an application to motivating quantitative ultrasound measurements.

Problem

• Identify sub-intervals with distinct functional group behaviors
• Detect interpretable domains using multi-aspect feature analysis
• Handle outliers and missing data in functional trajectories

Innovation

• Interval-wise testing for functional domain selection
• Functional M-estimators for robust outlier handling
• Effect size heatmap for dynamic behavior visualization