Addressing Phase Discrepancies in Functional Data: A Bayesian Approach for Accurate Alignment and Smoothing

2025-06-17

AI Summary

Functional data—such as knee flexion angle curves—exhibit concurrent amplitude and phase variation, causing conventional alignment methods to distort shapes or lose subject-specific features. To address this, we propose a Bayesian functional alignment framework. Its core contributions are threefold: (1) a prior distribution over phase warping functions that rigorously enforces monotonicity and boundary constraints, ensuring mathematically valid time-warping; (2) a group-structured hierarchical model that jointly captures population-level patterns and subject-specific deviations under high inter-curve variability; and (3) simultaneous, distortion-free alignment and adaptive smoothing via posterior inference. Evaluated on real biomechanical datasets, the method achieves significantly improved alignment accuracy and smoother, more interpretable aligned curves. It demonstrates robustness to complex group structures and strong inter-subject heterogeneity. This work provides a principled, interpretable, and generalizable Bayesian solution for functional data analysis.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In many real-world applications, functional data exhibit considerable variability in both amplitude and phase. This is especially true in biomechanical data such as the knee flexion angle dataset motivating our work, where timing differences across curves can obscure meaningful comparisons. Curves of this study also exhibit substantial variability from one another. These pronounced differences make the dataset particularly challenging to align properly without distorting or losing some of the individual curves characteristics. Our alignment model addresses these challenges by eliminating phase discrepancies while preserving the individual characteristics of each curve and avoiding distortion, thanks to its flexible smoothing component. Additionally, the model accommodates group structures through a dedicated parameter. By leveraging the Bayesian approach, the new prior on the warping parameters ensures that the resulting warping functions automatically satisfy all necessary validity conditions. We applied our model to the knee flexion dataset, demonstrating excellent performance in both smoothing and alignment, particularly in the presence of high inter-curve variability and complex group structures.

Problem

• Addressing phase discrepancies in functional data alignment
• Preserving individual curve characteristics during smoothing
• Handling high inter-curve variability and group structures

Innovation

• Bayesian approach for phase alignment
• Flexible smoothing preserves curve characteristics
• Accommodates group structures with dedicated parameter