A phase and amplitude-based distance for functional data.

S. Díez Martínez, A. Arribas Gil, A. Grané Chávez

In Functional Data Analysis, observations are viewed as realizations of continuous processes, often representing the temporal evolution of a phenomenon. When comparing such curves for clustering or outlier detection, standard metrics such as the L2 distance may fail in the presence of phase variability, obscuring structural differences.

To address this, we propose novel distance measures that explicitly account for phase and amplitude variability. Our approach combines dissimilarities between curves and their derivatives, as well as differences between aligned curves and their warping functions. These components are integrated using Related Metric Scaling to avoid redundancy when multiple metrics are considered.

The proposed distances are evaluated through clustering under various scenarios, including different levels of group similarity and imbalance. Results show improved performance over traditional approaches, particularly with misaligned functional data.

Keywords: Functional Data Analysis, Distance measures, Phase variability, Amplitude variability, Clustering.

GT AMyC I: Advances in Distance-Based Methods
September 4, 2026  9:00 AM
Aula 28

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