DeepJAM: Joint alignment of multivariate quasi-periodic functional data using deep learning

• Published in: Statistics and computing Vol. 35; no. 5
• Main Authors: Pham, Vi Thanh, Nielsen, Jonas Bille, Kofoed, Klaus Fuglsang, Kühl, Jørgen Tobias, Jensen, Andreas Kryger
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2025; Springer Nature B.V
• Subjects: Alignment; Amplitudes; Artificial Intelligence; Artificial neural networks; Computer Science; Electrocardiography; Machine learning; Multivariate analysis; Original Paper; Periodic functions; Probability and Statistics in Computer Science; Statistical analysis; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Wearable technology; Elastic Phase-Amplitude Separation; Functional Data; Quasi-Periodic Functions; Multiscale Time Warping; Joint Multivariate Alignment; Deep Learning
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-025-10678-8

The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often ignore the phase variability and instead focus on the variability in the observed amplitude. We present a novel method for joint alignment of multivariate quasi-periodic functions using deep neural networks, decomposing, but retaining all the information in the data by preserving both phase and amplitude variability. Our proposed neural network uses a special activation of the output that builds on the unit simplex transformation, and we utilize a loss function based on the Fisher-Rao metric to train our model. Furthermore, our method is unsupervised and can provide an optimal common template function as well as subject-specific templates. We demonstrate our method on two simulated datasets and one real example, comprising data from 12-lead 10s electrocardiogram recordings.