Joint Alignment of Multivariate Quasi-Periodic Functional Data Using Deep Learning

• URL: http://arxiv.org/abs/2312.09422v1
• Date: Tue, 14 Nov 2023 10:09:40 GMT
• Title: Joint Alignment of Multivariate Quasi-Periodic Functional Data Using Deep Learning
• Authors: Vi Thanh Pham (1), Jonas Bille Nielsen (2), Klaus Fuglsang Kofoed (2 and 3), J{\o}rgen Tobias K\"uhl (4), Andreas Kryger Jensen (1) ((1) Section of Biostatistics, Department of Public Health, Faculty of Health and Medical Sciences, University of Copenhagen, (2) Department of Cardiology and Radiology, Copenhagen University Hospital, (3) Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, (4) Department of Cardiology, Zealand University Hospital)
• Abstract summary: We present a novel method for joint alignment of multivariate quasi-periodic functions using deep neural networks. Our proposed neural network uses a special activation of the output that builds on the unit simplex transformation. We demonstrate our method on two simulated datasets and one real example, comprising data from 12-lead 10s electrocardiogram recordings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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