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

arXiv: https://arxiv.org/abs/2312.09422 · HTML: https://mlsanity.com/paper/2312.09422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Can recurrent neural networks warp time?](https://mlsanity.com/paper/1804.11188/) (2018)
- [Temporal Transformer Networks: Joint Learning of Invariant and Discriminative Time Warping](https://mlsanity.com/paper/1906.05947/) (2019)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [Learning to Exploit Invariances in Clinical Time-Series Data using Sequence Transformer Networks](https://mlsanity.com/paper/1808.06725/) (2018)
- [Elastic depths for detecting shape anomalies in functional data](https://mlsanity.com/paper/1907.06759/) (2019)

## Abstract (arXiv)

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.