# Online EM for Functional Data

arXiv: https://arxiv.org/abs/1604.00570 · HTML: https://mlsanity.com/paper/1604.00570/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2016.

## Built on by (most cited first, 3 of 3)

- [Review of Clustering Methods for Functional Data](https://mlsanity.com/paper/2210.00847/) (2022)
- [A Class of Two-Timescale Stochastic EM Algorithms for Nonconvex Latent Variable Models](https://mlsanity.com/paper/2203.10186/) (2022)
- [Towards frugal unsupervised detection of subtle abnormalities in medical imaging](https://mlsanity.com/paper/2309.02458/) (2023)

## Abstract (arXiv)

A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model generalizes the Bayesian dense deformable template model (Allassonni`ere et al., 2007), a hierarchical model in which the template is the function to be estimated and the deformation is a nuisance, assumed to be random with a known prior distribution. The templates are estimated using a Monte Carlo version of the online Expectation-Maximization algorithm, extending the work from Capp'e and Moulines (2009). Our sequential inference framework is significantly more computationally efficient than equivalent batch learning algorithms, especially when the missing data is high-dimensional. Some numerical illustrations on curve registration problem and templates extraction from images are provided to support our findings.