# Statistical learning of spatiotemporal patterns from longitudinal manifold-valued networks

arXiv: https://arxiv.org/abs/1709.08491 · HTML: https://mlsanity.com/paper/1709.08491/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2017.

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

- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Deep Unsupervised Anomaly Detection in Brain Imaging: Large-Scale Benchmarking and Bias Analysis](https://mlsanity.com/paper/2512.01534/) (2025)
- [Variational Inference for Longitudinal Data Using Normalizing Flows](https://mlsanity.com/paper/2303.14220/) (2023)

## Abstract (arXiv)

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. The model learns a typical group-average trajectory characterizing the propagation of measurement changes across the graph nodes. The subject-specific trajectories are defined via spatial and temporal transformations of the group-average scenario, thus estimating the variability of spatiotemporal patterns within the group. To estimate population and individual model parameters, we adapted a stochastic version of the Expectation-Maximization algorithm, the MCMC-SAEM. The model is used to describe the propagation of cortical atrophy during the course of Alzheimer's Disease. Model parameters show the variability of this average pattern of atrophy in terms of trajectories across brain regions, age at disease onset and pace of propagation. We show that the personalization of this model yields accurate prediction of maps of cortical thickness in patients.