# Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data

## TL;DR

This paper presents a probabilistic model combining spatio-temporal matrix factorization and monotonic Gaussian Processes to analyze high-dimensional brain imaging data, effectively disentangling disease progression patterns.

## Contribution

It introduces a novel spatio-temporal Gaussian Process model with monotonic constraints for brain disease progression analysis, incorporating anatomically plausible priors and multi-scale sparse spatial coding.

## Key findings

- Successfully disentangles disease trajectories in synthetic data
- Reveals key brain regions involved in neurodegeneration
- Identifies disease-specific temporal progression patterns

## Abstract

We introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic trajectories, the temporal sources are defined as monotonic and time-reparametrized Gaussian Processes. To account for the non-stationarity of brain images, we model the spatial sources as sparse codes convolved at multiple scales. The method was tested on synthetic data favourably comparing with standard blind source separation approaches. The application on large-scale imaging data from a clinical study allows to disentangle differential temporal progression patterns mapping brain regions key to neurodegeneration, while revealing a disease-specific time scale associated to the clinical diagnosis.