Project
AA5-3 (was EF1-18)
Manifold-Valued Graph Neural Networks
Project Heads
Christoph von Tycowicz, Gabriele Steidl
Project Members
Martin Hanik
Project Duration
01.01.2022 − 31.12.2023
Located at
FU Berlin
Description
Geometry-aware, data-analytic approaches improve understanding and assessment of pathophysiological processes. In this project, we derive a new theoretical framework for deep neural networks that can cope with geometric data and apply it for classification of musculoskeletal illness from both shape and movement patterns. As part of the process, we develop the necessary software in Python and make it accessible through the Morphomatics library. The source code is freely available on GitHub, and there are tutorials that can be run live on Binder.
In an application of graph neural networks to manifolds, we studied how well the latter can predict cognitive measures from brain connectomes. The latter are graphs with edge weights determined by correlations in brain activity, and they can be thought of as symmetric positive-definite matrices, which constitute a cone-like manifold. In our work, we could show that (a) graph neural networks outperform state-of-the-art in the prediction of two common cognitive scores and (b) these results can sometimes even be improved by only using a learned representative subset of samples for training.
To generalize layers for manifold-valued features, we are investigating diffusion processes as they allow for information transfer in embedded graphs. In the figures below, you can see a graph that is embedded in the two-dimensional sphere and the flow of (other) vertices of a graph under a diffusion-like process.
External Website
Related Publications
- Cristoph von Tycowicz. Towards shape-based knee osteoarthritis classification using graph convolutional networks, In 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020), pp. 750–753, 2020. Preprint.
- Ivan Sipiran et al., SHREC 2021: Retrieval of Cultural Heritage Objects, Computers and Graphics, Vol. 100, pp. 1–20, 2021.
- Felix Ambellan, Martin Hanik, Christoph von Tycowicz, Morphomatics, 2021
- Martin Hanik, Mehmet Arif Demirtaş, Mohammed Amine Gharsallaoui, Islem Rekik. Predicting cognitive scores with graph neural networks through sample selection learning, Brain Imaging and Behavior, Vol.16, pp. 1123-1138, 2022. Preprint.
- Ariel Caputo et al. SHREC 2022 Track on Online Detection of Heterogeneous Gestures, Computers and Graphics, Vol.107, pp. 241-251, 2022. Preprint.
- Adele Myers et al. ICLR 2022 Challenge for Computational Geometry & Topology: Design and Results, Proceedings of Topology, Algebra, and Geometry in Learning, pp. 269-276, Vol.196, Proceedings of Machine Learning Research, 2022
