TY  - JOUR
A1  - Hanik, Martin
A1  - Steidl, Gabriele
A1  - von Tycowicz, Christoph
T1  - Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs
T2  - International Journal of Computer Vision
N2  - We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant under node permutations and the feature manifold's isometries. These properties have led to a beneficial inductive bias in many deep-learning tasks. Furthermore, they enable novel, more flexible feature designs.
Numerical examples on synthetic data and an Alzheimer's classification application on triangle meshes of the right hippocampus demonstrate the usefulness of our new layers: While they apply to a much broader class of problems, they outperform task-specific state-of-the-art networks.
Y1  - 2026
UR  - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/9363
VL  - 134
PB  - Springer
ER  -