Dennis Giannacopoulos

Yasmin Salehi, Dennis Giannacopoulos

Graph clustering plays a crucial role in graph representation learning but often faces challenges in achieving feature-space diversity. While Deep Modularity Networks (DMoN) leverage modularity maximization and collapse regularization to ensure structural separation, they lack explicit mechanisms for feature-space separation, assignment dispersion, and assignment-confidence control. We address this limitation by proposing Deep Modularity Networks with Diversity-Preserving Regularization (DMoN-DPR), which introduces three novel regularization terms: distance-based for inter-cluster separation, variance-based for per-cluster assignment dispersion, and an assignment-entropy penalty with a small positive weight, encouraging more confident assignments gradually. Our method significantly enhances label-based clustering metrics on feature-rich benchmark datasets (paired two-tailed t-test, $p\leq0.05$), demonstrating the effectiveness of incorporating diversity-preserving regularizations in creating meaningful and interpretable clusters.

Yasmin Salehi, Dennis Giannacopoulos

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms -- e.g., random forests, artificial neural networks (ANNs) -- with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures. Empirically, we demonstrate that the proposed architecture, PhysGNN, promises accurate and fast soft tissue deformation approximations, and is competitive with the state-of-the-art (SOTA) algorithms while promising enhanced computational feasibility, therefore suitable for neurosurgical settings.