Cortical Surface-based Alzheimer's Disease Classification using Simplicial Neural Networks

다국어 초록 (Multilingual Abstract)

The complex folding structure of cerebral cortex poses great challenges to the tasks of analyzing the surface of the brain. There have been great efforts to apply convolutional neural networks to MRI images. However, when processing the cerebral cortex in the highly regular 3D voxel space, the adjacent voxels do not guarantee to be also adjacent on the actual surface. Such limitation of volumetric processing of the non-Euclidean surface leads to development of surface-based networks for cerebral cortex. In contrary to volume-based networks, recent surface-based analysis network typically uses convolutional networks on the surface graph data in non-Euclidean space. This line of work respects the topology of the cerebral cortex by modeling the thin surface as a graph and directly exploits the surface geometry. Our paper expands the surface-based analysis with a new approach by modeling the cortical surface as a higher-order structure, simplicial complex, and take advantage of such structure using higher-order message passing network. We conduct multiple experiment to show the effectiveness of our higher-order simplicial message passing network requires careful design. It shows the effectiveness of modeling cortical surface as simplicial complex, and we illustrate the advantages of our proposed message passing method on cortical surface with Alzheimer's Disease classification.

목차 (Table of Contents)

• Chapter1. Introduction 1
• Chapter1.1. Graph Convolutional Network-based method. 4
• Chapter1.2. Spherical CNN-based method 5
• Chapter1.3. Simplicial Complex. 7
• Chapter1.4. Simplicial Neural Networks. 9
• Chapter2. Materials and Methods 11
• Chapter2.1. Surface Mesh as Simplicial Complex. 12
• Chapter2.2. Message Passing on Cortical Simplicial Complex. 15
• Chapter2.3. Dataset and preprocessing 21
• Chapter2.4. Training and Implementation Details 22
• Chapter2.4.1. Network Architecture. 22
• Chapter2.4.2. Training Hyperparameters . 28
• Chapter3. Results. 30
• Chapter4. Discussion 37
• Chapter5. Conclusion 38
• Reference 39
• 국문요지. 45