Dilated Convolutional Neural Networks for Sequential Manifold-valued Data.

Area of Science:

• Neuroimaging
• Deep Learning
• Computational Anatomy

Background:

• Deep neural networks (DNNs) are being extended to non-standard data types like graphs and manifold-valued data.
• Incorporating data geometry into model design can yield significant empirical improvements.
• Sequential manifold-valued data, common in neuroimaging (e.g., symmetric positive definite matrices), presents unique analytical challenges.

Purpose of the Study:

• To develop a deep learning architecture for analyzing sequential manifold-valued neuroimaging data.
• To address computational and technical issues associated with recurrent models for this data type.
• To investigate the utility of Riemannian geometry in deep learning for neuroimaging.

Main Methods:

• Development of a dilated convolutional neural network (CNN) architecture tailored for manifold-valued sequences.
• Derivation of network modules that explicitly incorporate Riemannian manifold structure.
• Leveraging weighted Fréchet Mean (wFM) calculations for network operations.

Main Results:

• The proposed dilated CNN architecture effectively processes sequential manifold-valued data.
• The model successfully identifies brain fiber bundles related to Alzheimer's disease (AD) pathology load.
• Significant associations were found even in cognitively healthy subjects.

Conclusions:

• Dilated convolutional neural networks offer a viable alternative to recurrent models for manifold-valued sequence analysis in neuroimaging.
• The integration of Riemannian geometry enhances the performance of deep learning models for complex data.
• This approach shows promise for early detection and understanding of neurodegenerative diseases like AD through group difference analysis.