Scalable Geometric Learning with Correlation-Based Functional Brain Networks

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation matrices. While earlier attempts have embraced the quotient geometry of the correlation manifold, they remain limited by computational inefficiency and numerical instability, particularly in high-dimensional contexts. This paper presents a novel geometric framework that employs diffeomorphic transformations to embed correlation matrices into a Euclidean space, preserving salient manifold properties and enabling large-scale analyses. The proposed method integrates with established learning algorithms - regression, dimensionality reduction, and clustering - and extends naturally to population-level inference of brain networks. Simulation studies demonstrate both improved computational speed and enhanced accuracy compared to conventional manifold-based approaches. Moreover, applications in real neuroimaging scenarios illustrate the framework's utility, enhancing behavior score prediction, subject fingerprinting in resting-state fMRI, and hypothesis testing in electroencephalogram data. An open-source MATLAB toolbox is provided to facilitate broader adoption and advance the application of correlation geometry in functional brain network research.

Automated identification of neural cells in the multi-photon images using deep-neural networks

The advancement of the neuroscientific imaging techniques has produced an unprecedented size of neural cell imaging data, which calls for automated processing. In particular, identification of cells from two photon images demands segmentation of neural cells out of various materials and classification of the segmented cells according to their cell types. To automatically segment neural cells, we used U-Net model, followed by classification of excitatory and inhibitory neurons and glia cells using a transfer learning technique. For transfer learning, we tested three public models of resnet18, resnet50 and inceptionv3, after replacing the fully connected layer with that for three classes. The best classification performance was found for the model with inceptionv3. The proposed application of deep learning technique is expected to provide a critical way to cell identification in the era of big neuroscience data.

Geometric Convolutional Neural Network for Analyzing Surface-Based Neuroimaging Data

The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a spherical surface and renders pattern recognition in a multi-shell mesh structure. The classification accuracy for sex was significantly higher than that of SVM and image based CNN. It only uses MRI thickness data to classify gender but this method can expand to classify disease from other MRI or fMRI data