Related papers: mSPD-NN: A Geometrically Aware Neural Framework fo…

State-space models (SSMs) have become a cornerstone for unraveling brain dynamics, revealing how latent neural states evolve over time and give rise to observed signals. By combining the flexibility of deep learning with the principled…

Neuroimaging provides essential tools for characterizing brain activity by quantifying connectivity strength between remote regions, using different modalities that capture different aspects of connectivity. Yet, decoding meaningful neural…

Existing multimodal stress/pain recognition approaches generally extract features from different modalities independently and thus ignore cross-modality correlations. This paper proposes a novel geometric framework for multimodal…

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The…

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…

Finding the biomarkers associated with ASD is helpful for understanding the underlying roots of the disorder and can lead to earlier diagnosis and more targeted treatment. A promising approach to identify biomarkers is using Graph Neural…

Statistical analysis on non-Euclidean spaces typically relies on distances as the primary tool for constructing likelihoods. However, manifold-valued data admits richer structures in addition to Riemannian distances. We demonstrate that…

Autism spectrum disorder (ASD) is a complex neurodevelopmental condition characterized by atypical functional brain connectivity and subtle structural alterations. rs-fMRI has been widely used to identify disruptions in large-scale brain…

Multi-modal neuroimaging technology has greatlly facilitated the efficiency and diagnosis accuracy, which provides complementary information in discovering objective disease biomarkers. Conventional deep learning methods, e.g. convolutional…

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…

Tremendous recent literature show that associations between different brain regions, i.e., brain connectivity, provide early symptoms of neurological disorders. Despite significant efforts made for graph neural network (GNN) techniques,…

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled…

Graph-based medical image segmentation represents anatomical structures using boundary graphs, providing fixed-topology landmarks and inherent population-level correspondences. However, their clinical adoption has been hindered by a major…

Brain graph super-resolution (SR) is an under-explored yet highly relevant task in network neuroscience. It circumvents the need for costly and time-consuming medical imaging data collection, preparation, and processing. Current SR methods…

We propose a novel matrix autoencoder to map functional connectomes from resting state fMRI (rs-fMRI) to structural connectomes from Diffusion Tensor Imaging (DTI), as guided by subject-level phenotypic measures. Our specialized autoencoder…

Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…