Related papers: Manifold-regression to predict from MEG/EEG brain …

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…

Electroencephalography (EEG) and Magnetoencephalography (MEG) are pivotal in understanding brain activity but are limited by their poor spatial resolution. EEG/MEG source imaging (ESI) infers the high-resolution electric field distribution…

We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages. Our approach formulates the alignment learning problem as a domain adaptation problem…

Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach…

MEG and EEG are noninvasive functional neuroimaging techniques that provide recordings of brain activity with high temporal resolution, and thus provide a unique window to study fast time-scale neural dynamics in humans. However, the…

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume that…

Electroencephalography (EEG) analysis is an important domain in the realm of Brain-Computer Interface (BCI) research. To ensure BCI devices are capable of providing practical applications in the real world, brain signal processing…

Electroencephalography (EEG) signals are promising as alternatives to other biometrics owing to their protection against spoofing. Previous studies have focused on capturing individual variability by analyzing task/condition-specific EEG.…

Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between the Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…

In modern neuroscience, functional magnetic resonance imaging (fMRI) has been a crucial and irreplaceable tool that provides a non-invasive window into the dynamics of whole-brain activity. Nevertheless, fMRI is limited by hemodynamic…

Electroencephalography provides a non-invasive window into brain activity, offering valuable insights for neurological research, brain-computer interfaces, and clinical diagnostics. However, the development of robust machine learning models…

Continuous electroencephalography (EEG) is routinely used in neurocritical care to monitor seizures and other harmful brain activity, including rhythmic and periodic patterns that are clinically significant. Although deep learning methods…

Electroencephalogram (EEG) signals generally exhibit low signal-to-noise ratio (SNR) and high inter-subject variability, making generalization across subjects and domains challenging. Recent advances in deep learning, particularly…

Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…

Non-invasive decoding of imagined speech remains challenging due to weak, distributed signals and limited labeled data. Our paper introduces an image-based approach that transforms magnetoencephalography (MEG) signals into time-frequency…