Related papers: RepSPD: Enhancing SPD Manifold Representation in E…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…

Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices,…

Surgical phase recognition plays a critical role in developing intelligent assistance systems for minimally invasive procedures such as Endoscopic Submucosal Dissection (ESD). However, the high visual similarity across different phases and…

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

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…

Stress significantly contributes to both mental and physical disorders, yet traditional self-reported questionnaires are inherently subjective. In this study, we introduce a novel framework that employs geometric machine learning to detect…

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…

Auditory attention decoding (AAD) algorithms decode the auditory attention from electroencephalography (EEG) signals that capture the listener's neural activity. Such AAD methods are believed to be an important ingredient towards so-called…

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing…

Visual neural decoding aims to extract and interpret original visual experiences directly from human brain activity. Recent studies have demonstrated the feasibility of decoding visual semantic categories from electroencephalography (EEG)…

Objective. In this article, we present data and methods for decoding speech articulations using surface electromyogram (EMG) signals. EMG-based speech neuroprostheses offer a promising approach for restoring audible speech in individuals…

In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…

Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…

Recent studies have shown that aggregating convolutional features of a pre-trained Convolutional Neural Network (CNN) can obtain impressive performance for a variety of visual tasks. The symmetric Positive Definite (SPD) matrix becomes a…

In diagnosing neurological disorders from electroencephalography (EEG) data, foundation models such as Transformers have been employed to capture temporal dynamics. Additionally, Graph Neural Networks (GNNs) are critical for representing…

The generalization and robustness of an electroencephalogram (EEG)-based computer aided diagnostic system are crucial requirements in actual clinical practice. To reach these goals, we propose a new EEG representation that provides a more…

Accurate classification of EEG signals is crucial for brain-computer interfaces (BCIs) and neuroprosthetic applications, yet many existing methods fail to account for the non-Euclidean, manifold structure of EEG data, resulting in…