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In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…

Biological neural networks (BNNs) have been established as a powerful and adaptive substrate that offer the potential for incredibly energy and data efficient information processing with distinct learning mechanisms. Yet a core challenge to…

In this paper, we propose a general procedure for establishing the geometric landscape connections of a Riemannian optimization problem under the embedded and quotient geometries. By applying the general procedure to the fixed-rank positive…

Human emotions are difficult to convey through words and are often abstracted in the process; however, electroencephalogram (EEG) signals can offer a more direct lens into emotional brain activity. Recent studies show that deep learning…

Due to large intra-subject and inter-subject variabilities of electroencephalogram (EEG) signals, EEG-based brain-computer interfaces (BCIs) usually need subject-specific calibration to tailor the decoding algorithm for each new subject,…

EEG signals capture brain activity with high temporal and low spatial resolution, supporting applications such as neurological diagnosis, cognitive monitoring, and brain-computer interfaces. However, effective analysis is hindered by…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…

The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

Brain biometrics based on electroencephalography (EEG) have been used increasingly for personal identification. Traditional machine learning techniques as well as modern day deep learning methods have been applied with promising results. In…

Automated analysis of electroencephalography (EEG) has recently undergone a paradigm shift. The introduction of transformer architectures and self-supervised pretraining (SSL) has led to the development of EEG foundation models. These…

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited…

The application of Riemannian geometry in the decoding of brain-computer interfaces (BCIs) has swiftly garnered attention because of its straightforwardness, precision, and resilience, along with its aptitude for transfer learning, which…

Electroencephalography (EEG) is establishing itself as an important, low-cost, noninvasive diagnostic tool for the early detection of Parkinson's Disease (PD). In this context, EEG-based Deep Learning (DL) models have shown promising…

Electroencephalography (EEG) classification plays a key role in brain-computer interface (BCI) systems, yet it remains challenging due to the low signal-to-noise ratio, temporal variability of neural responses, and limited data…

Embedding learning has found widespread applications in recommendation systems and natural language modeling, among other domains. To learn quality embeddings efficiently, adaptive learning rate algorithms have demonstrated superior…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

The efficacy of Electroencephalogram (EEG) classifiers can be augmented by increasing the quantity of available data. In the case of geometric deep learning classifiers, the input consists of spatial covariance matrices derived from EEGs.…

Token embeddings play a crucial role in language modeling but, despite this practical relevance, their theoretical understanding remains limited. Our paper addresses the gap by characterizing the structure of embeddings obtained via…