Related papers: Tangent space spatial filters for interpretable an…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

Understanding how the brain encodes visual information is a central challenge in neuroscience and machine learning. A promising approach is to reconstruct visual stimuli, essentially images, from functional Magnetic Resonance Imaging (fMRI)…

Recent advances in brain-vision decoding have driven significant progress, reconstructing with high fidelity perceived visual stimuli from neural activity, e.g., functional magnetic resonance imaging (fMRI), in the human visual cortex. Most…

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…

We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann and one of the options of a metric on a diffeological space in the sense of Iglesias-Zemmour. As a consequence, the…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…

The convolution operation suffers from a limited receptive filed, while global modeling is fundamental to dense prediction tasks, such as semantic segmentation. In this paper, we apply graph convolution into the semantic segmentation task…

We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each tangent space is equipped with a positive definite inner…

Brain-computer interface (BCI) technology enables direct communication between the brain and external devices through electroencephalography (EEG) signals. However, existing decoding models often mix common and personalized components,…

Motor imagery brain--machine interfaces enable us to control machines by merely thinking of performing a motor action. Practical use cases require a wearable solution where the classification of the brain signals is done locally near the…

Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are…

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…

Interpretability is a critical factor in applying complex deep learning models to advance the understanding of brain disorders in neuroimaging studies. To interpret the decision process of a trained classifier, existing techniques typically…

Motor imagery (MI) classification is key for brain-computer interfaces (BCIs). Until recent years, numerous models had been proposed, ranging from classical algorithms like Common Spatial Pattern (CSP) to deep learning models such as…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

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…