Related papers: Matrix Manifold Neural Networks++
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…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…
Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…
Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…
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,…
Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…
Symmetric positive definite (SPD) matrices (e.g., covariances, graph Laplacians, etc.) are widely used to model the relationship of spatial or temporal domain. Nevertheless, SPD matrices are theoretically embedded on Riemannian manifolds.…
Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative…
Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations…
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…
Image set-based visual classification methods have achieved remarkable performance, via characterising the image set in terms of a non-singular covariance matrix on a symmetric positive definite (SPD) manifold. To adapt to complicated…
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 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…
Deep neural networks (DNNs) have shown much empirical success in solving perceptual tasks across various cognitive modalities. While they are only loosely inspired by the biological brain, recent studies report considerable similarities…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
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…
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…
The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the…
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…