Related papers: Deep manifold-to-manifold transforming network for…

Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…

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…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Unsupervised domain adaptation is effective in leveraging the rich information from the source domain to the unsupervised target domain. Though deep learning and adversarial strategy make an important breakthrough in the adaptability of…

Estimating matrices in the symmetric positive-definite (SPD) cone is of interest for many applications ranging from computer vision to graph learning. While there exist various convex optimization-based estimators, they remain limited in…

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…

In recent years, Transformer-based auto-attention mechanisms have been successfully applied to the analysis of a variety of context-reliant data types, from texts to images and beyond, including data from non-Euclidean geometries. In this…

Deep unfolding networks have recently gained popularity in the context of solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with…

Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models,…

In this paper, covariance matrices are exploited to encode the deep convolutional neural networks (DCNN) features for facial expression recognition. The space geometry of the covariance matrices is that of Symmetric Positive Definite (SPD)…

Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent and thus has a slow convergence. In addition, softmax, as a decision layer, may ignore the distribution information of the data during…

The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The…

Semantic segmentation has achieved great accuracy in understanding spatial layout. For real-time tasks based on dynamic scenes, we extend semantic segmentation in temporal domain to enhance the spatial accuracy with motion. We utilize a…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

Neuroimaging provides essential tools for characterizing brain activity by quantifying connectivity strength between remote regions, using different modalities that capture different aspects of connectivity. Yet, decoding meaningful neural…

This paper introduces an extension of the backpropagation algorithm that enables us to have layers with constrained weights in a deep network. In particular, we make use of the Riemannian geometry and optimization techniques on matrix…

Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…

In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the…