Related papers: DreamNet: A Deep Riemannian Network based on SPD M…

Industrial sensor networks produce complex signals with nonlinear structure and shifting distributions. We propose RIE-SenseNet, a novel geometry-aware Transformer model that embeds sensor data in a Riemannian manifold to tackle these…

Deep learning models are state-of-the-art in compressive spectral imaging (CSI) recovery. These methods use a deep neural network (DNN) as an image generator to learn non-linear mapping from compressed measurements to the spectral image.…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, existing Riemannian…

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…

Deep learning has largely reshaped remote sensing (RS) research for aerial image understanding and made a great success. Nevertheless, most of the existing deep models are initialized with the ImageNet pretrained weights. Since natural…

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…

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…

Deep learning is an effective end-to-end method for Polarimetric Synthetic Aperture Radar(PolSAR) image classification, but it lacks the guidance of related mathematical principle and is essentially a black-box model. In addition, existing…

This paper proposes a Riemannian adaptive optimization algorithm to optimize the parameters of deep neural networks. The algorithm is an extension of both AMSGrad in Euclidean space and RAMSGrad on a Riemannian manifold. The algorithm helps…

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…

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…

In a previous work, we proposed a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing…

Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks…

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…

Purpose: In sleep medicine, assessing the evolution of a subject's sleep often involves the costly manual scoring of electroencephalographic (EEG) signals. In recent years, a number of Deep Learning approaches have been proposed to automate…

Purpose: To systematically investigate the influence of various data consistency layers, (semi-)supervised learning and ensembling strategies, defined in a $\Sigma$-net, for accelerated parallel MR image reconstruction using deep learning.…

Recently, a massive number of deep learning based approaches have been successfully applied to various remote sensing image (RSI) recognition tasks. However, most existing advances of deep learning methods in the RSI field heavily rely on…

Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a nonlinear function (generator) to map latent samples into the data space.…