Related papers: Siegel Neural Networks

In recent years, deep learning techniques revolutionized the way remote sensing data are processed. Classification of hyperspectral data is no exception to the rule, but has intrinsic specificities which make application of deep learning…

Neural network on Riemannian symmetric space such as hyperbolic space and the manifold of symmetric positive definite (SPD) matrices is an emerging subject of research in geometric deep learning. Based on the well-established framework of…

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…

Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data structures prevalent in real-world datasets. Notably, residual connections, which facilitate the direct flow of information across layers, have been…

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…

We introduce Hyperdimensional Graph Learner (HDGL), a novel method for node classification and link prediction in graphs. HDGL maps node features into a very high-dimensional space (\textit{hyperdimensional} or HD space for short) using the…

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP),…

Self-Supervised Learning (SSL) has been shown to learn useful and information-preserving representations. Neural Networks (NNs) are widely applied, yet their weight space is still not fully understood. Therefore, we propose to use SSL to…

Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate…

The paper proposes the ScatterNet Hybrid Deep Learning (SHDL) network that extracts invariant and discriminative image representations for object recognition. SHDL framework is constructed with a multi-layer ScatterNet front-end, an…

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing…

Similarity analysis is one of the crucial steps in most fMRI studies. Representational Similarity Analysis (RSA) can measure similarities of neural signatures generated by different cognitive states. This paper develops Deep…

Recent studies have shown that aggregating convolutional features of a pre-trained Convolutional Neural Network (CNN) can obtain impressive performance for a variety of visual tasks. The symmetric Positive Definite (SPD) matrix becomes a…

Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…

Deep learning-based hyperspectral image super-resolution (SR) methods have achieved great success recently. However, most existing models can not effectively explore spatial information and spectral information between bands simultaneously,…

Recent research has shown the great potential of deep learning algorithms in the hyperspectral image (HSI) classification task. Nevertheless, training these models usually requires a large amount of labeled data. Since the collection of…

It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

The continually increasing number of complex datasets each year necessitates ever improving machine learning methods for robust and accurate categorization of these data. This paper introduces Random Multimodel Deep Learning (RMDL): a new…