Related papers: Extrinsic Methods for Coding and Dictionary Learni…

Learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes that preserve the…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…

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…

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…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

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…

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

This work proposes a geometric insight into equivariant message passing on Riemannian manifolds. As previously proposed, numerical features on Riemannian manifolds are represented as coordinate-independent feature fields on the manifold. To…

Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…

Objective: Improve the reconstructed image with fast and multi-class dictionaries learning when magnetic resonance imaging is accelerated by undersampling the k-space data. Methods: A fast orthogonal dictionary learning method is introduced…

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…