Related papers: A Simple Riemannian Manifold Network for Image Set…

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…

Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures are not well suited. Our goal in this paper is to…

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…

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…

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge…

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…

In the domain of pattern recognition, using the CovDs (Covariance Descriptors) to represent data and taking the metrics of the resulting Riemannian manifold into account have been widely adopted for the task of image set classification.…

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…

This paper advocates Riemannian multi-manifold modeling in the context of network-wide non-stationary time-series analysis. Time-series data, collected sequentially over time and across a network, yield features which are viewed as points…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…

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…

In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…

Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…

An important task in image processing and neuroimaging is to extract quantitative information from the acquired images in order to make observations about the presence of disease or markers of development in populations. Having a…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…

We propose a novel study of generating unseen arbitrary viewpoints for infrared imagery in the non-linear feature subspace . Current methods use synthetic images and often result in blurry and distorted outputs. Our approach on the contrary…

Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…