Related papers: Geometry-aware Similarity Learning on SPD Manifold…

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There…

Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…

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…

Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance…

Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…

Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and…

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…

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…

The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need 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…

The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be…

This paper introduces sparse coding and dictionary learning for Symmetric Positive Definite (SPD) matrices, which are often used in machine learning, computer vision and related areas. Unlike traditional sparse coding schemes that work in…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

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…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

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…

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…