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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 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…

Due to its promising classification performance, sparse representation based classification(SRC) algorithm has attracted great attention in the past few years. However, the existing SRC type methods apply only to vector data in Euclidean…

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…

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.…

Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…

In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…

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…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

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…

Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. As such, there is…

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…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

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…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

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…

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…

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…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…