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Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional…

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.…

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…

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…

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…

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…

We present an improved Locality Preserving Projections (LPP) method, named Gloablity-Locality Preserving Projections (GLPP), to preserve both the global and local geometric structures of data. In our approach, an additional constraint of…

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…

We present a novel Discriminant Locality Preserving Projections (DLPP) algorithm named Collaborative Discriminant Locality Preserving Projection (CDLPP). In our algorithm, the discriminating power of DLPP are further exploited from two…

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…

For image recognition, an extensive number of methods have been proposed to overcome the high-dimensionality problem of feature vectors being used. These methods vary from unsupervised to supervised, and from statistics to graph-theory…

Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…

The model of low-dimensional manifold and sparse representation are two well-known concise models that suggest each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…

Owing to the advances in computational techniques and the increase in computational power, atomistic simulations of materials can simulate large systems with higher accuracy. Complex phenomena can be observed in such state-of-the-art…

Symmetric positive definite (SPD) matrices (e.g., covariances, graph Laplacians, etc.) are widely used to model the relationship of spatial or temporal domain. Nevertheless, SPD matrices are theoretically embedded on Riemannian manifolds.…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

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…