Riemannian approaches in brain-computer interfaces: a review
Although promising from numerous applications, current brain-computer interfaces (BCIs)
still suffer from a number of limitations. In particular, they are sensitive to noise, outliers and …
still suffer from a number of limitations. In particular, they are sensitive to noise, outliers and …
A riemannian network for spd matrix learning
Z Huang, L Van Gool - Proceedings of the AAAI conference on artificial …, 2017 - ojs.aaai.org
Abstract 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 …
many image and video processing tasks, thanks to their ability to learn appropriate statistical …
Gromov-wasserstein averaging of kernel and distance matrices
This paper presents a new technique for computing the barycenter of a set of distance or
kernel matrices. These matrices, which define the inter-relationships between points …
kernel matrices. These matrices, which define the inter-relationships between points …
Review of Riemannian distances and divergences, applied to SSVEP-based BCI
The firstgeneration of brain-computer interfaces (BCI) classifies multi-channel
electroencephalographic (EEG) signals, enhanced by optimized spatial filters. The second …
electroencephalographic (EEG) signals, enhanced by optimized spatial filters. The second …
Kernel methods on Riemannian manifolds with Gaussian RBF kernels
In this paper, we develop an approach to exploiting kernel methods with manifold-valued
data. In many computer vision problems, the data can be naturally represented as points on …
data. In many computer vision problems, the data can be naturally represented as points on …
Kernel methods on the Riemannian manifold of symmetric positive definite matrices
Abstract Symmetric Positive Definite (SPD) matrices have become popular to encode image
information. Accounting for the geometry of the Riemannian manifold of SPD matrices has …
information. Accounting for the geometry of the Riemannian manifold of SPD matrices has …
Riemannian geometry of symmetric positive definite matrices via Cholesky decomposition
Z Lin - SIAM Journal on Matrix Analysis and Applications, 2019 - SIAM
We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of
symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a …
symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a …
Sparse coding and dictionary learning for symmetric positive definite matrices: A kernel approach
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 …
more appropriately by considering non-Euclidean geometry. This paper tackles the problem …
Conic geometric optimization on the manifold of positive definite matrices
S Sra, R Hosseini - SIAM Journal on Optimization, 2015 - SIAM
We develop geometric optimization on the manifold of Hermitian positive definite (HPD)
matrices. In particular, we consider optimizing two types of cost functions:(i) geodesically …
matrices. In particular, we consider optimizing two types of cost functions:(i) geodesically …
SymNet: A simple symmetric positive definite manifold deep learning method for image set classification
By representing each image set as a nonsingular covariance matrix on the symmetric
positive definite (SPD) manifold, visual classification with image sets has attracted much …
positive definite (SPD) manifold, visual classification with image sets has attracted much …