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Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter.
Geometric Learning with Positively Decomposable Kernels
Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS).
Differential geometry with extreme eigenvalues in the positive semidefinite cone
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 machine learning.
The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications.
Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds.
Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices
Its main contribution is to prove that Riemannian Gaussian distributions of real, complex, or quaternion covariance matrices are equivalent to orthogonal, unitary, or symplectic log-normal matrix ensembles.
Node-wise monotone barrier coupling law for formation control
We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators.
Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces
Hidden Markov models with observations in a Euclidean space play an important role in signal and image processing.
Inductive Geometric Matrix Midranges
Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems.
