Related papers: Kernel Methods on Riemannian Manifolds with Gaussi…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty…

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…

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…

Riemannian manifolds have been widely employed for video representations in visual classification tasks including video-based face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the…

This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present ageneral positive definite kernel setting using bilinear forms, and we provide new…

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…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning applications. This famous technique, known as Random Fourier…

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…

This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…

Motivated by the surge of interest in Koopman operator theory, we propose a machine-learning alternative based on a functional Bayesian perspective for operator-theoretic modeling of unknown, data-driven, nonlinear dynamical systems. This…