Related papers: Mapped Variably Scaled Kernels: Applications to So…

This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…

Maximum Variance Unfolding (MVU) and its variants have been very successful in embedding data-manifolds in lower dimensional spaces, often revealing the true intrinsic dimension. In this paper we show how to also incorporate supervised…

Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…

In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…

In this paper, we propose a scalable image compression scheme, including the base layer for feature representation and enhancement layer for texture representation. More specifically, the base layer is designed as the deep learning feature…

Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…

Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…

Morphological reconstruction (MR) is often employed by seeded image segmentation algorithms such as watershed transform and power watershed as it is able to filter seeds (regional minima) to reduce over-segmentation. However, MR might…

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…

Using a lemma of Davis on Gram matrices applied to the classical Orthogonal Polynomials to generate reproducing kernel interpolation over the classical domains for polynomials. These kernels have terms which are exact over the rational…

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…

Neural Radiance Fields (NeRFs) have unmatched fidelity on large, real-world scenes. A common approach for scaling NeRFs is to partition the scene into regions, each of which is assigned its own parameters. When implemented naively, such an…

So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the…

Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

We show that programmable photonic circuit architectures composed of alternating mixing layers and active layers offer a high degree of flexibility. This alternating configuration enables the systematic tailoring of both the network's depth…

The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very…

In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which…

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…

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…