Related papers: Exact heat kernel on a hypersphere and its applica…
Finding a suitable density function is essential for density-based clustering algorithms such as DBSCAN and DPC. A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in these…
This paper studies the empirical measures of eigenvalues and singular values for random matrices drawn from the heat kernel measures on the unitary groups $\mathbb{U}_N$ and the general linear groups $\mathbb{GL}_N$, for $N\in\mathbb{N}$.…
The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…
Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…
This paper is concerned with the Poisson and heat equations on spaces of constant curvature. More explicitly we provide new methods for obtaining old and new explicit formulas for the Poisson and heat semigroups on the Euclidean, spherical…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Genomic sequence analysis plays a crucial role in various scientific and medical domains. Traditional machine-learning approaches often struggle to capture the complex relationships and hierarchical structures of sequence data when working…
In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating…
Helioseismic inferences of large-scale flows in the solar interior necessitate accounting for the curvature of the Sun, both in interpreting systematic trends introduced in measurements as well as the sensitivity kernel that relates…
The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…
The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, once the harmonic…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest $\varepsilon$-chain between two points $x,y$ is…