11 citations · 21 across the 17 of their papers we have counts for
18 papers
Kriging via variably scaled kernels
Gianluca Audone, Francesco Marchetti, Emma Perracchione +1
Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance betw…
Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements
Sara Avesani, Leevan Ling, Francesco Marchetti +1
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spac…
A fast surrogate cross validation algorithm for meshfree RBF collocation approaches
Francesco Marchetti
Cross validation is an important tool in the RBF collocation setting, especially for the crucial tuning of the shape parameter related to the radial basis function. In this paper,…
More properties of -Chebyshev functions and points
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti +1
Recently, -Chebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related…
Mapped Variably Scaled Kernels: Applications to Solar Imaging
Francesco Marchetti, Emma Perracchione, Anna Volpara +3
Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In thi…
Moving Least Squares Approximation using Variably Scaled Discontinuous Weight Function
Mohammad Karimnejad Esfahani, Stefano De Marchi, Francesco Marchetti
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications a…
Data-driven kernel designs for optimized greedy schemes: A machine learning perspective
Tizian Wenzel, Francesco Marchetti, Emma Perracchione
Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE c…
Interpolation with the polynomial kernels
Giacomo Elefante, Wolfgang Erb, Francesco Marchetti +3
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are r…
Polynomial mapped bases: theory and applications
Stefano De Marchi, Giacomo Elefante, Elisa Francomano +1
In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-…
Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications
Stefano De Marchi, Federico Lot, Francesco Marchetti +1
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 con…
A stochastic extended Rippa's algorithm for LpOCV
Leevan Ling, Francesco Marchetti
In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm […
On Kosloff Tal-Ezer Least-Squares Quadrature Formulas
Giacomo Cappellazzo, Wolfgang Erb, Francesco Marchetti +1
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is…
Convergence analysis for image interpolation in terms of the cSSIM
Francesco Marchetti, Gabriele Santin
Assessing the similarity of two images is a complex task that attracts significant efforts in the image processing community. The widely used Structural Similarity Index Measure (S…
Efficient Reduced Basis Algorithm (ERBA) for kernel-based approximation
Francesco Marchetti, Emma Perracchione
The main purpose of this work is the one of providing an efficient scheme for constructing reduced interpolation models for kernel bases. In literature such problem is mainly addre…
Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA) method
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti
The mapped bases or Fake Nodes Approach (FNA), introduced in [10], allows to change the set of nodes without the need of resampling the function. Such scheme has been successfully…
Score-oriented loss (SOL) functions
Francesco Marchetti, Sabrina Guastavino, Michele Piana +1
Loss functions engineering and the assessment of forecasting performances are two crucial and intertwined aspects of supervised machine learning. This paper focuses on binary class…
On -Chebyshev functions and points of the interval
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti
In this paper, we introduce the class of -Chebyshev functions and corresponding points, which can be seen as a family of {\it generalized} Chebyshev polynomials and points.…
Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
Stefano De Marchi, Wolfgang Erb, Francesco Marchetti +2
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study…