arXiv subjects

Rosanna Campagna

Publications and source records attributed to Rosanna Campagna.

6 recordsLinked to original sources

arXiv2026

A regularization method for planar offset curves and bi-offset recognition

Offset curves for planar trajectories are interesting in the generation of tool paths for numerically controlled industrial machines and in trajectory planning methods for autonomous driving systems. Theoretical offset curves may exhibit peculiar singularities, including self-intersections, which limit their use in practical applications. Existing approaches address these issue through geometric filtering techniques to detect and remove undesirable features but the computation of accurate and well-behaved offset curves remains a challenging task. We assume a first stage of functional approximation of trajectories by penalized Hermite spline regression enabling the simultaneous fitting of positions and tangents. The regularization is imposed on the second derivatives, effectively mitigating the jerk effect, which is particularly relevant in motion planning and path smoothing applications. Then, taking into account the geometrical pointwise properties of the resulting curve, we design two offset curves through the simultaneous approximation of function values and derivatives. Then, a mathematical model to obtain the so-called bi-offset as most fitting as with the original generator curve is proposed, also relating the offset range and pointwise curvature values. The adaptive reconstruction of the center line from the external boundaries is a topic of interest and is the main focus of our work. Numerical experiments confirm the reliability of our approach at every stage of the resolution process.

math.NA↗

arXiv2026

Accuracy and stability of Artificial Neural Networks for HP-Splines frequency parameter selection

This paper explores the use of artificial neural networks for the stable and data-driven selection of the frequency parameter in hyperbolic polynomial penalized splines (HP-splines). This parameter defines the underlying spline space and is essential for adapting the model to exponential patterns in the data, such as those encountered in signal processing. The theoretical approximation properties of deep neural network architectures are investigated to establish a connection between classical spline-based regression and modern data-driven learning methods. Based on this analysis, a neural network is designed to predict optimal HP-spline parameters by balancing approximation accuracy, stability analysis, and complexity control, thereby producing neural architectures that are both expressive and stable. Numerical experiments confirm that the proposed approach achieves both high accuracy and stable performance, validating the theoretical findings.

math.NA↗

arXiv2025

An algorithm for a constrained P-spline

Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications. Several penalized spline regression models are available in the literature, and the most commonly used ones in real-world applications are P-splines, which enjoy the advantages of penalized models while being easy to generalize across different functional spaces and higher degree order, because of their discrete penalty term. To face the different requirements imposed by the nature of the problem or the physical meaning of the expected values, the P-spline definition is often modified by additional hypotheses, often translated into constraints on the solution or its derivatives. In this framework, our work is motivated by the aim of getting approximation models that fall within pre-established thresholds. Specifically, starting from a set of observed data, we consider a P-spline constrained between some prefixed bounds. In our paper, we just consider 0 as lower bound, although our approach applies to more general cases. We propose to get nonnegativity by imposing lower bounds on selected sample points. The spline can be computed through a sequence of linearly constrained problems. We suggest a strategy to dynamically select the sample points, to avoid extremely dense sampling, and therefore try to reduce as much as possible the computational burden. We show through some computational experiments the reliability of our approach and the accuracy of the results compared to some state-of-the-art models.

stat.ME↗

arXiv2022

Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines

This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials $e^{αx},\, e^{-αx}$ and linear functions multiplied by these exponentials, $xe^{+αx}$ and $xe^{-αx}$. Here, we show that these type of penalized splines reproduce function in the space $\{e^{-αx},\ x e^{-αx}\}$, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments.

math.NA↗

arXiv2021

Greedy algorithms for learning via exponential-polynomial splines

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 consequent oscillations of the approximant. To partially overcome this issue, we introduce two algorithms which perform an adaptive selection of the spline interpolation points based on the minimization either of the sample residuals ($f$-greedy), or of an upper bound for the approximation error based on the spline Lebesgue function ($λ$-greedy). Both methods allow us to obtain an adaptive selection of the sampling points, i.e. the spline nodes. However, while the {$f$-greedy} selection is tailored to one specific target function, the $λ$-greedy algorithm is independent of the function values and enables us to define a priori optimal interpolation nodes.

math.NA↗

arXiv2020

Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines

The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our attention towards kernel models that have the advantage of being meshfree. Precisely, the proposed numerical method makes use of the so-called Variably Scaled Kernels (VSKs), which are introduced to implement a feature augmentation-like strategy based on discrete data. Due to the possible uncertainty on the data and since we are interested in modelling the behaviour of the considered dynamics, we seek for a regularized solution by ridge regression. Focusing on polyharmonic splines, we investigate their implementation in the VSK setting and we provide error bounds in Beppo-Levi spaces. The performances of the method are then tested on functions which are common in the framework of the Laplace transform inversion. Comparisons with Support Vector Regression (SVR) are also carried out and show that the proposed method is effective particularly since it does not require to train complex architecture constructions.

math.NA↗