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This study introduces an efficient workflow for functional data analysis in classification problems, utilizing advanced orthogonal spline bases. The methodology is based on the flexible Splinets package, featuring a novel spline…
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may…
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
Probability density functions form a specific class of functional data objects with intrinsic properties of scale invariance and relative scale characterized by the unit integral constraint. The Bayes spaces methodology respects their…
In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and…
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…
Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a…
Infinite-dimensional orthonormal basis expansions play a central role in representing and computing with function spaces due to their favorable linear algebraic properties. However, common bases such as Fourier or wavelets are fixed and do…
In this paper, we will outline a novel data-driven method for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…
In this paper, we explore how different selections of basis functions impact the efficacy of frequency domain techniques in statistical independence tests, and study different algorithms for extracting low-dimensional algebraic relations…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
Parametric surrogate models of electric machines are widely used for efficient design optimization and operational monitoring. Addressing geometry variations, spline-based computer-aided design representations play a pivotal role. In this…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…