Related papers: Spline Based Methods for Functional Data on Multiv…
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered…
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…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
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…
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…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution,…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
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…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
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…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice;…