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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;…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
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…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
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…
A new benchmark dataset for functional data analysis (FDA) is presented, focusing on the reconstruction of eye movements from EEG data. The contribution is twofold: first, open challenges and evaluation metrics tailored to FDA applications…
The continuous advances in data collection and storage techniques allow us to observe and record real-life processes in great detail. Examples include financial transaction data, fMRI images, satellite photos, earths pollution distribution…
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…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…
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…
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 many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA…
Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…
We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have…