Functional data analysis: interpolation, registration, and nearest neighbors in scikit-fda
Author
Marcos Manchón, PabloAdvisor
Suárez González, AlbertoEntity
UAM. Departamento de Ingeniería InformáticaDate
2019-06Subjects
Functional data analysis; interpolation; registration; Informática; MatemáticasEsta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
Functional Data Analysis (FDA) is a branch of Statistics devoted to the study of random quantities
that depend on a continuous parameter, such as time series or curves in space. In FDA the data
instances can be viewed as random functions sampled from an underlying stochastic process.
In this work we consider three different tasks in FDA: the use of interpolation techniques to estimate
the values of the functions at unobserved points, the registration of these type of data, and the solution
of classification and regression problems in which the instances are characterized by functional
attributes. In particular, in this project the scikit-fda package for FDA in Python has been extended with
functionality in these areas.
Generally, the data instances considered in FDA consist of a collection of observations at a discrete
values of the parameter on which they depend (e.g. time or space). For some applications it is convenient,
and in some cases necessary, to estimate the value of these functions at unobserved points. This
can be achieved through the use of interpolation from the available measurements.
In some applications, the functions observed have similar shapes, but exhibit variability whose origin
can be traced to distortions in the scale of the continuous parameter on which the data depend.
Registration consists in characterizing this variability and eliminating it from the sample considered.
In this work we also address classification and regression problems with data that are characterized
by functions. Specifically, we design nearest neighbors estimators based on the notion of closeness
among samples.
Specifically, in this work the scikit-fda package has been extended to include interpolation methods
based on splines. The package has also been endowed with tools for data registration using either
shifts, landmark alignment, or elastic registration, which makes use of the Fisher-Rao metric to align
the functions in a sample. In addition, models based on nearest neighbors have been included to carry
out regression, with both scalar and functional response, and classification.
Files in this item
Google Scholar:Marcos Manchón, Pablo
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