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Functional Data Analysis (FDA)
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Special Issue "Functional Data Analysis (FDA)"

A special issue of Stats (ISSN 2571-905X).

Deadline for manuscript submissions: 31 October 2021.

Special Issue Editor

Dr. Manuel Oviedo de la Fuente
E-Mail Website
SciProfiles
Guest Editor
Department of Mathematics, University of A Coruña, 15008 A Coruña, Spain
Interests: functional data analysis; R programming; computational statistics; applied statistics; time series; spatial statistics; biostatistics

Special Issue Information

Dear Colleagues,

In the big data era, large amounts of data are continuously recorded over a time interval at a known spatial location or at discrete time points. Functional data analysis (FDA) deals with the analysis of this data in the form of functions. The functional data atom is a function such as a curve, a biomedical image, a shape, a sound, genomic data, or more general objects. This Special Issue will present a collection of manuscripts on new exploratory tools for functional data (or applications for functional data objects). Currently, there is a need for exploratory tools for complex data objects (functional objects) that are reproducible or automatable, such as registration (alignment and dynamic time warping), dimension reduction in 1 and 2 dimensions (tensor product basis, smoothing, kernels, wavelets and spline basis, PCA, PLS, principal curves), measures of centrality and outliers (depth for multivariate functional data and outlier detection), sparse functional data, as well as tools for visualizing results of predictive models (functional response model, functional time series, spatiotemporal dependence data), ensemble methods (boosting, bagging, random forest), feature selection (regularization), unsupervised learning (clustering), and supervised classification of functional data.

I am looking forward to receiving your submissions.

The papers extended from the abstract presented/published in the workshop, IWFOS 2021 (https://iwfos2021.sci.muni.cz/), will be “free of charge” in this Special Issue if they are accepted.

Sincerely,

Dr. Manuel Oviedo de la Fuente
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Stats is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamic time warping
  • dimension reduction
  • principal curves
  • functional depth
  • outlier detection
  • spatiotemporal dynamics
  • smoothing and kernel
  • functional time series
  • feature selection methods
  • ensemble learning
  • visualization

Published Papers (3 papers)

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Article
Curve Registration of Functional Data for Approximate Bayesian Computation
by
Anthony Ebert
,
Kerrie Mengersen
,
Fabrizio Ruggeri
and
Paul Wu
Stats 2021, 4(3), 762-775; https://doi.org/10.3390/stats4030045 - 07 Sep 2021
Viewed by 156
Abstract
Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional data that are not only subject to noise along their y axis but also to a random warping along [...] Read more.
Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional data that are not only subject to noise along their y axis but also to a random warping along their x axis, which we refer to as the time axis. Conventional distances on functions, such as the L2 distance, are not informative under these conditions. The Fisher–Rao metric, previously generalised from the space of probability distributions to the space of functions, is an ideal objective function for aligning one function to another by warping the time axis. We assess the usefulness of alignment with the Fisher–Rao metric for approximate Bayesian computation with four examples: two simulation examples, an example about passenger flow at an international airport, and an example of hydrological flow modelling. We find that the Fisher–Rao metric works well as the objective function to minimise for alignment; however, once the functions are aligned, it is not necessarily the most informative distance for inference. This means that likelihood-free inference may require two distances: one for alignment and one for parameter inference. Full article
(This article belongs to the Special Issue Functional Data Analysis (FDA))
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Article
Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines
by
Lauren N. Berry
and
Nathaniel E. Helwig
Stats 2021, 4(3), 701-724; https://doi.org/10.3390/stats4030042 - 02 Sep 2021
Viewed by 256
Abstract
Functional data analysis techniques, such as penalized splines, have become common tools used in a variety of applied research settings. Penalized spline estimators are frequently used in applied research to estimate unknown functions from noisy data. The success of these estimators depends on [...] Read more.
Functional data analysis techniques, such as penalized splines, have become common tools used in a variety of applied research settings. Penalized spline estimators are frequently used in applied research to estimate unknown functions from noisy data. The success of these estimators depends on choosing a tuning parameter that provides the correct balance between fitting and smoothing the data. Several different smoothing parameter selection methods have been proposed for choosing a reasonable tuning parameter. The proposed methods generally fall into one of three categories: cross-validation methods, information theoretic methods, or maximum likelihood methods. Despite the well-known importance of selecting an ideal smoothing parameter, there is little agreement in the literature regarding which method(s) should be considered when analyzing real data. In this paper, we address this issue by exploring the practical performance of six popular tuning methods under a variety of simulated and real data situations. Our results reveal that maximum likelihood methods outperform the popular cross-validation methods in most situations—especially in the presence of correlated errors. Furthermore, our results reveal that the maximum likelihood methods perform well even when the errors are non-Gaussian and/or heteroscedastic. For real data applications, we recommend comparing results using cross-validation and maximum likelihood tuning methods, given that these methods tend to perform similarly (differently) when the model is correctly (incorrectly) specified. Full article
(This article belongs to the Special Issue Functional Data Analysis (FDA))
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Article
An FDA-Based Approach for Clustering Elicited Expert Knowledge
by
Carlos Barrera-Causil
,
Juan Carlos Correa
,
Andrew Zamecnik
, and
Fernando Marmolejo-Ramos
Stats 2021, 4(1), 184-204; https://doi.org/10.3390/stats4010014 - 04 Mar 2021
Viewed by 926
Abstract
Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile [...] Read more.
Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets. Full article
(This article belongs to the Special Issue Functional Data Analysis (FDA))
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Founctional Data Analysis and Manifold Estimaton

Authors: James Ramsay

Affiliation: Université McGilldisabled, Montreal, Canada
Abstract: This paper aims to explore the natural extension of functional data analysis to the task of estimating manifolds, flat or curved, embedded in a high-dimensional over—space.

Algorithmic approaches such as principal curve and surface analysis have been well explored in statistics, and the optimization of familiar manifolds such as hyper-planes, Stiefel manifolds and and hyper-spherical surfaces have received a lot of attention recently in the numerical analysis community. This paper will be in part a review for statisticians of these methods and the concepts in differential that they involve.

The paper will also illustrate manifold estimation problem by the estimation a space curve over which multinomial vectors evolve smoothly, along with the locations of observation locations on the curve. Lessons learned along the way point to some interesting research projects.

 

Title: Statistical picking of multidimensional waveforms

Authors:  Nicoletta D’Angelo 1 , Giada Adelfio1,2,  Marcello Chiodi 1,2, Antonino D’Alessandro 2.
Affiliations: 

  1. Dipartimento di Scienze Economiche, Aziendali e Statistiche, Università degli Studi di Palermo, Palermo, Italia
  2. Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italia.

Abstract:

In this paper, we propose a new approach based on the fit of a generalized linear regression model for detecting change-points in the variance of multivariate-heteroscedastic Gaussian variables, with a piecewise constant variance function.

Applying this new approach on multiple waveforms, our method provides simultaneous change-point detection on functional time series.

The proposed approach can be used as a new picking algorithm for the automatic identification of the arrival times of the P-waves and S-waves on different seismograms recorded on the same seismic event.

Indeed, a seismogram is a record of the ground motion at a measuring station as a function of time, and it typically records motions in three cartesian axes (x, y, and z), with the z-axis perpendicular to the Earth's surface and the x- and y- axes parallel to the surface.

Our method is tested on a dataset of simulated waveforms while aiming at capturing the variations in the performance due to some characteristics of both the seismic

event and its detection, which in turn affect some characteristics of the waveforms.

 

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