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Functional Data Analysis (FDA)
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Functional Data Analysis (FDA)

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

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 17490

Special Issue Editor

Dr. Manuel Oviedo de la Fuente

E-Mail Website
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

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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 1600 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

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Published Papers (5 papers)

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41 pages, 6203 KiB  
Article
A Geometric Perspective on Functional Outlier Detection
by Moritz Herrmann and Fabian Scheipl
Stats 2021, 4(4), 971-1011; https://doi.org/10.3390/stats4040057 - 24 Nov 2021
Cited by 4 | Viewed by 3207
Abstract
We consider functional outlier detection from a geometric perspective, specifically: for functional datasets drawn from a functional manifold, which is defined by the data’s modes of variation in shape, translation, and phase. Based on this manifold, we developed a conceptualization of functional outlier [...] Read more.
We consider functional outlier detection from a geometric perspective, specifically: for functional datasets drawn from a functional manifold, which is defined by the data’s modes of variation in shape, translation, and phase. Based on this manifold, we developed a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed taxonomies. Our theoretical and experimental analyses demonstrated several important advantages of this perspective: it considerably improves theoretical understanding and allows describing and analyzing complex functional outlier scenarios consistently and in full generality, by differentiating between structurally anomalous outlier data that are off-manifold and distributionally outlying data that are on-manifold, but at its margins. This improves the practical feasibility of functional outlier detection: we show that simple manifold-learning methods can be used to reliably infer and visualize the geometric structure of functional datasets. We also show that standard outlier-detection methods requiring tabular data inputs can be applied to functional data very successfully by simply using their vector-valued representations learned from manifold learning methods as the input features. Our experiments on synthetic and real datasets demonstrated that this approach leads to outlier detection performances at least on par with existing functional-data-specific methods in a large variety of settings, without the highly specialized, complex methodology and narrow domain of application these methods often entail. Full article
(This article belongs to the Special Issue Functional Data Analysis (FDA))
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21 pages, 416 KiB  
Article
Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)
by Mohamed Alahiane, Idir Ouassou, Mustapha Rachdi and Philippe Vieu
Stats 2021, 4(4), 793-813; https://doi.org/10.3390/stats4040047 - 27 Sep 2021
Cited by 2 | Viewed by 3454
Abstract
Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is [...] Read more.
Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z, where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology. Full article
(This article belongs to the Special Issue Functional Data Analysis (FDA))
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15 pages, 519 KiB  
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 - 7 Sep 2021
Viewed by 2968
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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24 pages, 3455 KiB  
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 - 2 Sep 2021
Cited by 13 | Viewed by 3758
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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21 pages, 1045 KiB  
Article
An FDA-Based Approach for Clustering Elicited Expert Knowledge
by Carlos Barrera-Causil, Juan Carlos Correa, Andrew Zamecnik, Francisco Torres-Avilés and Fernando Marmolejo-Ramos
Stats 2021, 4(1), 184-204; https://doi.org/10.3390/stats4010014 - 4 Mar 2021
Cited by 1 | Viewed by 3081
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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