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Article

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

Department of Statistics and O.R. and IEMath-GR, University of Granada, 18071 Granada, Spain
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(11), 2085; https://doi.org/10.3390/math8112085
Received: 9 November 2020 / Revised: 17 November 2020 / Accepted: 19 November 2020 / Published: 22 November 2020
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches. View Full-Text
Keywords: functional data analysis; functional principal components; varimax rotation; B-splines; COVID-19 functional data analysis; functional principal components; varimax rotation; B-splines; COVID-19
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MDPI and ACS Style

Acal, C.; Aguilera, A.M.; Escabias, M. New Modeling Approaches Based on Varimax Rotation of Functional Principal Components. Mathematics 2020, 8, 2085. https://doi.org/10.3390/math8112085

AMA Style

Acal C, Aguilera AM, Escabias M. New Modeling Approaches Based on Varimax Rotation of Functional Principal Components. Mathematics. 2020; 8(11):2085. https://doi.org/10.3390/math8112085

Chicago/Turabian Style

Acal, Christian, Ana M. Aguilera, and Manuel Escabias. 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components" Mathematics 8, no. 11: 2085. https://doi.org/10.3390/math8112085

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