fdWasserstein-package {fdWasserstein} | R Documentation |
Application of Optimal Transport to Functional Data Analysis
Description
A package containing functions developed to support statistical analysis on functional covariance operators. In particular,
Function
dwasserstein
computes the Wasserstein-Procrustes distance between two covariances.Function
gaussBary
computes the Frechet mean of K covariances with respect to the Procrustes metrics (equivalently, the Wasserstein barycenter of centered Gaussian processes with corresponding covariances) via steepest gradient descent. See Masarotto, Panaretos & Zemel (2019).Function
tangentPCA
performs the tangent space principal component analysis considered in Masarotto, Panaretos & Zemel (2022).Function
wassersteinTest
lets to test the null hypothesis that K covariances are equal using the methodology suggested by Masarotto, Panaretos & Zemel (2022).Function
wassersteinCluster
implements the soft partion procedure proposed by Masarotto & Masarotto (2023).
Author(s)
Valentina Masarotto [aut, cph, cre], Guido Masarotto [aut, cph]
Maintainer: Valentina Masarotto <v.masarotto@math.leidenuniv.nl>
References
Masarotto, V., Panaretos, V.M. & Zemel, Y. (2019) "Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes", Sankhya A 81, 172-213 doi:10.1007/s13171-018-0130-1
Masarotto, V., Panaretos, V.M. & Zemel, Y. (2022) "Transportation-Based Functional ANOVA and PCA for Covariance Operators", arXiv, https://arxiv.org/abs/2212.04797
Masarotto, V. & Masarotto, G. (2023) "Covariance-based soft clustering of functional data based on the Wasserstein-Procrustes metric", Scandinavian Journal of Statistics, doi:10.1111/sjos.12692.