Revisited clustering approaches to accommodate functional
data by allowing to jointly align the data during the clustering
process. Currently, shift, dilation and affine transformations
only are available to perform alignment. The k-mean algorithm has
been extended to integrate alignment and is fully parallelized.
Hierarchical clustering will soon be available as well. References:
Sangalli L.M., Secchi P., Vantini S., Vitelli V. (2010) "k-mean
alignment for curve clustering" <doi:10.1016/j.csda.2009.12.008>.

Concurrent Regression and History Index Models for Functional
Data
c(person(given = "Satarupa",
family = "Bhattacharjee",
role = c("aut", "cre"),
email = "sbhattacharjee@ucdavis.edu"),
person(given = "Yaqing",
family = "Chen",
role = "aut"),
person(given = "Changbo",
family = "Zhu",
role = "aut"),
person(given = "Han",
family = "Chen",
role = "aut"),
person(given = "Yidong",
family = "Zhou",
role = "aut"),
person(given = "Álvaro",
family = "Gajardo",
role = "aut"),
person(given = "Hans-Georg",
family = "Müller",
role = c("cph", "ths", "aut")))
Provides implementation of concurrent or varying coefficient regression methods for
functional data. The implementations are done for both dense and sparsely observed functional
data. Pointwise confidence bands can be constructed for each case. Further, the influence of
past predictor values is modeled by a smooth history index function,
while the effects on the response are described by smooth varying coefficient functions,
which are very useful in analyzing real data such as COVID data.
References: Yao, F., Müller, H.G., Wang, J.L. (2005) <doi: 10.1214/009053605000000660>.
Sentürk, D., Müller, H.G. (2010) <doi: 10.1198/jasa.2010.tm09228>.
MASS, Rcpp (>= 0.11.5), Matrix, pracma, numDeriv, testthat
Satarupa Bhattacharjee [aut, cre],
Yaqing Chen [aut],
Changbo Zhu [aut],
Han Chen [aut],
Yidong Zhou [aut],
Álvaro Gajardo [aut],
Hans-Georg Müller [cph, ths, aut]

Functional Data Analysis for Density Functions by Transformation
to a Hilbert Space
A. Petersen, P. Z. Hadjipantelis and H.G. Mueller
An implementation of the methodology described in
Petersen and Mueller (2016) <doi:10.1214/15-AOS1363> for the functional
data analysis of samples of density functions.  Densities are first
transformed to their corresponding log quantile densities, followed by
ordinary Functional Principal Components Analysis (FPCA).  Transformation
modes of variation yield improved interpretation of the variability in the
data as compared to FPCA on the densities themselves.  The standard
fraction of variance explained (FVE) criterion commonly used for functional
data is adapted to the transformation setting, also allowing for an
alternative quantification of variability for density data through the
Wasserstein metric of optimal transport.