Calculate a multivariate functional principal component analysis
for data observed on different dimensional domains. The estimation algorithm
relies on univariate basis expansions for each element of the multivariate
functional data (Happ & Greven, 2018)

`MFPCA`

is an `R`

-package for calculating a PCA for multivariate functional data observed on different domains, that may also differ in dimension. The estimation algorithm relies on univariate basis expansions for each element of the multivariate functional data.

`MFPCA`

allows to calculate a principal component analysis for multivariate (i.e. combined) functional data on up to three-dimensional domains:

- Standard functional data defined on a (one-dimensional) interval.
- Functional data with two-dimensional domains (images).
- Functional data with three-dimensional domains (3D images, e.g. brain scans).

It implements various univariate bases:

- Univariate functional PCA (only one-dimensional domains).
- Spline bases (one- and two-dimensional domains; with optional smoothing penalty).
- Cosine bases (two- and three-dimensional domains; fast implementation built on DCT).
- Tensor PCA (two-dimensional domains; UMPCA approach from Lu et al. (2009) and FCP_TPA approach from Allen (2013)).
- Given basis functions, e.g. from a previous univariate PCA.

The representation of the data is based on the object-oriented `funData`

package, hence all functionalities for plotting, arithmetics etc. included therein may be used.

The `MFPCA`

pacakge is available on `CRAN`

. To install the latest version directly from GitHub, please use `devtools::install_github("ClaraHapp/MFPCA")`

(install `devtools`

before).

If you would like to use the cosine bases make sure that the `C`

-library `fftw3`

is installed on your computer before you install `MFPCA`

. Otherwise, `MFPCA`

is installed without the cosine bases and will throw an error if you attempt to use functions that need `fftw3`

.

The `MFPCA`

package depends on the `R`

-package `funData`

for representing (multivariate) functional data. It uses functionalities from
`abind`

,
`foreach`

,
`irlba`

,
`Matrix`

,
`mgcv`

and
`plyr`

.

The theoretical foundations of multivariate functional principal component analysis are described in:

C. Happ, S. Greven (2018): Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains.
*Journal of the American Statistical Association*, 113(522): 649-659 .

Please use GitHub issues for reporting bugs or issues.

- Consequent use of
`seq_len(x)`

instead of`1:x`

. - Use of type-safe
`vapply`

instead of`sapply`

, where applicable.

- New univariate expansion type
`fda`

, which allows to use all basis functions implemented in package**fda**. - Correct typos in documentation.
- Theoretical paper is now finally published.

- Skip third party tests on CRAN that lead to ATLAS/MKL/OpenBLAS issues. Add warning to documentation files.

- Function
`screeplot`

for`MFPCAfit`

objects now with integers only on x-axis and optional parameter`ylim`

. - Separate
`print`

function for objects of class`summary.MFPCAfit`

. - Configure-file now with correct version number.
- Links to MFPCA paper and software paper in DESCRIPTION file, as well as to ORCID.

- Tolerance for
`splineFunction2Dpen`

unit tests reduced due to ATLAS/OpenBLAS/MKL issues.

- The main
`MFPCA`

method now returns an object of class`MFPCAfit`

for which new functions (`plot`

,`predict`

,`summary`

, ...) have been implemented. The methods can use`names`

of functional data objects (requires funData 1.2). - It is now possible to pass a given basis decomposition for elements (e.g. from previous PCA).
- Univariate decompositions (xxxBasis) and expansions (xxxFunction) are not exported any more, but should be accessed using the
`univDecomp`

and`univExpansion`

meta-functions. - New function
`multivExpansion`

to calculate a multivariate basis expansion. - More argument checking for user-facing functions including unit tests.
- Tolerance for regression tests reduced to 1e-5.
- References have been updated.

- New parameter
`bootstrapStrat`

in`MFPCA`

main function enables stratified bootstrap. Bootstrap CIs for eigenvalues are returned, too. `MFPCA`

function now returns the eigenvectors and normFactors that are calculated within the MFPCA calculation. They can be used to calculate out-of-sample predictions.`fcptpaBasis`

now returns eigenvalues and has new option to normalize the eigenfunctions.- Unit test coverage has been increased to almost 100%.