FSVD for a pair of dense or sparse functional data.
FSVD(
Ly1,
Lt1,
Ly2,
Lt2,
FPCAoptns1 = NULL,
FPCAoptns2 = NULL,
SVDoptns = list()
)A list containing the following fields:
The selected (or user specified) bandwidth for smoothing the cross-covariance function across the support of sample 1.
The selected (or user specified) bandwidth for smoothing the cross-covariance function across the support of sample 2.
The smoothed cross-covariance between samples 1 & 2.
A list of length nsvd, each entry containing the singular value estimates for the FSC estimates.
The number of singular components used.
The canonical correlations for each dimension.
A percentage indicating the total variance explained by chosen FSCs with corresponding 'FVEthreshold'.
An nWorkGrid by K matrix containing the estimated singular functions for sample 1.
An nWorkGrid by K matrix containing the estimated singular functions for sample 2.
A vector of length nWorkGrid1. The internal regular grid on which the singular analysis is carried on the support of sample 1.
A vector of length nWorkGrid2. The internal regular grid on which the singular analysis is carried on the support of sample 2.
A n by K matrix containing the singular scores for sample 1.
A n by K matrix containing the singular scores for sample 2.
A list of options used by the SVD and the FPCA's procedures.
A list of n vectors containing the observed values for each individual. Missing values specified by NAs are supported for dense case (dataType='dense').
A list of n vectors containing the observation time points for each individual corresponding to y. Each vector should be sorted in ascending order.
A list of n vectors containing the observed values for each individual. Missing values specified by NAs are supported for dense case (dataType='dense').
A list of n vectors containing the observation time points for each individual corresponding to y. Each vector should be sorted in ascending order.
A list of options control parameters specified by list(name=value) for the FPC analysis of sample 1. See `?FPCA'.
A list of options control parameters specified by list(name=value) for the FPC analysis of sample 2. See `?FPCA'.
A list of options control parameters specified by list(name=value) for the FSVD analysis of samples 1 & 2. See `Details`.
Available control options for SVDoptns are:
The bandwidth value for the smoothed cross-covariance function across the direction of sample 1; positive numeric - default: determine automatically based on 'methodBwCov'
The bandwidth value for the smoothed cross-covariance function across the direction of sample 2; positive numeric - default: determine automatically based on 'methodBwCov'
The bandwidth choice method for the smoothed covariance function; 'GMeanAndGCV' (the geometric mean of the GCV bandwidth and the minimum bandwidth),'CV','GCV' - default: 10% of the support
The user defined mean of sample 1 used to centre it prior to the cross-covariance estimation. - default: determine automatically based by the FPCA of sample 1
The user defined mean of sample 2 used to centre it prior to the cross-covariance estimation. - default: determine automatically based by the FPCA of sample 2
The maximum number of singular components to consider; default: min(20, N-1), N:# of curves.
Smoothing kernel choice, common for mu and covariance; "rect", "gauss", "epan", "gausvar", "quar" - default: "gauss"; dense data are assumed noise-less so no smoothing is performed.
Logical describing if the routine should remove diagonal raw cov for cross cov estimation (default: FALSE)
Logical describing if the routine should return functional singular scores or not (default: TRUE)
String describing if the regularisation of the composite cross-covariance matrix should be done using 'sigma1' or 'rho' (see ?FPCA for details) (default: 'sigma2')
String specifying the routine used to find the optimal bandwidth 'grid-search', 'bobyqa', 'l-bfgs-b' (default: 'l-bfgs-b')
Logical describing if the routine should flip the sign of the singular components functions or not after the SVD of the cross-covariance matrix. (default: FALSE)
Indicator to use gam smoothing instead of local-linear smoothing (semi-parametric option) (default: FALSE)
The type of design we have for sample 1 (usually distinguishing between sparse or dense functional data); 'Sparse', 'Dense', 'DenseWithMV' - default: determine automatically based on 'IsRegular'
The type of design we have for sample 2 (usually distinguishing between sparse or dense functional data); 'Sparse', 'Dense', 'DenseWithMV' - default: determine automatically based on 'IsRegular'
Yang, W., Müller, H.G., Stadtmüller, U. (2011). Functional singular component analysis. J. Royal Statistical Society B73, 303-324.