remfpca {ReMFPCA}

A Class for 'ReMFPCA' objects

Description

The 'remfpca' class represents regularized functional principal components components.

The ‘remfpca' class represents regularized functional principal components (’ReMFPCs') components.

Usage

Remfpca(
  mvmfd_obj,
  ncomp,
  alpha = NULL,
  centerfns = TRUE,
  alpha_orth = TRUE,
  penalty_type = "coefpen"
)

Arguments

mvmfd_obj

An 'mvmfd' object representing the multivariate functional data.

ncomp

The number of functional principal components to retain.

alpha

A list or vector specifying the regularization parameter(s) for each variable. If NULL, the regularization parameter is estimated internally.

centerfns

Logical indicating whether to center the functional data before analysis.

alpha_orth

Logical indicating whether to perform orthogonalization of the regularization parameters.

penalty_type

The type of penalty to be applied on the coefficients. The types "coefpen" and "basispen" is supported. Default is "coefpen".

Active bindings

pc_mfd

an object of class 'mvmfd' where the first indices (fields) represents harmonics and second indices represents variables

lsv

= Left singular values vectors

values

= the set of eigenvalues

alpha

= The vector of penalties parameters

GCVs

= generalized cross validations

mean_mfd

a multivariate functional data object giving the mean function

Methods

Public methods

• remfpca$new()

• remfpca$clone()

Method new()

Usage

remfpca$new(
  mvmfd_obj,
  ncomp,
  alpha = NULL,
  centerfns = TRUE,
  alpha_orth = TRUE,
  penalty_type = "coefpen"
)

Arguments

mvmfd_obj

An 'mvmfd' object representing the multivariate functional data.

ncomp

The number of functional principal components to retain.

alpha

A list or vector specifying the regularization parameter(s) for each variable. If NULL, the regularization parameter is estimated internally.

centerfns

Logical indicating whether to center the functional data before analysis.

alpha_orth

Logical indicating whether to perform orthogonalization of the regularization parameters.

penalty_type

The type of penalty to be applied on the coefficients. The types "coefpen" and "basispen" is supported. Default is "coefpen".

Method clone()

The objects of this class are cloneable with this method.

Usage

remfpca$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

mvmfd

Examples

require(fda)
# Brownian Bridge simulation on [0,1]
M <- 110 # number of components
N <- 20 # number of instances
n <- 100 # number of grides
t0 <- seq(0, 1, len = n)
j <- 1:M
alpha1 <- list(a1 = 2^seq(0, 1, length.out = 3), a2 = 2^seq(0, 1, length.out = 3))
psi_1 <- function(t, m) sin(m * pi * t) # eigenfunction of BB
psi_2 <- function(t, m) sin((2 * m - 1) * pi / 2 * t) # eigenfunction of BM
PC_1 <- outer(t0, j, FUN = psi_1) # n by M matrix
PC_2 <- outer(t0, j, FUN = psi_2) # n by M matrix
Z <- matrix(rnorm(N * M), nr = M)
lambda <- matrix(2 / (pi * (2 * j - 1)), nr = M, nc = N)
X_1t <- PC_1 %*% (lambda * Z)
X_2t <- PC_2 %*% (lambda * Z)
noise <- rnorm(n * N, 0, 0.1)
X_1 <- X_1t + noise
X_2 <- X_2t + noise
bs <- create.bspline.basis(c(0, 1), 51)
mdbs <- Basismfd(bs)
mfd1 <- Mfd(X = X_1, mdbs = mdbs)
mfd2 <- Mfd(X = X_2, mdbs = mdbs)
mvmfd_obj <- Mvmfd(mfd1, mfd2)
k <- 2
Re0 <- Remfpca(mvmfd_obj, ncomp = k, alpha = c(0, 0))
fpc0 <- Re0$pc_mfd
scores0 <- inprod_mvmfd(mvmfd_obj, fpc0)
dim(scores0)
Re0$alpha
Re1 <- Remfpca(mvmfd_obj, ncomp = k, alpha = alpha1)
Re1$alpha
Re3 <- Remfpca(mfd1, ncomp = k, alpha = alpha1$a1)
Re3$alpha