MFPCA (version 1.3-10)

univDecomp: Univariate basis decomposition

Description

This function calculates a univariate basis decomposition for a (univariate) functional data object.

Usage

univDecomp(type, funDataObject, ...)

Value

scores

A matrix of scores (coefficients) for each observation based on the prespecified basis functions.

B

A matrix containing the scalar products of the basis functions. Can be NULL if the basis functions are orthonormal.

ortho

Logical. If TRUE, the basis functions are all orthonormal.

functions

A functional data object, representing the basis functions. Can be NULL if the basis functions are not estimated from the data, but have a predefined form. See Details.

Arguments

type

A character string, specifying the basis for which the decomposition is to be calculated.

funDataObject

A funData object, representing the (univariate) functional data samples.

...

Further parameters, passed to the function for the particular basis to use.

Warning

The options type = "DCT2D" and type = "DCT3D" have not been tested with ATLAS/MKL/OpenBLAS.

Details

Functional data \(X_i(t)\) can often be approximated by a linear combination of basis functions \(b_k(t)\) $$X_i(t) = \sum_{k = 1}^K \theta_{ik} b_k(t), i = 1, \ldots, N.$$ The basis functions may be prespecified (such as spline basis functions or Fourier bases) or can be estimated from the data (e.g. by functional principal component analysis) and are the same for all observations \(X_1(t), \ldots, X_n(t)\). The coefficients (or scores) \(\theta_{ik}\) reflect the weight of each basis function \(b_k(t)\) for the observed function \(X_i(t)\) and can be used to characterize the individual observations.

See Also

MFPCA, univExpansion, fpcaBasis, splineBasis1D, splineBasis1Dpen, splineBasis2D, splineBasis2Dpen, umpcaBasis, fcptpaBasis, fdaBasis, dctBasis2D, dctBasis3D

Examples

# generate some data
dat <- simFunData(argvals = seq(0,1,0.01), M = 5,
                  eFunType = "Poly", eValType = "linear", N = 100)$simData

# decompose the data in univariate functional principal components...
decFPCA <- univDecomp(type = "uFPCA", funDataObject = dat, npc = 5)
str(decFPCA)

# or in splines (penalized)
decSplines <- univDecomp(type = "splines1Dpen", funDataObject = dat) # use mgcv's default params
str(decSplines)