fda.usc (version 2.1.0)

fdata2pc: Principal components for functional data

Description

Compute (penalized) principal components for functional data.

Usage

fdata2pc(fdataobj, ncomp = 2, norm = TRUE, lambda = 0, P = c(0, 0, 1), ...)

Value

• d The standard deviations of the functional principal components.

• rotation are also known as loadings. A fdata class object whose rows contain the eigenvectors.

• x are also known as scores. The value of the rotated functional data is returned.

• fdataobj.cen The centered fdataobj object.

• mean The functional mean of fdataobj object.

• l Vector of index of principal components.

• C The matched call.

• lambda Amount of penalization.

• P Penalty matrix.

Arguments

fdataobj

fdata class object.

ncomp

Number of principal components.

norm

=TRUE the norm of eigenvectors (rotation) is 1.

lambda

Amount of penalization. Default value is 0, i.e. no penalization is used.

P

If P is a vector: coefficients to define the penalty matrix object. By default P=c(0,0,1) penalize the second derivative (curvature) or acceleration. If P is a matrix: the penalty matrix object.

...

Further arguments passed to or from other methods.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

Details

Smoothing is achieved by penalizing the integral of the square of the derivative of order m over rangeval:

• m = 0 penalizes the squared difference from 0 of the function

• m = 1 penalize the square of the slope or velocity

• m = 2 penalize the squared acceleration

• m = 3 penalize the squared rate of change of acceleration

References

Venables, W. N. and B. D. Ripley (2002). Modern Applied Statistics with S. Springer-Verlag.

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. tools:::Rd_expr_doi("10.1016/j.chemolab.2008.06.009")

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

See Also

See Also as svd and varimax.

Examples

 if (FALSE) {
 n= 100;tt= seq(0,1,len=51)
 x0<-rproc2fdata(n,tt,sigma="wiener")
 x1<-rproc2fdata(n,tt,sigma=0.1)
 x<-x0*3+x1
 pc=fdata2pc(x,lambda=1)
 summary(pc)
 }