# fdata2pc

0th

Percentile

##### Principal components for functional data

Compute (penalized) principal components for functional data.

Keywords
multivariate
##### Usage
fdata2pc(fdataobj, ncomp = 2, norm = TRUE, lambda = 0, P = c(0, 0, 1), ...)
##### Arguments
fdataobj

fdata class object.

ncomp

Number of principal comoponents.

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.

##### 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

##### 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.

##### 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. http://dx.doi.org/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. http://www.jstatsoft.org/v51/i04/

• fdata2pc
##### Examples
# NOT RUN {

# }
# NOT RUN {
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)

# }
Documentation reproduced from package fda.usc, version 2.0.2, License: GPL-2

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