Principal components for functional data
Compute (penalized) principal components for functional data.
fdata2pc(fdataobj, ncomp = 2, norm = TRUE, lambda = 0, P = c(0, 0, 1), ...)
fdataobj |
|
ncomp |
Number of principal comoponents. |
norm |
=TRUE the norm of eigenvectors |
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. |
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
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.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
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/
## 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) ## End(Not run)
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