XploRe Help : fdaspca

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	fda
See also:	evalfd meanfd data2fd

Quantlet:		fdaspca
Description:		performs the smoothed functional PCA

Usage:	`{fpcaresult,values,varprop,scores} = fdaspca(fdobject,lambda,lfd,npc{,norm})`
Input:
	`fdobject`	list, functional (fd) object with n repetitions
	`lambda`	scalar, smoothing parameter
	`lfd`	list, LDO object, linear differential opereator
	`npc`	scalar, number of eigenfunctions, default = 4
	`norm`	string, normalization type, if norm=="orthonorm" fpcaresult.coef are orthonormalized (with respect to the basis penalty matrix), if norm=="norm" the coefficients are renormalized to norm=1, default is no normalization
Output:
	`fpcaresult`	list, functional (fd) object
	`values`	vector, npc x 1, eigenvalues
	`varprop`	vector, npc x 1, variance proportions
	`scores`	n x npc matrix, principal scores

Note:

orthogonalization is usefull just for lambda>0, for lambda=0 is orthogonality quaranteed

Example:

library("plot") library("fda") axeson() y = read("dailtemp.dat") tvec=#(1:365)/365 fdb = createfdbasis("fourier", #(0,1),31,1) fdtempf31=data2fd(y,tvec,fdb) fdapc=fdaspca(fdtempf31,0.0,2,4) Tempdi=createdisplay(1,1) grtempf=grfd(fdapc.fpcaresult,grid(0,1/100,100),0,#(0,1,2,3)) show(Tempdi,1,1,grtempf)

Result:

first 4 eigenfunctions are plotted

Author: M. Benko 20041205 license MD*Tech