# fdata2pc: Principal components for functional data In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fdata2pc R Documentation

## 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), ...)
```

### 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.

### 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.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es

### 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. 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/

### Examples

``` ## 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)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.