rrcov (version 1.3-4)

PcaLocantore: Spherical Principal Components

Description

The Spherical Principal Components procedure was proposed by Locantore et al., (1999) as a functional data analysis method. The idea is to perform classical PCA on the data, projected onto a unit sphere. The estimates of the eigenvectors are consistent and the procedure is extremely fast. The simulations of Maronna (2005) show that this method has very good performance.

Usage

PcaLocantore(x, ...)
## S3 method for class 'default':
PcaLocantore(x, k = 0, kmax = ncol(x), delta = 0.001, 
    na.action = na.fail, scale = FALSE, signflip = TRUE, trace=FALSE, ...)
## S3 method for class 'formula':
PcaLocantore(formula, data = NULL, subset, na.action, \dots)

Arguments

formula

a formula with no response variable, referring only to numeric variables.

data

an optional data frame (or similar: see model.frame) containing the variables in the formula formula.

subset

an optional vector used to select rows (observations) of the data matrix x.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is

...

arguments passed to or from other methods.

x

a numeric matrix (or data frame) which provides the data for the principal components analysis.

k

number of principal components to compute. If k is missing, or k = 0, the algorithm itself will determine the number of components by finding such k that $l_k/l_1 >= 10.E-3$ and $\Sigma_{j=1}^k l_j/

kmax

maximal number of principal components to compute. Default is kmax=10. If k is provided, kmax does not need to be specified, unless k is larger than 10.

delta

an accuracy parameter

scale

a logical value indicating whether the variables should be scaled to have unit variance (only possible if there are no constant variables). As a scale function mad is used but alternatively, a vector of length equal the number of

signflip

a logical value indicating wheather to try to solve the sign indeterminancy of the loadings - ad hoc approach setting the maximum element in a singular vector to be positive. Default is signflip = FALSE

trace

whether to print intermediate results. Default is trace = FALSE

Value

• An S4 object of class PcaLocantore-class which is a subclass of the virtual class PcaRobust-class.

Details

PcaLocantore, serving as a constructor for objects of class PcaLocantore-class is a generic function with "formula" and "default" methods. For details see the relevant references.

References

N. Locantore, J. Marron, D. Simpson, N. Tripoli, J. Zhang and K. Cohen K. (1999), Robust principal components for functional data. Test, 8, 1-28. R. Maronna, D. Martin and V. Yohai (2006), Robust Statistics: Theory and Methods. Wiley, New York. R. Maronna (2005). Principal components and orthogonal regression based on robust scales. Technometrics, 47, 264-273. Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. URL http://www.jstatsoft.org/v32/i03/.

Examples

## PCA of the Hawkins Bradu Kass's Artificial Data
##  using all 4 variables
    data(hbk)
    pca <- PcaLocantore(hbk)
    pca

## Compare with the classical PCA
    prcomp(hbk)

## or  
    PcaClassic(hbk)
    
## If you want to print the scores too, use
    print(pca, print.x=TRUE)

## Using the formula interface
    PcaLocantore(~., data=hbk)

## To plot the results:

    plot(pca)                    # distance plot
    pca2 <- PcaLocantore(hbk, k=2)  
    plot(pca2)                   # PCA diagnostic plot (or outlier map)
    
## Use the standard plots available for for prcomp and princomp
    screeplot(pca)    
    biplot(pca)