rrcov (version 1.7-6)

PcaCov: Robust PCA based on a robust covariance matrix

Description

Robust PCA are obtained by replacing the classical covariance matrix by a robust covariance estimator. This can be one of the available in rrcov estimators, i.e. MCD, OGK, M or S estimator.

Usage

PcaCov(x, ...)
# S3 method for default
PcaCov(x, k = ncol(x), kmax = ncol(x), cov.control=CovControlMcd(), 
    scale = FALSE, signflip = TRUE, crit.pca.distances = 0.975, trace=FALSE, ...)
# S3 method for formula
PcaCov(formula, data = NULL, subset, na.action, ...)

Value

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

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 na.fail if that is unset. The default is na.omit.

...

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 \(\Sigma_{j=1}^k l_j/\Sigma_{j=1}^r l_j >= 0.8\). It is preferable to investigate the scree plot in order to choose the number of components and then run again. Default is k=ncol(x).

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.

cov.control

specifies which covariance estimator to use by providing a CovControl-class object. The default is CovControlMcd-class which will indirectly call CovMcd. If cov.control=NULL is specified, the classical estimates will be used by calling CovClassic

.

scale

a value indicating whether and how the variables should be scaled to have unit variance (only possible if there are no constant variables). If scale=FALSE (default) or scale=NULL no scaling is performed (a vector of 1s is returned in the scale slot). If scale=TRUE the data are scaled by the estimator used to compute the covariance matrix (MCD by default). Alternatively it can be a function like sd or Qn or a vector of length equal the number of columns of x. The value is passed to the underlying function and the result returned is stored in the scale slot. Default is scale=FALSE.

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 = TRUE

crit.pca.distances

criterion to use for computing the cutoff values for the orthogonal and score distances. Default is 0.975.

trace

whether to print intermediate results. Default is trace = FALSE

Author

Valentin Todorov

Details

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

References

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. tools:::Rd_expr_doi("10.18637/jss.v032.i03").

Examples

## PCA of the Hawkins Bradu Kass's Artificial Data
##  using all 4 variables
    data(hbk)
    pca <- PcaCov(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
    PcaCov(~., data=hbk)

## To plot the results:

    plot(pca)                    # distance plot
    pca2 <- PcaCov(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)