PcaProj {rrcov}

Robust Principal Components based on Projection Pursuit (PP): Croux and Ruiz-Gazen (2005) algorithm

Description

A fast and simple algorithm for approximating the PP-estimators for PCA: Croux and Ruiz-Gazen (2005)

Usage

    PcaProj(x, ...)
    ## Default S3 method:
PcaProj(x, k = 0, kmax = ncol(x), scale=FALSE, 
        na.action = na.fail, crit.pca.distances = 0.975, trace=FALSE, ...)
    ## S3 method for class 'formula'
PcaProj(formula, data = NULL, subset, na.action, ...)

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, it is set to the number of columns of the data. It is preferable to investigate the scree plot in order to choose the number of components and then run again. Default is k=0.

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.

scale

a value indicating whether and how the variables should be scaled. 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 to have unit variance. Alternatively it can be a function like sd or mad 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

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

Details

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

Value

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

Author(s)

Valentin Todorov [e-mail]

References

C. Croux, A. Ruiz-Gazen (2005). High breakdown estimators for principal components: The projection-pursuit approach revisited, Journal of Multivariate Analysis, 95, 206–226.

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

Examples

    # multivariate data with outliers
    library(mvtnorm)
    x <- rbind(rmvnorm(200, rep(0, 6), diag(c(5, rep(1,5)))),
                rmvnorm( 15, c(0, rep(20, 5)), diag(rep(1, 6))))
    # Here we calculate the principal components with PcaProj
    pc <- PcaProj(x, 6)
    # we could draw a biplot too:
    biplot(pc)

    # we could use another calculation method and another objective function, and
    # maybe only calculate the first three principal components:
    pc <- PcaProj(x, k=3, method="qn", CalcMethod="sphere")
    biplot(pc)

    # now we want to compare the results with the non-robust principal components
    pc <- PcaClassic(x, k=3)
    # again, a biplot for comparision:
    biplot(pc)