OutlierPCDist {rrcovHD}

Outlier identification in high dimensions using the PCDIST algorithm

Description

The function implements a simple, automatic outlier detection method suitable for high dimensional data that treats each class independently and uses a statistically principled threshold for outliers. The algorithm can detect both mislabeled and abnormal samples without reference to other classes.

Usage

    OutlierPCDist(x, ...)
    ## Default S3 method:
OutlierPCDist(x, grouping, control, k, explvar, trace=FALSE, ...)
    ## S3 method for class 'formula'
OutlierPCDist(formula, data, ..., 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 matrix or data frame.

grouping

grouping variable: a factor specifying the class for each observation.

control

a control object (S4) for one of the available control classes, e.g. CovControlMcd-class, CovControlOgk-class, CovControlSest-class, etc., containing estimation options. The class of this object defines which estimator will be used. Alternatively a character string can be specified which names the estimator - one of auto, sde, mcd, ogk, m, mve, sfast, surreal, bisquare, rocke. If 'auto' is specified or the argument is missing, the function will select the estimator (see below for details)

k

Number of components to select for PCA. If missing, the number of components will be calculated automatically

explvar

Minimal explained variance to be used for calculation of the number of components in PCA. If explvar is not provided, automatic dimensionality selection using profile likelihood, as proposed by Zhu and Ghodsi will be used.

trace

whether to print intermediate results. Default is trace = FALSE

Details

If the data set consists of two or more classes (specified by the grouping variable grouping) the proposed method iterates through the classes present in the data, separates each class from the rest and identifies the outliers relative to this class, thus treating both types of outliers, the mislabeled and the abnormal samples in a homogenous way.

The first step of the algorithm is dimensionality reduction using (classical) PCA. The number of components to select can be provided by the user but if missing, the number of components will be calculated either using the provided minimal explained variance or by the automatic dimensionality selection using profile likelihood, as proposed by Zhu and Ghodsi.

Value

An S4 object of class OutlierPCDist which is a subclass of the virtual class Outlier.

Author(s)

Valentin Todorov [e-mail]

References

A.D. Shieh and Y.S. Hung (2009). Detecting Outlier Samples in Microarray Data, Statistical Applications in Genetics and Molecular Biology 8.

M. Zhu, and A. Ghodsi (2006). Automatic dimensionality selection from the scree plot via the use of profile likelihood. Computational Statistics & Data Analysis, 51, pp. 918–930.

Filzmoser P & Todorov V (2013). Robust tools for the imperfect world, Information Sciences 245, 4–20. doi:10.1016/j.ins.2012.10.017.

See Also

OutlierPCDist, Outlier

Examples

data(hemophilia)
obj <- OutlierPCDist(gr~.,data=hemophilia)
obj

getDistance(obj)            # returns an array of distances
getClassLabels(obj, 1)      # returns an array of indices for a given class
getCutoff(obj)              # returns an array of cutoff values (for each class, usually equal)
getFlag(obj)                #  returns an 0/1 array of flags
plot(obj, class=2)          # standard plot function