wrap {cellWise}

Wrap the data.

Description

Transforms multivariate data X using the wrapping function with b = 1.5 and c = 4. By default, it starts by calling checkDataSet to clean the data and estLocScale to estimate the location and scale of the variables in the cleaned data, yielding the vectors (\hat{\mu}_1,\ldots,\hat{\mu}_d) and (\hat{\sigma}_1,\ldots,\hat{\sigma}_d) where d is the number of variables. Alternatively, the user can specify such vectors in the arguments locX and scaleX. In either case, the data cell x_{ij} containing variable j of case i is transformed to

y_{ij} = \hat{\mu}_j - b_j + \hat{\sigma}_j*\psi((x_{ij} - \hat{\mu}_j)/\hat{\sigma}_j)/a_j

in which a_j and b_j are such that for any fixed j the average of y_{ij} equals \hat{\mu}_j and the standard deviation of y_{ij} equals \hat{\sigma}_j.

Usage

wrap(X, locX = NULL, scaleX = NULL, precScale = 1e-12,
     imputeNA = TRUE, checkPars = list())

Arguments

X

the input data. It must be an n by d matrix or a data frame.

locX

The location estimates of the columns of the input data X. Must be a vector of length d.

scaleX

The scale estimates of the columns of the input data X. Must be a vector of length d.

precScale

The precision scale used throughout the algorithm. Defaults to 1e-12

imputeNA

Whether or not to impute the NAs with the location estimate of the corresponding variable. Defaults to TRUE.

checkPars

Optional list of parameters used in the call to checkDataSet. The options are:

• coreOnly
  If TRUE, skip the execution of checkDataset. Defaults to FALSE

• numDiscrete
  A column that takes on numDiscrete or fewer values will be considered discrete and not retained in the cleaned data. Defaults to 5.

• precScale
  Only consider columns whose scale is larger than precScale. Here scale is measured by the median absolute deviation. Defaults to 1e-12.

• silent
  Whether or not the function progress messages should be printed. Defaults to FALSE.

Value

A list with components:

• Xw
  The wrapped data.

• colInWrap
  The column numbers of the variables which were wrapped. Variables which were filtered out by checkDataSet (because of a (near) zero scale for example), will not appear in this output.

• loc
  The location estimates for all variables used for wrapping.

• scale
  The scale estimates for all variables used for wrapping.

Author(s)

Raymaekers, J. and Rousseeuw P.J.

References

Raymaekers, J., Rousseeuw P.J. (2019). Fast robust correlation for high dimensional data. Technometrics, 63(2), 184-198. (link to open access pdf)

See Also

estLocScale

Examples

library(MASS) 
set.seed(12345) 
n <- 100; d <- 10
X <- mvrnorm(n, rep(0, 10), diag(10))
locScale <- estLocScale(X)
Xw <- wrap(X, locScale$loc, locScale$scale)$Xw
# For more examples, we refer to the vignette:
## Not run: 
vignette("wrap_examples")

## End(Not run)