DDC {cellWise}

Detect Deviating Cells

Description

This function aims to detect cellwise outliers in the data. These are entries in the data matrix which are substantially higher or lower than what could be expected based on the other cells in its column as well as the other cells in its row, taking the relations between the columns into account. Note that this function first calls checkDataSet and analyzes the remaining cleaned data.

Usage

DDC(X, DDCpars = list())

Arguments

X

X is the input data, and must be an n by d matrix or a data frame.

DDCpars

A list of available options:

• fracNA
  Only consider columns and rows with fewer NAs (missing values) than this fraction (percentage). Defaults to 0.5.

• numDiscrete
  A column that takes on numDiscrete or fewer values will be considered discrete and not used in the analysis. Defaults to 3.

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

• cleanNAfirst
  If "columns", first columns then rows are checked for NAs. If "rows", first rows then columns are checked for NAs. "automatic" checks columns first if d \geq 5n and rows first otherwise. Defaults to "automatic".

• tolProb
  Tolerance probability, with default 0.99, which determines the cutoff values for flagging outliers in several steps of the algorithm.

• corrlim
  When trying to estimate z_{ij} from other variables h, we will only use variables h with |\rho_{j,h}| \ge corrlim. Variables j without any correlated variables h satisfying this are considered standalone, and treated on their own. Defaults to 0.5.

• combinRule
  The operation to combine estimates of z_{ij} coming from other variables h: can be "mean", "median", "wmean" (weighted mean) or "wmedian" (weighted median). Defaults to wmean.

• returnBigXimp
  If TRUE, the imputed data matrix Ximp in the output will include the rows and columns that were not part of the analysis (and can still contain NAs). Defaults to FALSE.

• silent
  If TRUE, statements tracking the algorithm's progress will not be printed. Defaults to FALSE.

• nLocScale
  When estimating location or scale from more than nLocScale data values, the computation is based on a random sample of size nLocScale to save time. When nLocScale = 0 all values are used. Defaults to 25000.

• fastDDC
  Whether to use the fastDDC option or not. The fastDDC algorithm uses approximations to allow to deal with high dimensions. Defaults to TRUE for d > 750 and FALSE otherwise.

• standType
  The location and scale estimators used for robust standardization. Should be one of "1stepM", "mcd" or "wrap". See estLocScale for more info. Only used when fastDDC = FALSE. Defaults to "1stepM".

• corrType
  The correlation estimator used to find the neighboring variables. Must be one of "wrap" (wrapping correlation), "rank" (Spearman correlation) or "gkwls" (Gnanadesikan-Kettenring correlation followed by weighting). Only used when fastDDC = FALSE. Defaults to "gkwls".

• transFun
  The transformation function used to compute the robust correlations when fastDDC = TRUE. Can be "wrap" or "rank". Defaults to "wrap".

• nbngbrs
  When fastDDC = TRUE, each column is predicted from at most nbngbrs columns correlated to it. Defaults to 100.

Value

A list with components:

• DDCpars
  The list of options used.

• colInAnalysis
  The column indices of the columns used in the analysis.

• rowInAnalysis
  The row indices of the rows used in the analysis.

• namesNotNumeric
  The names of the variables which are not numeric.

• namesCaseNumber
  The name of the variable(s) which contained the case numbers and was therefore removed.

• namesNAcol
  Names of the columns left out due to too many NA's.

• namesNArow
  Names of the rows left out due to too many NA's.

• namesDiscrete
  Names of the discrete variables.

• namesZeroScale
  Names of the variables with zero scale.

• remX
  Cleaned data after checkDataSet.

• locX
  Estimated location of X.

• scaleX
  Estimated scales of X.

• Z
  Standardized remX.

• nbngbrs
  Number of neighbors used in estimation.

• ngbrs
  Indicates neighbors of each column, i.e. the columns most correlated with it.

• robcors
  Robust correlations.

• robslopes
  Robust slopes.

• deshrinkage
  The deshrinkage factor used for every connected (i.e. non-standalone) column of X.

• Xest
  Predicted X.

• scalestres
  Scale estimate of the residuals X - Xest.

• stdResid
  Residuals of orginal X minus the estimated Xest, standardized by column.

• indcells
  Indices of the cells which were flagged in the analysis.

• Ti
  Outlyingness value of each row.

• medTi
  Median of the Ti values.

• madTi
  Mad of the Ti values.

• indrows
  Indices of the rows which were flagged in the analysis.

• indNAs
  Indices of all NA cells.

• indall
  Indices of all cells which were flagged in the analysis plus all cells in flagged rows plus the indices of the NA cells.

• Ximp
  Imputed X.

Author(s)

Raymaekers J., Rousseeuw P.J., Van den Bossche W.

References

Rousseeuw, P.J., Van den Bossche W. (2018). Detecting Deviating Data Cells. Technometrics, 60(2), 135-145. (link to open access pdf)

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

checkDataSet,cellMap

Examples

library(MASS); set.seed(12345)
n <- 50; d <- 20
A <- matrix(0.9, d, d); diag(A) = 1
x <- mvrnorm(n, rep(0,d), A)
x[sample(1:(n * d), 50, FALSE)] <- NA
x[sample(1:(n * d), 50, FALSE)] <- 10
x[sample(1:(n * d), 50, FALSE)] <- -10
x <- cbind(1:n, x)
DDCx <- DDC(x)
cellMap(DDCx$stdResid)

# For more examples, we refer to the vignette:
## Not run: 
vignette("DDC_examples")

## End(Not run)