scripts/builtin/outlierBySd.dml

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# Builtin function for detecting and repairing outliers using standard deviation 
#
# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME            TYPE      DEFAULT     MEANING
# ---------------------------------------------------------------------------------------------
# X               Double    ---       Matrix X  
# k               Double    3         threshold values 1, 2, 3 for 68%, 95%, 99.7% respectively (3-sigma rule)
# repairMethod    Integer   1         values: 0 = delete rows having outliers, 1 = replace outliers as  zeros 
#                                             2 = replace outliers as missing values 
# max_iterations  Integer   0         values: 0 = arbitrary number of iteration until all outliers are removed, 
#                                     n = any constant defined by user
# ---------------------------------------------------------------------------------------------
 

#Output(s)
# ---------------------------------------------------------------------------------------------
# NAME            TYPE    DEFAULT     MEANING
# ---------------------------------------------------------------------------------------------
# Y               Double   ---     Matrix X with no outliers

m_outlierBySd = function(Matrix[Double] X, Double k = 3, Integer repairMethod = 1, 
  Integer max_iterations, Boolean verbose = TRUE) return(Matrix[Double] Y) 
{
  sumPrevious = 0
  sumNext = 1
  counter = 0
  
  if( k < 1 | k > 7)
    stop("outlierBySd: invalid argument - k should be in range 1-7 found "+k)

  while( max_iterations == 0 | counter < max_iterations )
  {
    colSD = colSds(X)
    colMean = (colMeans(X))

    upperBound = colMean + k * colSD
    lowerBound = colMean - k * colSD

    outlierFilter = (X < lowerBound) | (X > upperBound)

		if(sum(outlierFilter) > 1 & sumNext != 0 & sumPrevious != sumNext) {
      #TODO why is the check with sumPrevious and sumNext necessary
      temp = replace(target=X, pattern = NaN, replacement = 0)
      sumPrevious = sum(temp)
      X = fix_outliers_sd(X, outlierFilter, repairMethod)
      temp = replace(target=X, pattern = NaN, replacement = 0)
      sumNext = sum(temp)
    }
    else
      max_iterations = - 1;

    counter = counter + 1; 
  }
  Y = X
  if(verbose) {
    print("last outlier filter:\n"+ toString(outlierFilter))
    print("Total executed iterations = "+counter)
    print("Upper-bound of data was calculated using Mean + k * Standard Deviation")
    print("lower-bound of data was calculated using Mean - k * Standard Deviation")
    print("Anything less than the lower-bound and greater than the upper-bound was treated as outlier")
    if(sum(Y) == 0)
      print("output is a zero matrix due to iterative evaluation of outliers ")
    print("output:\n"+ toString(Y))
  }
}

fix_outliers_sd = function(Matrix[Double] X, Matrix[Double] outlierFilter, Integer repairMethod = 2)
  return(Matrix[Double] fixed_X)
{
  rows = nrow(X)
  cols = ncol(X)
  if(repairMethod == 0) {
    sel = (rowMaxs(outlierFilter) == 0)
    X = removeEmpty(target = X, margin = "rows", select = sel)
  }
  else if(repairMethod == 1)
    X = (outlierFilter == 0) * X
  else if (repairMethod == 2) {    
    outlierFilter = replace(target = (outlierFilter == 0), pattern = 0, replacement = NaN)
    X = outlierFilter * X
  }
  else
    stop("outlierBySd: invalid argument - repair required 0-1 found: "+repairMethod)

  fixed_X = X
}