Application of the Variable Precision Rough Sets Model to Estimate the Outlier Probability of Each Element

Algorithm 3

Pseudo-code of the FIND_OUTLIER_REGION algorithm.

FIND_OUTLIER_REGION (U, X, R): OUTLIERS

    Pseudo-code                               Comments

1     S = BUILD_β_OUTLIER_REGION (U, X, R)  Step 1: calculation of the dependences between

                                     internal borders

2     <M, ExcepDegree> = BUILD_μ_OUTLIER_REGION (U, X, R)    Step 2: calculation of the

                                      outlier region

                                 Integration of the regions

3     for each                       For each element of the universe

4      D[e] = {}

5      for each     Values where e belongs to an internal border with no other internal border

6       D[e] = D[e] ∪ M[e][r] ∩ S[r]

7       OUTLIERS[e] = ExcepDegree[e] ∩ {D[e] × [0, 1]}  Intersection between the outlier regions

                                         and

8     return OUTLIERS                          Return all regions