| BUILD_β_OUTLIER_REGION (U, X, R): S |
| Pseudo-code Comments |
| 1 for each |
| 2 for each |
| 3 S1[r][q] = {[0, 0.5)} Start solving Sub-problem No. 1 |
| 4 S3[r][q] = {[0, 0.5)} Start solving Sub-problem No. 3 |
| 5 S2[r] = {[0, 0.5)} Start solving Sub-problem No. 2 |
| 6 for each r ∈ R |
| 7 Pr = CLASSIFY-ELEMENTS (U, r) Partition induced by the equiv. relation r |
| 8 class-max = 0 starting the null minimum value [r] |
| 9 for each class ∈ Pr |
| 10 case1[r][class] = {[min(c(class, X), 1 - c(class, X)), 0.5)} Obtain the solution for the |
| equivalence class for Case1 |
| 11 class-max = max(class-max, c(class, X), 1 - c(class, X)) Update the null minimum value[r] |
| 12 for each Searching the solution for the equiv. class of case2 |
| 13 q-min = min(c(class, X), 1 - c(class, X)) Minimum error of the equiv. classes according to |
| q with elements of the equiv. class according to i |
| 14 for each e ∈ class For each class element |
| 15 q-class = CLASSIFY-ELEMENT(U, q, e) Obtain equiv. class to which it belongs |
| according to q |
| 16 q-min = min(q-min, c(q-class, X), 1– c(q-class, X)) Update the minimum value |
| 17 case2[r][q][class] = [0, q-min)} Obtain the solution of the equiv. class for Case 2 |
| 18 S1[r][q] = S1[r][q] ∩ (case1[r][class] ∪ case2[r][q][class]) Update S1 with new ranges of |
| the equiv. class |
| 19 S2[r] = S2[r] ∩ {[class-max, 0.5)} Update S2 with new ranges of the equiv. class |
| 20 for each Update S3 from the S1 values |
| 21 for each |
| 22 S3[q][r] = S1[r][q] ∩ S1[q][r] Obtain the solution for which the internal border r is |
| equal to q |
| 23 for each Calculate the outlier region for each internal border |
| 24 A = {} β for which the internal border r contains the other internal border |
| 25 for each |
| 26 A = A ∪ (S1[q][r]–S3[q][r]–S2[q]) Update set A |
| 27 S[r] = {[0, 0.5)} - A − S2[r] Values for which the internal border r has no internal border |
| 28 return S Return the solution |
