The Optimal Distortion Value for a certain data set is the minimized value of epsilon returned by CPLEX. The results for the scoring matrices we used and the perturbation values tested are listed in the table below:
| Scoring Matrix | Perturbation | Optimal Distortion |
|---|---|---|
| BLOSUM45 | 0% | 0.0 |
| 1% | 0.0 | |
| 5% | 0.0 | |
| 10% | 0.0 | |
| BLOSUM62 | 0% | 0.0 |
| 1% | 0.0 | |
| 5% | 0.0 | |
| 10% | 0.0 | |
| 15% | 0.0 | |
| 20% | 5.03172 E-315 | |
| 25% | 5.0697 E-315 | |
| 50% | 5.17923 E-315 | |
| PAM250 | 0% | 5.1166 E-315 |
| 1% | 5.11561 E-315 | |
| 5% | 5.12659 E-315 | |
| 10% | 5.11532 E-315 |
The BLOSUM Matrices were shown to have a theoretical minimum of no distortion, even with slight perturbation. The higher perturbations done on BLOSUM62 were done to see how high the perturbation had to go before some distortion was inevitable. The PAM Matrix that we used, PAM250, must always have some slight distortion, although this result was not affected by perturbations up to 10%, as with the BLOSUM matrices.