
| No Filter   |                 |                  |     |    |     |    |
|-------------|-----------------|------------------|-----|----|-----|----|
| Noise       | Majority Filter | Consensus Filter |     |    |     |    |
| Level       | MAJ             | NN               | MAJ | N  | MAJ | NN |
| p           |                 |                  |     |    |     |    |

The results for the remaining four datasets are shown in Tables in the Appendix In one case credit an individual method linear machine was more accurate than or approximately equivalent to the majority vote classifier for every filtering method  For the other three datasets the majority vote classifier was on average better than the single best classifier Excluding the scene segmentation data applying a majority or consensus filter and then building a classifier using the single best algorithm outperformed a majority vote classifier without filtering for noise levels of and higher  Except for the nise case for the road and scene segmentation data and the case for the scene data filtering improved the accuracy of the majority vote classifier over not filtering In addition in many cases particularly at higher noise levels filtering applied with the best individual classifier obtained better accuracies than applying the majority vote classifier to unfiltered data These last two results demonstrate that for these datasets majority vote classifiers cannot replace filtering

## 4.7 Filter Precision

To assess the filters ability to identify mislabeled instances we examined the intersection between the set of instances that were corrupted and the set of instances that were tagged as mislabeled In Figure this is the area M N D The results of this analysis for the land cover data are shown in Table Each row in the table reports the average over the ten runs of the number of instances discarded by each filter D SF D MF D CF the number of instances corrupted in the data M and for each filter the number of instances in the intersection of the set of corrupted data and the set of discarded data Ideally the set of instances discarded should completely intersect the set of noisy instances  Since we may have noisy instances over and above the number of artificially corrupted instances we cannot know the exact number Therefore in this analysis we approximate our calculations of precision by assuming that the only noisy instances are those that we explicitly corrupted  In this case we would like the intersection between the instances discarded and the instances corrupted to be In practice we see that this is not the case Results for the remaining four d at asets are given in Tables of the Appendix In Tables we report estimates of the probabilities that each filter makes E and E
represents the probability of throwing out good data and can be estimated errors  P E
as