Fig. 1. Selection of parameter k in the kNN based algorithms, that is,  and . For values of k>30 the improvement is almost unappreciable.

Fig. 2. AUC–FR results obtained on increasing the number of redundant copies of the relevant variables. In addition to the rankers used in the comparative study, we have also used a version of our algorithm with redundancy detection disabled, labeled as SPE w/o GS.

Fig. 3. This graphic shows the effect of increasing redundancy on the average time in seconds needed to complete a single experiment (training on 30 different data sets).

Fig. 4. AUC–FR scores obtained increasing the number of input variables by adding irrelevant ones.

Fig. 5. Effect on the running time of the variations in the number of input variables.

Fig. 6. This graphic shows the AUC–FR scores obtained by the rankers depending on the complexity of the relation between the relevant variables and the target output.

Fig. 7. Running time and complexity.

Fig. 8. AUC–FR for Weston et al.'s nonlinear problems. In (A) we used the original definition of the problems while in (B) we standardized input variables before applying the algorithms.

Fig. 9. AUC–FR obtained on XOR-like problems. We have experimented with several degrees of complexity, from the classical bi-dimensional XOR up to problems with 5 relevant input variables.

Fig. 10. Percentage of cases where complementary anti-correlated variables are unpleasantly considered redundant by . Notice that when classes are separated more than 0.54σ our ranker behaves satisfactorily since it never detects redundancy between the complementary variables. The table at the right shows the average correlation coefficients between x₁ and x₂ in the data sets of the experiments.

Fig. 11. When classes are separated at least as in (A)  behaves correctly, considering that there is no redundancy in the input variables. When classes are closer than in (B) our ranker always discards one of the variables.

Different combinations of ranking criteria and redundancy detection give rise to different input variable rankers