## 3 Results and Discussion
### Results for the So-Called Difficult Datasets  
An important part of the datasets reached a classification accuracy near or equal 100% (Tables A1-A4, in Appendix A), while others did not even reach 70%. This was the reason we considered splitting up the dataset into two groups, one being formed only by what we may call the difficult datasets, for which the classification accuracy using SVM-L (best classifier in the previous work) was \(\leq\)90% using the original set of raw features. The list of difficult datasets (in Table A2) is the following: (1) Count 20 chips NO case x30 sorted; (2) Count 20 chips WITH case x30 sorted; (3) Count 20 papers x10; (4) Distance 3 mugs 10 distances; (5) Distance 3 mugs grouped by material; (6) Flip 10 creditcards NO case; (7) Identify 10 creditcards NO case; (8) Identify 5 colors x 20 chips; (9) Identify 6 users by palm; (10) Identify 6 users by touch behavior sorted; (11) Order 3 coasters NO case; (12) Order 3 creditcards NO case sorted; (13) Order 4 creditcards NO case sorted. For the other datasets, simple methods may have good accuracy results, with little room for improvement. The entire experimental framework was repeated considering only this (difficult) subgroup of datasets, and the results are as follows. Table 7 shows the average accuracies and average ranks, obtained using only the difficult datasets. The average accuracy for SVM-LOB is 78.199 and for SVM-L: it is 87.173. The average rank of SVM-LOB is 23.115 and 6.654 for SVM-L:All. Table 8 summarizes the results in Table 7 for each feature set, averaging the results of RF, SVM-L and SVM-G. The best feature set is (t), with an average accuracy of 85.58% and an average rank of 10.987. The average accuracy is 77.922 and the rank is 23.090 for (OB). Figure 8: Posteriors for the Bayesian sign-rank tests for SVM-G, from all the datasets. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Accuracy** & **Method** & **Rank** \\ \hline SVM-L:t & 87.173 & SVM-L:All & 6.654 \\ SVM-G:t & 87.092 & SVM-L:Ot & 7.154 \\ SVM-L:All & 86.550 & SVM-L:t & 7.538 \\ SVM-G:All & 86.278 & SVM-G:t & 7.731 \\ SVM-L:Ot & 86.226 & SVM-G:Ot & 7.846 \\ SVM-G:Ot & 85.924 & SVM-G:All & 8.308 \\ Stacking+All & 85.215 & Stacking+All & 9.577 \\ Stacking:All & 84.908 & Stacking:All & 11.654 \\ SVM-L:T & 84.458 & SVM-G:OT & 11.808 \\ SVM-G:OT & 84.407 & SVM-L:OT & 12.654 \\ SVM-L:OT & 84.319 & SVM-L:T &  
Given again the large number of methods (Classifier:Feature Set) tested, they were divided depending on the type of classifier used: RF, SVM-L, and SVM-G. These average ranks (for the difficult datasets) are shown in Table 9.  
Figure 9 shows the critical difference diagrams for the Nemenyi test, for the three classifiers. The difference of the average ranks between RF:OB and the best feature sets with RF is greater than the critical difference. The distance of SVM-LOB to the best feature sets with SVM-L is also greater. Nevertheless, the differences for SVM-G:OB and other feature sets with SVM-G are smaller than the critical difference. Figures 10-12 show the Bayesian Signed-Rank Tests posteriors, for the RF, SVM-L, and SVM-G classifiers, respectively, for the difficult datasets. In Figure 10, for RF, the feature sets with more favorable results when compared to (OB) are (t), (OT), (Ot), and (All), with a probability of 1.000 for the corresponding feature set, and 0.000 for (OB). For SVM-L (Figure 11), the best feature sets are, again, (t), (OT), (Ot), and (All), with a probability of 1.000 for the corresponding feature set, and 0.000 for (OB).