## 5 Results and Analysis  
This section presents the results of the empirical studies and their analyses. We will compare the results obtained by AA-\(k\)NN with the results obtained by applying the pre-processing step ProLSFEO-LDL. In Table 4 the best outcome for each dataset and measure is highlighted in bold. The last row is the average aggregation result of each column. The best average is also highlighted in bold. As those algorithms have been tested using 10-fcv, the performance is represented using \"mean\(\pm\)standard deviation\". The Wilcoxon test and Bayesian Sign test [33; 34] are used to validate the results of the empirical comparisons. In the Bayesian Sign test, a distribution of the differences of the results achieved using methods \(L\) (AA-\(k\)NN) and \(R\) (ProLSFEO-LDL) is computed into a graphical space divided into three regions: left, rope and right. The location of most of the distribution in these sectors indicates the final decision: the superiority of algorithm \(L\), statistical equivalence and the superiority of algorithm \(R\), respectively. KEEL package [69] has been used to compute the Wilcoxon test and the R package rNPBST [70] was used to extract the graphical representations of the Bayesian Sign tests analyzed in the following empirical studies. The Rope limit parameter used to represent the Bayesian Sign test is 0.0001. The outcome of both statistical tests applied to our method is represented in Table 5 (Wilcoxon test) and Figure 2 (Bayesian Sign test). Comparing ProLSFEO-LDL with the standard LDL learner AA-\(k\)NN, we reach the following conclusions:  
* The results of the different measures shown in Table 4 highlights the best ranking of ProLSFEO-LDL in the large majority of the datasets and measures. * The Wilcoxon Signed Ranks test corroborates the significance of the differences between our approach and AA-\(k\)NN. As we can see in Table 5, all the hypotheses of equivalence are rejected with small p-values. * With regard to the Bayesian Sign test, Figure 2 graphically represent the statistical significance in terms of precision between ProLSFEO-LDL and AA-\(k\)NN. The following heat-maps clearly indicate the significant superiority of ProLSFEO-LDL, as the computed distributions are always located in the right region. \begin{table}
\begin{tabular}{c c l c} \hline \hline
**Algorithm** & **Parameter** & **Description** & **Value** \\ \hline ProLSFEO-LDL & N & Population size & 100 \\  & G & Number of generations & 500 \\  & t & Threshold & 10 \\  & \(k\) & Number of selected neighbors & 4 \\  & & in AA-\(k\)NN used for fitness function & \\ \hline AA-\(k\)NN & \(k\) & Number of selected neighbors & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the parameters. Another interesting information to analyse is the reduction ratio obtained by the proposed method. In Figure 3 we show the percentage of selected prototypes and features with respect to the initial training set. In the case of features we represent the average percentage since each of the output labels can be represented by a different number of features. The average percentage is around 53% for both, prototypes and features, varying more significantly for the SJAFFE and SBU_3 DFE datasets where the reduction ratio decreases significantly. This percentaje of data reduction will have a huge impact in the performance of the learner. In instance-based methods like AA-\(k\)NN, the fact of handling about half of the prototypes and features, will lead to a reduction of computation time in the prediction phase.