# Simultaneous Instance and Attribute Selection for Noise Filtering
## 4 Discussion  
In the experimental analysis, we considered different levels of noise (5%, 10%, 15%, and the original training data). We applied the classifier under each of those conditions (Figure 3) before and after preprocessing the training data with the simultaneous instance and feature selection algorithms. We use the HOEM dissimilarity [29] in all comparisons. We show that the 1-NN classifier degrades as noise increases, and using the proposed algorithm contributes to diminishing the classifier's error (Figure 4). Considering the data without noise and with 5% noise, the averaged classifier error with and without preprocessing is similar (0.211 vs. 0.227 and 0.250 vs. 0.249, respectively). However, as the noise increases, the error results with preprocessing are much lower than the results without it (0.291 vs. 0.254 and 0.308 vs. 0.268, respectively). Figure 3: Experimental configuration for each dataset. The 1-NN classifier was trained before (baseline) and after each preprocessing algorithm, considering four scenarios: without noise and with noise of 5%, 10%, and 15%. Then, the performance over the testing set was computed. Table 2 shows the detailed classifier error results for the 1-NN classifier after preprocessing with ROFS. The detailed results for the 1-NN without preprocessing and after preprocessing with other compared algorithms can be found in the Supplementary Materials under the folders \"summaries\" and \"results per fold\". As mentioned in the Materials and Methods section, we compare the results of ROFS with respect to the following exiting algorithms for simultaneous instance and feature selection: AKH-GA [12], DS [16], IN-GA [11], KJ-GA [7], RMHC-FP1 [13], SOFSA [20], TCCS [21], and the classifier without preprocessing (baseline). All methods were executed with their default parameters, as in the EPIC software version 1.0.0.7 [30]. We did not fine-tune the parameters of any algorithm (ROFS included). Figure 5 shows the averaged classifier error of the 1-NN after using the preprocessing algorithms and the ones for the 1-NN classifier without any preprocessing (baseline). As shown, the proposed ROFS beats all other preprocessing algorithms and improves the 1-NN in all noisy scenarios. It is only slightly surpassed by 1-NN in noise-free environments. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Datasets** & **0\% Noise** & **5\% Noise** & **10\% Noise** & **15\% Noise** \\ \hline autos & 0.444 & 0.509 & 0.507 & 0.430 \\ breast-w & 0.060 & 0.054 & 0.046 & 0.059 \\ credit-a & 0.174 & 0.201 & 0.188 & 0.197 \\ diabetes & 0.293 & 0.299 & 0.298 & 0.319 \\ heart-c & 0.254 & 0.284 & 0.286 & 0.290 \\ hepatitis & 0.226 & 0.226 & 0.221 & 0.273 \\ iris & 0.107 & 0.080 & 0.040 & 0.080 \\ labor & 0.137 & 0.233 & 0.213 & 0.207 \\ lymph & 0.181 & 0.291 & 0.270 & 0.298 \\ post-operative & 0.333 & 0.311 & 0.422 & 0.444 \\ primary-tumor & 0.623 & 0.634 & 0.640 & 0.655 \\ vehicle & 0.336 & 0.359 & 0.364 & 0.348 \\ vote & 0.062 & 0.065 & 0.090 & 0.110 \\ wine & 0.073 & 0.068 & 0.085 & 0.112 \\ zoo & 0.098 & 0.126 & 0.138 & 0.198 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed classifier error for 1-NN with ROFS preprocessing. Figure 4: Impact of ROFS preprocessing in the averaged performance of 1-NN, according to classifier error. While comparing ROFS with other algorithms according to classifier error, Figure 6 presents the results of ROFS minus the best-performing algorithm for each noise percent analyzed. As shown, the worst results of ROFS were obtained for the autos dataset without noise and with 5% noise, in which ROFS had a drop of 18% in performance. For the remaining datasets, ROFS had very good results with respect to the best-performing method (including the baseline classifier) with less than 7% noise. We believe the reasons why ROFS had bad results for the autos dataset and no so good results for iris and labor datasets for noise-free scenarios do not depend on the characteristics of the overlapping region of the data but on the results of the condensing algorithm.