# Simultaneous Instance and Attribute Selection for Noise Filtering
## 4 Discussion
We hypothesize that the more representative the results of the condensation method, the more accurate ROFS will be. We will need more datasets and more controlled experiments to test that hypothesis, and we will address that behavior in future works. Figure 5: Comparison of the averaged classifier error obtained by 1-NN with and without preprocessing. Figure 6: Subtraction of the classifier error obtained by 1-NN with ROFS preprocessing with respect to the classifier error obtained by the best-performing algorithm (with and without preprocessing) for the analyzed scenarios. In addition, we want to evaluate each algorithm's ability to remove or not remove each of the noisy instances. We then computed the percentage of noise removal for each of the compared algorithms. In Table 3, we summarize the averaged percent of noisy instances filtered by each method (algorithms appear in alphabetical order). Both DS and ROFS were able to effectively deal with noisy environments, having noise filtering percents around 90%. This behavior is expected because Ds uses RNG-Edit + MCS for instance selection, and RNG-Edit is designed for noise filtering. The evolutionary methods have noise detection rates around 50%, while SOFSA and TCCS almost do not detect noise at all (less than 20% of noise was detected). Evolutionary methods have a combination of objectives in their fitness functions, and they tend to keep half of instances and features. On the other hand, SOFSA and TCCS do not include any mechanism to detect noise. In selecting both features and instances to improve training data, our first concern is to keep the classifiers' performance as high as possible. However, we also want to minimize the number of features and instances in the training data. Tables 4 and 5 present the averaged results, for instance, retention and feature retention of the compared preprocessing methods, respectively. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Methods** & **0\% Noise** & **5\% Noise** & **10\% Noise** & **15\% Noise** \\ \hline AKH-GA & 0.502 & 0.500 & 0.502 & 0.496 \\ DS & 0.130 & 0.125 & 0.125 & 0.130 \\ IN-GA & 0.481 & 0.474 & 0.478 & 0.475 \\ KJ-GA & 0.489 & 0.485 & 0.49 & 0.486 \\ RMMIC-FP1 & 0.494 & 0.492 & 0.499 & 0.502 \\ ROFS & 0.135 & 0.134 & 0.134 & 0.137 \\ SOFSA & 0.609 & 0.592 & 0.608 & 0.631 \\ TCCS & 0.547 & 0.545 & 0.572 & 0.607 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Averaged instance retention of the compared preprocessing methods. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Methods** & **5\% Noise** & **10\% Noise** & **15\% Noise** \\ \hline AKH-GA & 0.521 & 0.514 & 0.513 \\ DS & 0.907 & 0.911 & 0.899 \\ IN-GA & 0.522 & 0.500 & 0.510 \\ KJ-GA & 0.503 & 0.489 & 0.492 \\ RMHC-FP1 & 0.513 & 0.493 & 0.501 \\ ROFS & 0.931 & 0.927 & 0.930 \\ SOFSA & 0.136 & 0.169 & 0.178 \\ TCCS & 0.161 & 0.186 & 0.183 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of averaged noise detection and filtering for the compared algorithms. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Methods** & **0\% Noise** & **5\% Noise** & **10\% Noise** & **15\% Noise** \\ \hline AKH-GA & 0.509 & 0.513 & 0.506 & 0.511 \\ DS & 0.937 & 0.931 & 0.931 & 0.933 \\ IN-GA & 0.451 & 0.451 & 0.446 & 0.456 \\ KJ-GA & 0.475 & 0.468 & 0.465 & 0.490 \\ RMHC-FP1 & 0.500 & 0.497 & 0.512 & 0.506 \\ ROFS & 0.604 & 0.613 & 0.619 & 0.619 \\ SOFSA & 0.809 & 0.799 & 0.804 & 0.813 \\ TCCS & 0.758 & 0.767 & 0.775 & 0.791 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Averaged feature retention of the compared preprocessing methods. According to instance retention, the best method is DS (12.5-13% of retained instances), closely followed by ROFS (13.4-13.7% of retained instances). The remaining methods retained around 50% of instances. For feature selection, the methods keeping the lowest number of features are the evolutionary ones, preserving around 50% of them. The proposed ROFS retained around 60% of all features, followed by TCCS and SOFSA (around 80%), and finally, DS (over 90% of retained features).