## 3 Results and Discussion
### Performance Evaluation and Comparison with Other Methods
The second best performance in terms of error rate for the training datasets is obtained by the SVM algorithm, for which the error rate is different from zero for only three cases. This is not surprising given the way the prototypes and the separating boundaries are determined in MCLNN and SVM, respectively. Figure 4: (**a**) Positions of learned prototypes (Simulation 1, Table 3) (**b**) Positions of extracted strong elements (Simulation 1, Table 3) (**c**) Positions of learned prototypes (Simulation 2, Table 3) (**d**) Positions of extracted strong elements (Simulation 2, Table 3). Similar results are obtained on the test datasets, for which both MCLNN and SVM outperform the remaining two algorithms in the ability to generalize the learned classification task to correctly predict the labels of new objects, that were not seen during the training process (Table 8). These are very encouraging results, considering that the proposed algorithm is essentially a prototype generator, and that the generated prototypes are not necessarily and specifically intended for classification tasks. Indeed, as for other algorithms of the same category, the generated prototypes can be used for other applications, such as image and data compression. Another advantage of the proposed algorithm is its low sensitivity to parameter initialization, to which we dedicate the next subsection. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameter** & **Values** & **Description** \\ \hline MCLNN & \(m\) & [1.10,5.00] & Fuzziness factor \\  & \(\gamma\) & [0.01,0.9] & Acceptance threshold \\  & \(\delta\) & [0.01,0.9] & Threshold step \\ \hline SVM & \(\mathcal{C}\) & [0.01,50.00] & Penalty parameter of the error \\  & \(K\) & [’rb\(\prime\),’sigmoid’, ’linear’,’poly’] & Kernel function \\  & \(\alpha\) & [1,5] & Degree of the polynomial kernel function \\ \hline MLP & \(\eta\) & [0.01,0.9] & Learning rate \\  & \(H\) & [1,2] & Number of hidden layers \\  & \(\text{C}^{1}\) & [1,30] & Number of neurons of the 1 st hidden layer \\  & \(\text{C}^{2}\) & [1,30] & Number of neurons of the 2 nd hidden layer \\ \hline LVQI & \(\eta\) & [0.01,0.9] & Learning rate \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical values of algorithmic parameters for the four compared methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **LVQ1** & **MLP** & **SVM** & **MCLNN** \\ \hline Breast Cancer (1) & 27.20 & 28.00 & 2.40 & 0.00 \\ Breast Cancer (2) & 3.57 & 7.63 & 0.00 & 0.00 \\ diabetes & 23.70 & 34.54 & 0.00 & 0.00 \\ german & 29.00 & 30.00 & 0.00 & 0.00 \\ ionosphere & 15.14 & 4.42 & 0.63 & 0.00 \\ iris & 7.41 & 1.48 & 0.74 & 0.00 \\ switzerlan & 57.73 & 55.67 & 0.00 & 0.00 \\ unbalanced & 1.43 & 1.43 & 0.00 & 0.00 \\ va proc & 74.38 & 66.94 & 0.00 & 0.00 \\ vote & 9.52 & 2.86 & 0.00 & 0.00 \\ wdbc & 13.65 & 17.35 & 0.00 & 0.00 \\ wine & 27.78 & 46.91 & 0.00 & 0.00 \\ wpbc & 23.30 & 23.86 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the best error rates given by different techniques and the proposed neural architecture applied to the training dataset (learning phase). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **LVQ1** & **MLP** & **SVM** & **MCLNN** \\ \hline Breast Cancer (1) & 25.93 & 18.52 & 14.81 & 14.81 \\ Breast Cancer (2) & 2.99 & 7.46 & 1.49 & 2.99 \\ diabetes & 28.95 & 31.58 & 27.63 & 27.63 \\ german & 30.00 & 30.00 & 28.00 & 27.00 \\ ionosphere & 14.71 & 0.00 & 0.00 & 2.94 \\ iris & 6.67 & 0.00 & 0.00 & 0.00 \\ switzerlan & 37.50 & 25.00 & 12.50 & 12.50 \\ unbalanced & 1.18 & 1.18 & 1.18 & 1.18 \\ va & 77.78 & 55.56 & 33.33 & 33.33 \\ vote & 4.55 & 0.00 & 0.00 & 0.00 \\ wdbc & 10.71 & 14.29 & 1.79 & 7.14 \\ wine & 25.00 & 50.00 & 0.00 & 0.00 \\ wpbc & 22.22 & 22.22 & 11.11 & 11.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the best error rates given by different techniques and the proposed neural architecture applied to the testing dataset (exploitation phase).