## 3 Results and Discussion
### Performance Evaluation and Comparison with Other Methods  
To evaluate the performance of the proposed architecture in predicting the labels of new objects based on the learned prototypes, and compare this performance with other methods, two performance measures are used: (1) the error rate, or percentage of misclassified objects, which is computed for both training and test datasets, and (2) the sensitivity to parameter initialization, measured for each parameter by the largest interval of initial values that lead to the best results. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{Found Prototypes (According to Simulation 1 of Table 3)} \\ \hline
**Prototypes** & **Network** & **Features** & **Label** \\ \hline
1 & 1 & \{5.006, 3.418, 1.465, 0.244\} & 1 \\
2 & 1 & \{5.894, 2.745, 4.391, 1.431\} & 2 \\
3 & 1 & \{6.848, 3.075, 5.725, 2.066\} & 3 \\ \hline
1 & 2 & \{5.100, 2.500, 3.000, 1.100\} & 2 \\
2 & 2 & \{6.483, 2.833, 5.017, 1.667\} & 3 \\ \hline \multicolumn{4}{c}{Extracted Strong Elements (According to Simulation 1 of Table 3)} \\ \hline
**Strong** & **Network** & **Features** & **Label** \\ \hline
1 & 1 & \{6.700, 3.000, 5.000, 1.700\} & 2 \\
2 & 1 & \{5.800, 2.700, 5.100, 1.900\} & 3 \\
3 & 1 & \{4.900, 2.500, 4.500, 1.700\} & 3 \\
4 & 1 & \{5.700, 2.500, 5.000, 2.000\} & 3 \\
5 & 1 & \{6.000, 2.200, 5.000, 1.500\} & 3 \\
6 & 1 & \{5.600, 2.800, 4.900, 2.000\} & 3 \\
7 & 1 & \{6.300, 2.700, 4.900, 1.800\} & 3 \\
8 & 1 & \{6.200, 2.800, 4.800, 1.800\} & 3 \\
9 & 1 & \{6.100, 3.000, 4.900, 1.800\} & 3 \\
10 & 1 & \{6.300, 2.800, 5.100, 1.500\} & 3 \\
11 & 1 & \{6.000, 3.000, 4.800, 1.800\} & 3 \\
12 & 1 & \{5.900, 3.000, 5.100, 1.800\} & 3 \\ \hline
1 & 2 & \{7.000, 3.200, 4.700, 1.400\} & 2 \\
2 & 2 & \{6.900, 3.100, 4.900, 1.500\} & 2 \\
3 & 2 & \{6.800, 2.800, 4.800, 1.400\} & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prototypes and strong elements according to simulation 1 of Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{Found Prototypes (According to Simulation 2 of Table 3)} \\ \hline
**Prototype** & **Network** & **Features** & **Label** \\ \hline
1 & 1 & \{5.015, 3.391, 1.526, 0.270\} & 1 \\
2 & 1 & \{5.916, 2.761, 4.405, 1.425\} & 2 \\
3 & 1 & \{6.716, 3.026, 5.552, 1.997\} & 3 \\ \hline
1 & 2 & \{6.512, 2.946, 4.810, 1.543\} & 2 \\
2 & 2 & \{6.006, 2.745, 4.878, 1.717\} & 3 \\ \hline
1 & 3 & \{5.293, 2.373, 3.659, 1.132\} & 2 \\
2 & 3 & \{7.431, 3.237, 6.290, 2.014\} & 3 \\ \hline \hline \multicolumn{4}{c}{Extracted Strong Elements (According to Simulation 2 of Table 3)} \\ \hline
**Strong** & **Network** & **Features** & **Label** \\ \hline
1 & 1 & \{4.900, 2.500, 4.500, 1.700\} & 3 \\ \hline
1 & 2 & \{5.900, 3.200, 4.800, 1.800\} & 2 \\
2 & 2 & \{6.000, 2.700, 5.100, 1.600\} & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Found prototypes and extracted strong elements according to simulation 2 of Table 3.  
For the sake of comparisons, these two performance measures are evaluated on different benchmark datasets for three well-known other algorithms, namely the learning vector quantization algorithm, LVQ1, the multilayer perceptron, MLP, and the support vector machine algorithm, SVM. Like the proposed method, the first algorithm, LVQ1, is also a prototype generator, while MLP tries to find non-linear separations between the \(c\) classes in the data space, and SVM the best possible separation boundaries among the \(c\) classes. To evaluate the error rate, we use the expression:  
\[Err=\frac{\sum_{k=1}^{n}E_{k}}{n}\;\times\;100\% \tag{14}\]  
where \(E_{k}\) is equal to 1 if the object \(k\) is misclassified, and to 0 otherwise; \(n\) is the number of objects of the used dataset. The best error rate is the smallest value obtained over 192,000 simulations for each method and each dataset. The algorithmic parameters used during these simulations for each algorithm are shown in Table 6.  
As shown by Table 7, the only algorithm for which the error rate is null for all training datasets is MCLNN.