## 4 Discussion  
The initial number of collected values was 500 for each dataset. During the first phase of classification using SVM, an anomaly detection ratio of 68.2%, 75.4% and 55.2% was observed correspondingly for Dts_1, Dts_2 and Dts_3. Comparing these results with the other two classifiers, namely linear discrimination (LD) and k-nearest neighbors (KNN), it could be seen that SVM achieved the best scores. We considered an anomaly, the Tuple [Sys,Dias], one or both metrics presenting a value not belonging to the IBP standard mentioned in Table 2. As a result, critical values were further penalized, providing a very realistic reading that did not neglect any data that could represent a danger. Table 15 epitomizes the results obtained and the calculated ratios. During the optimization phase of the SVM classifier parameters, the representative curves of the different data sets appeared to have the same behavior. The higher the C-axis value, the better the cross-validation score was, up to a certain constant value when it reached a steady-state score. It is worth noting that a large C resulted in a low bias and a high variance. This explained why the system significantly penalized the cost of misclassification by allowing the model to freely select more samples as support vectors. Otherwise, a small C led to a higher bias and a lower variance, this affected the decision surface to be smoother. For the three datasets, the C values ranged in [10.1, 40.4]. Initially, the gamma parameter specified the scale of influence of a single learning example. The higher the gamma value was, the more it tried to adjust accurately to the training data set. For the three datasets, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Datasets** & **C** & **Gamma (\(\gamma\))** \\ \hline Dts\_1 & 20.2 & 0.01 \\ Dts\_2 & 20.2 & 0.02 \\ Dts\_3 & 50.5 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Optimized C and Gamma parameters for the RBF-kernel. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Results** & **Dts\_1** & **Dts\_2** & **Dts\_3** \\ \hline Initial Length & 500 (100\%) & 500 (100\%) & 500 (100\%) \\ Normal Measures & 159 (31.8\%) & 123 (24.6\%) & 224 (44.8\%) \\ Anomalies (SVM) & 341 (68.2\%) & 377 (75.4\%) & 276 (55.2\%) \\ Anomalies (Normal Distribution) & 149 (29.8\%) & 120 (24\%) & 224 (44.8\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Summary of the achieved results and ratios associated to initial data. \(\gamma=0.01\). Mainly, increasing the values of C and \(\gamma\) might lead to overfitting the training data. During this critical learning process, both parameters were used to evaluate the performance of our system by comparing the training results with those of the cross validation scores. As mentioned above, the RBF-kernel based support vector machine returned the best results. This was illustrated using the confusion matrix as well as some metrics such as precision, recall, f1-score and accuracy. The plots in Figure 15 show that the training and validation scores increased to a certain point of stability with recorded slight differences. It was a sign of under-fitting. Then, the classifier operated properly for medium and high gamma levels. Note that before the optimization phase, accuracies ranged in [0.95, 0.99] (for SVM). Thus, it was effective in preserving our analysis from overfitting or/and underfitting to divide our test learning data into k = 5 folds. Using this process, the three datasets responded positively by returning results that far exceeded the decision thresholds and that we believed were ideal. In this study, we set a minimum accuracy threshold of 80%. Therefore, metric scores above this value were retained. This collection was largely exceeded since it sometimes reached a perfect score of 1 (100%) essentially when the k-fold based cross-validation was used to validate our study. Before being able to apply our normal distribution approach, it was essential to justify this step by testing whether our data allowed the use of this probabilistic solution.