## 4 Results
### Comparison among Different Classifiers
#### 4.2.6 Discriminant Analysis  
With DA, it is supposed that data produced by different classes fit a Gaussian distribution [47]. The algorithmic hyperparameter in this analysis is only the discriminant type, assumed to be quadratic, linear, diagonal quadratic or diagonal linear.  
According to the outcomes collected in Table 8, the training accuracy results to be 85.2-94.4%, while the testing accuracy 83.3-91.7%. The computing time turns out to be almost unaffected by the hyperparameter tuning, varying between 45.3 s and 48.7 s. If PCA is adopted, see model D2, training and testing accuracies decrease as compared with the previous classifiers. In model D4, some features are excluded, leading to only a 1% improvement of the training accuracy. Hence, there is no a clear indication as to whether the option of excluding some features, like e.g., top/bottom geometry, total diagrid length and maximum normal forces, has a positive effect on the accuracy of the ML model. That noted, it can be also remarked that, if both PCA and feature exclusion are plugged in, as for model D5, the accuracy has a general tendency to decrease.  
\begin{table}
\begin{tabular}{l l c c c c c c c c c} \hline \hline
**Model** & **Ensemble Method** & **Max Split** & **NoL/LR** & **Optimizer** & **Iterations** & **Excl. Feat.** & **PCA** & **Training Accuracy (\%)** & **Testing Acc. (\%)** & **Training Time (s)** \\ \hline E1 & RUSBoost & 38 & 71/9.04 & Bayesian & 40 & - & no & 98.1 & 100.0 & 123.3 \\ E2 & RUSBoost & 23 & 24/0.46 & grid search & grid div = 10 & - & no & 97.2 & 97.2 & 128.3 \\ E3 & AdaBoost & 3 & 20/0.10 & random search & 40 & - & no & 98.1 & 100.0 & 72.0 \\ E4 & RUSBoost & 14 & 12/0.98 & Bayesian & 40 & top/bottom geom. & no & 96.3 & 97.2 & 80.8 \\ E5 & RUSBoost & 25 & 65/0.85 & Bayesian & 40 & * & no & 98.1 & 100.0 & 105.9 \\ E6 & RUSBoost & 106 & 124/0.07 & Bayesian & 40 & * & yes & 85.2 & 94.4 & 129.4 \\ E7 & Bag & 66 & 61/1 & Bayesian & 40 & - & yes & 88.0 & 94.4 & 99.2 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Features of the EM models, and relevant accuracies achieved. Excl. feat. = excluded features (\(\ast\) = top/bottom geometry, diagrid total length, maximum, normal force); No. = number of learners; LR = learning rate.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Model** & **Distribution** & **Kernel Type** & **Support** & **Optimizer** & **Iterations** & **Excl. Feat.** & **PCA** & **Training Accuracy (\%)** & **Testing Acc. (\%)** & **Training Time (s)** \\ \hline N1 & kernel & Gaussian & unbounded & Bayesian & 30 & - & no & 90.7 & 91.7 & 85.5 \\ N2 & kernel & Box & positive & Bayesian & 30 & - & no & 92.6 & 88.9 & 109.7 \\ N3 & kernel & Box & positive & grid search & grid div = 10 & - & no & 92.6 & 88.9 & 13.7 \\ N4 & Gaussian & Triangle & positive & Bayesian & 30 & - & yes & 82.4 & 83.3 & 36.6 \\ N5 & kernel & Gaussian & unbounded & Bayesian & 30 & \(\ast\) & no & 91.7 & 88.9 & 66.3 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Features of the NB models, and relevant accuracies achieved. Excl. feat. = excluded features (\(\ast\) = top/bottom geometry, diagrid total length, maximum, normal force).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Model** & **Discriminant** & **Optimizer** & **Iterations** & **Excl. Feat.** & **PCA** & **Training Accuracy (\%)** & **Testing Acc. (\%)** & **Training Time (s)** \\ \hline D1 & linear & Bayesian & 40 & - & no & 93.5 & 86.1 & 47.8 \\ D2 & diag. quadratic & Bayesian & 40 & - & yes & 85.2 & 83.3 & 46.8 \\ D3 & linear & Bayesian & 40 & top/bottom geom. & no & 94.4 & 91.7 & 45.3 \\ D4 & linear & Bayesian & 40 & * & no & 95.4 & 91.7 & 47.9 \\ D5 & diag. quadratic & Bayesian & 40 & * & yes & 85.2 & 83.3 & 48.7 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Features of the DA models, and relevant accuracies achieved. Excl. feat. = excluded features (\(\ast\) = top/bottom geometry, diagrid total length, maximum, normal force).