# Accelerometer-Based Pavement Classification for Vehicle Dynamics Analysis Using Neural Networks
## 4 Discussion
### Multinomial Logistic Regression
The model exhibited strong performance across most \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Basalt Cube** & **Belgian Cobblestone** & **Concrete Cube** & **Cobblestone** & **Thump** & **Pothole** & **Grater** \\ \hline Sensitivity & 1.0000 & 0.9524 & 1.0000 & 0.8696 & 1.0000 & 1.0000 & 1.0000 \\ Specificity & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 0.9756 & 0.9917 \\ Pos Pred Value & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 0.8500 & 0.9500 \\ Neg Pred Value & 1.0000 & 0.9917 & 1.0000 & 0.9750 & 1.0000 & 1.0000 & 1.0000 \\ Prevalence & 0.1429 & 0.1500 & 0.1429 & 0.1643 & 0.1429 & 0.1214 & 0.1357 \\ Detection Rate & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 \\ Detection Prevalence & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 & 0.1429 \\ Balanced Accuracy & 1.0000 & 0.9762 & 1.0000 & 0.9348 & 1.0000 & 0.9878 & 0.9959 \\ AUC & 1.0000 & 0.9950 & 1.0000 & 1.0000 & 1.0000 & 0.9021 & 0.9838 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Confusion matrix for classifier based on Multinomial Logistic Regression. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Basalt Cube** & **Belgian Cobblestone** & **Concrete Cube** & **Cobblestone** & **Thump** & **Pothole** & **Grater** \\ \hline basalt cube & 20 & 0 & 0 & 0 & 0 & 0 \\ Belgian cobblestone & 0 & 20 & 0 & 0 & 0 & 0 \\ concrete cube & 0 & 0 & 20 & 0 & 0 & 0 \\ cobblestone & 0 & 0 & 0 & 20 & 0 & 0 \\ thump & 0 & 0 & 0 & 0 & 20 & 0 & 0 \\ pothole & 0 & 0 & 0 & 3 & 0 & 17 & 0 \\ grater & 0 & 1 & 0 & 0 & 0 & 0 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Confusion matrix for classifier based on Multinomial Logistic Regression. categories; however, the categorization of \"pits\" and \"grating\" surfaces proved to be more challenging. The multinomial logistic regression model exhibited commendable performance, with high accuracy across the majority of classes; however, the \"pit\" and \"grating\" classes were more challenging to discern. This suggests that certain surface types possess similar features to other coatings, resulting in categorization mistakes. The model may be enhanced to more effectively distinguish these surfaces, perhaps by using additional data or more advanced methodologies such as boosted regression trees, random forests. The accuracy of prediction on the test set is equal to 97.14%. Figure 12 presents the Receiver Operating Characteristics curves for each pavement type estimated for the test set in differentiating among seven distinct surface classes. The findings indicate that the majority of surfaces (basal pavement, concrete tiles, grating) exhibit an ideal curve that fully conforms to the top and left axes, with a maximum AUC (Area Under the Curve) of 1.0000. The classifier successfully differentiated between the signals of these surfaces, exhibiting neither false positives nor false negatives. Nonetheless, the separation of some surfaces was not very successful. The curve for the whole class has an elevated incidence of false positives, particularly at the outset, as it diverges from the upper axis and approaches diminished sensitivity at increased specificity values. This suggests that the model had more challenges in precisely differentiating the surface of \"potholes\" from other surfaces, particularly at lower thresholds. The curves for cobblestone and Belgian cobblestone lag somewhat behind the others; however, they remain around the top axis, indicating competent but imperfect categorization. The ROC curves indicate that the model proficiently and reliably identified the majority of surfaces, achieving optimal sensitivity and specificity, particularly for basalt pavement, concrete tile, and grating categories. Nevertheless, some classes, such as potholes and stone pavements, posed issues due to their curves exhibiting elevated rates of false positive and negative predictions, signifying the model's struggle to differentiate between these pavements.