# Accelerometer-Based Pavement Classification for Vehicle Dynamics Analysis Using Neural Networks
## 4 Discussion
### Multinomial Logistic Regression  
The parameters of multinomial logistic regression (see Section 2.2) have been estimated. The regularization parameter \(\lambda=0.15\). K-fold cross-validation was used during the learning process. The value of the logarithm of the likelihood function is equal to \(-570.019\). The table below shows the confusion matrix and the results of the metrics when recognizing the classifier on the test set. This confusion matrix (Table 5) illustrates the outcomes of the multinomial logistic regression classifier. Each row denotes the actual class, while the columns signify the projected class. Optimal predictions should occur only in the diagonal where the actual and projected classes coincide. The findings indicate that the majority of surfaces were accurately identified; nevertheless, some misclassifications were observed. The model accurately categorized basalt pavement, Belgian pavement, concrete tile, stone pavement, and mud, achieving 20 correct instances in each category, demonstrating its effectiveness in these classifications. Nonetheless, we see discrepancies in the surfaces of pits and grates. Among the 20 occurrences in the \"pit\" category, 3 instances were erroneously labeled as \"grated\", suggesting that the classifier sometimes conflated these two coats. This may result from the similar vibration patterns generated by various coatings, complicating their differentiation. Figure 11: ROC curve for classifier based on neural network. Furthermore, a sample of the \"grating\" surface was erroneously identified as \"concrete tiles\", indicating a minor discrepancy in the prediction of this surface category. The classifier achieved commendable results, precisely identifying the majority of surfaces. Misclassifications between \"pitted\" and \"grated\" coatings indicate that both categories may include similar characteristics that complicate their distinction. The findings indicate that although multinomial logistic regression is an effective methodology, it may struggle to categorize identical signals, necessitating extra data or more advanced techniques to enhance accuracy in these particular categories. Table 6 displays the performance metrics of the multinomial logistic regression classifier for seven surface categories. The primary metrics encompass sensitivity, specificity, positive and negative predictive values, balanced accuracy, and the Area Under the Curve, which facilitate the assessment of the classifier's proficiency in accurately differentiating between surface types. The findings indicate that the basalt pavement, concrete tile, thud, and grate categories had the highest sensitivity (1.0000), indicating that the model accurately identified all samples of these surfaces. The sensitivities for the Belgian pavement and stone pavement classes were lower, at 0.9524 and 0.8696, respectively. This indicates that certain classes posed more challenges for the model due to some samples being misclassified, as seen in the preceding confusion matrix. The specificity was very high for all classes, over 1.0000, with the exception of the \"pothole\" (0.9756) and \"grating\" (0.9917) surfaces. The model demonstrated proficiency in reliably identifying non-positive instances across several classifications; however, it sometimes erred, particularly in the categorization of \"pits\" and \"grating\". The Positive Predictive Value was uniformly elevated across all categories, attaining a value of 1.0000 in the majority, with the exceptions of the \"pit\" and \"grating\" categories, which exhibited somewhat lower values of 0.8500 and 0.9500, respectively. This indicates that the majority of the anticipated positive instances were accurate; nevertheless, the model sometimes misidentified \"pits\" and \"grating\" as other surface types. The AUC, indicating the classifier's capacity to differentiate between positive and negative instances, reached its peak (1.0000) for all categories except for the \"pit\" (0.9021) and \"grating\" (0.9838) surfaces.