## 3 ML Architectures and Results
### Recall Metric of Classifiers' Performance  
Beyond confusion tables, there are two performance metrics used in information retrieval, named Precision and Recall [38]. The latter, defined as  
\[Recall=\frac{N(\textit{true positive})}{N(\textit{true positive})+N(\textit{ false negative})}\,,\]  
is complementary to the confusion table since it highlights the classification sensitivity. The number \(N(\textit{false negative})\) is the sum of all non-diagonal element in the line of the confusion matrix, which corresponds to a certain class. Tables 2 and 3 present the Recall values for each of the seven classes calculated for the results obtained with the ANN and ANN+KNN classifiers and the same set of nine initial input parameters (eight MMEs + AoI). In the case of ANN+KNN, the kernel was designed to emphasize the classes \"clothes\", \"leaves\", \"rocks\", and \"wood\" by adding to the list of ANN inputs the corresponding \((\vec{\imath}\cdot<\overline{x}>_{i})\) as explained in Section 3.3. In other words, the the Recall values in two tables correspond to the data presented in Figures 5 and 8, respectively. Comparing the two tables, we notice an overall improvement, while it is considerable for the most \"problematic\" classes, namely \"leaves\" and \"wood\". tree and random forest algorithms when applied to the full set of Mueller matrix elements. Taking into account earlier published results as well [9], we suggest that ANNs are preferable as supervised ML architectures for supporting this kind of sensing for classification. As shown in the previous work [9] and further confirmed in this study, an overall accuracy over 95% can be achieved, which is much higher than the values reported in Ref. [29] for deep learning-assisted 3D integral imaging, both polarimetric and non-polarimetric (It should be noticed that the data used in Ref. [29] were obtained in adverse environmental conditions, while ours were collected in laboratory). However, the full Stokes-Mueller polarimetry may be too costly in the context of autonomous cars and, on the other hand, there are other sensing technologies, such as video cameras, LiDARS, and SONARs, which complement the surroundings' imaging to make the autonomous driving feasible [39]. Here, we have shown that, even without using all MMEs as attributes, one can obtain reasonably good classification results. Then, it is a question of cost/benefit to optimize the input dataset. The minimal set of just three essential MMEs, which is equivalent to using just two orthogonal linear polarizations, already permits to distinguish different types of car paint [40] but it is insufficient to distinguish between objects characterized by entirely diffuse scattering. A good compromise is to consider as attributes the MMEs \(M_{01}\), \(M_{02}\), \(M_{10}\)\(M_{11}\), \(M_{12}\), \(M_{20}\), \(M_{21}\), \(M_{22}\), plus AoI (It excludes the elements \(M_{03}\), \(M_{13}\), \(M_{23}\), \(M_{30}\), \(M_{31}\), \(M_{32}\), and \(M_{33}\) related to circular polarizations). With this set of input parameters, the overall accuracy rate obtained was 91%, compared to 96.2% obtained with the full set of MMEs. We verified that the angle of incidence has an impact on the accuracy of the classifiers, especially if a reduced number of MME attributes are used by the classifier. We developed a kernel approach with an ANN-KNN classifier (Figure 7), which employs the above set of MMEs and four new attributes defined as the internal product between the sample's attribute vector and the average attribute vectors for the classes \"clothes\", \"tree leaves\", \"rocks\", and \"wood\" in the training database. It yielded a further improved accuracy of 92.6% with the set of 13 attributes, of which only eight MMEs listed above and AoI have to be measured. This hybrid algorithm employing a kernel was shown to decrease the overall misclassification rate from 9% (using just ANN with eight MMEs + AoI) to 7.4% (an 18% reduction).