# Advanced Statistical Analysis of 3D Kinect Data: A Comparison of the Classification Methods
## 3 Results  
The overall classification results of parametric OLR model and non-parametric random forest (RF) model are summarised in Table 2. The neural network classifications for selected structures are shown in Tables 3 and 4. Given that our goal is not to precisely predict clinician's HB scores because they may be subjective, we consider both the correct classification of HB classes (model HB equals to clinician's HB) and the approximate classification (we tolerate the model HB to differ by at most 1 from the clinician's HB class). The accuracy (or recall) of individual HB classes and the overall accuracy are depicted in Table 5. By accuracy of an HB class, we denote the fraction of correctly classified samples by the model out of all samples in that HB class (assigned by a clinician). The overall accuracy is the fraction of correctly classified samples in all classes out of all samples. To complete the evaluation of the multi-class classification, Table 6 shows precision calculated for all HB classes individually. The precision of an HB class represents the probability that a sample given the HB class by a model is assigned the same class by a clinician. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**HB by**} & \multicolumn{4}{c}{**HB by**} \\ \cline{2-9}
**HB by a Clinician** & \multicolumn{4}{c}{**CNN-tp160k**} & \multicolumn{4}{c}{**CNN-tp4M**} \\ \cline{2-9}  & **1** & **2** & **3** & **6** & **1** & **2** & **3** & **6** \\ \hline
1 & 43 & 1 & 8 & 6 & 43 & 4 & 11 & 0 \\
2 & 8 & 6 & 4 & 3 & 9 & 9 & 3 & 0 \\
3 & 7 & 4 & 12 & 0 & 8 & 2 & 12 & 1 \\
6 & 5 & 1 & 3 & 11 & 4 & 1 & 1 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix with numbers of (mis) classified cases by CNN neural network structures on a test set (tp marks the number of trainable parameters). The parametric OLR model achieves an acceptable accuracy of exact classification and a sufficient accuracy of approximate classification, displaying only 20% of misclassified samples (predicted HB class differs by more than 1 from the clinician's evaluation). The rates indicate balanced accuracy for all four HB classes, not preferring the dominant HB1 class. Meanwhile, the correct accuracy of the individual HB classes is not consistent in the non-parametric model random forests because the model mainly predicts the dominant HB1 class. There is also much higher number of misclassified cases (31%). The accuracy of classification by neural networks differs substantially based on the architecture and number of trainable parameters. The GRU architecture provides sub-optimal results for both low and high number of parameters (see Table 5) with as much as 33% and 39% misclassified cases, respectively. In contrast, CNN based architectures achieved accuracies that are comparable to the parametric OLR model and benefit from higher amount of trainable parameters. The small (160 thousand parameters) CNN misclassified in 27% of test cases, while the large (4 million parameters) in only 21%. It is important to note that the number of trainable parameters of the presented neural network models \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**HB by a Model** & **OLR** & **OLR** & **OLR** & **OLR** & **OLR** & **OLR** \\ \hline
1 & 78\% & 59\% & 64\% & 60\% & 68\% & 67\% \\
2 & 38\% & 50\% & 39\% & 42\% & 50\% & 56\% \\
3 & 47\% & 26\% & 39\% & 28\% & 44\% & 44\% \\
6 & 70\% & 83\% & 36\% & 19\% & 55\% & 93\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of precision of classification of all models.