## 3 Proprioceptive Sensing
### Feature Selection
In addition, two combined selections have been also tested that use the intersection \(Int(PC,WB)\) and the union \(Un(PC,WB)\) of the selected feature set obtained from the \(PC\) and \(WB\) selection method. Finally, the training method \"All\" involves the use of the entire feature set. All the proposed selection methods for the terrain classifier achieve similar F1 score of about 93%. However, the intersection method \(\text{Int}(PC,WB)\) is the most suitable both for the F1 score and the size of the reduced feature set. Both single VI methods lead also to similar reduced feature sets. In fact, nine of the features selected by both \(WB\) and \(PC\) methods fall into the intersection \(\text{Int}(PC,WB)\). Taking all initial features (see \"All\" method), without any selection phase allows us to reach a good F1 score of 90.4%, but with a higher training set dimensionality and so a higher computational effort. Figure 5: Feature selection performance results for terrain (**a**) and slippage (**b**) classifier. The same selection procedure has been performed with the slippage classifier. _PC_ and _WB_ methods select different features. The most relevant features fall into the intersection, which has a slightly lower F1 but a minimal feature set, hence it can be preferred as the selection method. Table 6 collects the reduced feature space for both algorithms. Figure 6 shows the 3D scatter plot of the three statistical features that present the highest value of _WB_ and _PC_ index, respectively, for the terrain and high-slippage classifier. For visualization purposes and for the terrain classifier only, the corresponding 2D feature distribution is also shown in Figure 7. As seen from these figures, the feature distribution indicates a good separation level between sand and rock and it suggests the implementation of a classification algorithm. \begin{table}
\begin{tabular}{c c c c} \hline
**PC** & **WB** & **Int(PC,WB)** & **Un(PC,WB)** \\ \hline F5S1 & F5S1 & F2S1 & F1S1 \\ F4S1 & F4S1 & F3S1 & F2S1 \\ F4S2 & F4S2 & F4S1 & F3S1 \\ F3S2 & F3S1 & F5S1 & F4S1 \\ F3S1 & F4S4 & F8S1 & F5S1 \\ F2S1 & F2S1 & F11S1 & F8S1 \\ F4S4 & F8S1 & F4S2 & F11S1 \\ F8S1 & F11S2 & F7S2 & F3S2 \\ F1S1 & F11S1 & F4S4 & F4S2 \\ F11S1 & F7S2 & & F7S2 \\ F7S2 & & & F11S2 \\  & & & F4S4 \\ \hline F3S2 & F8S2 & F1S2 & F1S1 \\ F2S2 & F3S1 & F3S2 & F3S1 \\ F4S2 & F8S1 & & F5S1 \\ F1S2 & F3S2 & & F8S1 \\ F11S1 & F15S2 & & F11S1 \\ F1S3 & FSS1 & & F1S2 \\  & & & F1S2 \\  & & & F2S2 \\  & & & F1S1 & F3S2 \\  & & & F11S3 & F4S2 \\  & & & F11S2 \\  & & & F11S2 \\  & & & F11S2 \\  & & & F11S2 \\  & & & F11S3 \\ \hline \end{tabular}
\end{table} 
Table 6: Reduced feature sets for terrain (**a**) and slippage (**b**) classification. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **PC** & **WB** & **Int(PC,WB)** & **Un(PC,WB)** & **All** \\ \hline \(\mathbf{N}^{\text{o}}\) **features** & \(11\) & \(10\) & \(9\) & \(12\) & \(40\) \\ \hline \(\mathbf{F1}\) **score** & \(0.924\) & \(0.929\) & \(0.931\) & \(0.928\) & \(0.904\) \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of different feature selection methods for terrain classification. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **PC** & **WB** & **Int(PC,WB)** & **Un(PC,WB)** & **All** \\ \hline \(\mathbf{N}^{\text{o}}\) **features** & \(6\) & \(10\) & \(2\) & \(14\) & \(60\) \\ \hline \(\mathbf{F1}\) **score** & \(0.939\) & \(0.940\) & \(0.914\) & \(0.936\) & \(0.765\) \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of different feature selection methods for slippage classification.