## 4 Experimental validation
### Experiment III: seven activities  
Finally, the eleven available sequences have been used to train the HMM models, adding a new activity to the previous experiment configurations: _bending_ (see HMM on Figure 8). Results obtained  
\begin{table}
\begin{tabular}{l|c|c|c|c|c|c|c} Algorithm & Accuracy & \multicolumn{3}{c|}{Selection} \\ \hline BFS & 0.7442 & \(hu_{1},f\left(t,F\right),R_{\tilde{s}_{1},1}\left(t\right),R_{\Sigma_{\tilde{r} _{3}}}\left(t\right)_{2},R_{\tilde{s}_{6},1}\left(t\right),R_{\tilde{s}_{2} \tilde{2},2}\left(t\right),R_{\tilde{s}_{3},1}\left(t\right),R_{\tilde{s}_{1} \tilde{8},1}\left(t\right)\) \\ GA & 0.7501 & \(hu_{1},R_{\tilde{s}_{3},1}\left(t\right),R_{\tilde{s}_{3},2}\left(t\right),R_{ \Sigma_{\tilde{r}_{11}}}\left(t\right)_{1},\tilde{f}_{8}\left(t,F\right),R_{ \tilde{s}_{1}^{2},2}\left(t\right),tr_{\Sigma_{\tilde{r}_{1}^{3}}}\left(t,F \right)_{1}\) \\ \end{tabular}
\end{table}
Table 10: Results obtained by Best First Search (BFS) and Genetic Algorithm(GA) using all the training sequences  
\begin{table}
\begin{tabular}{l|c|c|c|c|c|c|c} class prediction & error & walking & stopped & falling & \multicolumn{1}{c|}{\(\quad\)} & \multicolumn{1}{c|}{\(\quad\)} & \multicolumn{1}{c}{\(\quad\)} \\ \hline error & 0.5514 & 0.1479 & 0.0210 & 0.1189 & 0.0040 & 0.0999 & 0.0569 \\ walking & 0.0111 & 0.8676 & 0.0603 & 0.0136 & 0.0118 & 0.0035 & 0.0320 \\ bending & 0.0318 & 0.3043 & 0.6304 & 0.0093 & 0.0039 & 0.0202 & 0 \\ stopped & 0.0606 & 0.0818 & 0.0596 & 0.7513 & 0.0139 & 0.0176 & 0.0153 \\ falling & 0.1293 & 0.2239 & 0.1139 & 0.0656 & 0.3301 & 0.0676 & 0.0695 \\ lied down & 0.0058 & 0.0361 & 0.2300 & 0.0926 & 0.0039 & 0.6218 & 0.0097 \\ rising & 0.0108 & 0.3459 & 0.1811 & 0.0405 & 0.0622 & 0.0216 & 0.3378 \\ \end{tabular}
\end{table}
Table 11: Relative Confusion matrix for de HMM generated using Best First Search  
\begin{table}
\begin{tabular}{l|c|c|c|c|c|c|c} class prediction & error & walking & stopped & falling & \multicolumn{1}{c|}{\(\quad\)} & \multicolumn{1}{c|}{\(\quad\)} & \multicolumn{1}{c|}{\(\quad\)} \\ \hline error & 0.2509 & 0.5818 & 0.0982 & 0.04 & 0.0036 & 0.0255 \\ walking & 0.0163 & 0.8656 & 0.0291 & 0.0404 & 0.0041 & 0.0445 \\ stopped & 0.0671 & 0.0439 & 0.7803 & 0.0044 & 0.0623 & 0.0421 \\ falling & 0.0939 & 0.0712 & 0.0 with GA and BFS can be seen on Table 10.  
Taking as the quality measure the global accuracy of the HMM induced by the result subsets, the solution found by GA is a bit better than the solution found by BFS. According to cobfusion matrices of both classifiers (Tables 11 and 12), solution found by BFS is better for predicting _falling_ and _error_ while the easiest are _walking_ and _stopped_, whereas the solution found by GA is better for _bending_, _stopped_, _lied down_ and _rising_.  
Solutions found by both BFS and GA include shape descriptors and optical flow and trajectory eccentricity measures.  
\begin{table}
\begin{tabular}{l|c|c|c|c|c|c|c} class prediction & error & walking & bending & stopped & falling & lied down & rising \\ \hline error & 0.4881 & 0.1512 & 0.0148 & 0.1413 & 0.0267 & 0.1176 & 0.0603 \\ walking & 0.0101 & 0.8562 & 0.0701 & 0.0174 & 0.0166 & 0.0032 & 0.0264 \\ bending & 0.0196 & 0.2844 & 0.6815 & 0.0116 & 0.0029 & 0 & 0 \\ stopped & 0.0571 & 0.0421 & 0.0870 & 0.7758 & 0.0086 & 0.0122 & 0.0172 \\ falling & 0.0874 & 0.6053 & 0.0390 & 0.0031 & 0.2059 & 0.0265 & 0.0328 \\ lied down & 0.0692 & 0.0125 & 0.0999 & 0.0011 & 0.0170 & 0.7753 & 0.0250 \\ rising & 0.1486 & 0.2635 & 0.0203 & 0.0034 & 0.0304 & 0.0034 & 0.5304 \\ \end{tabular}
\end{table}
Table 12: Relative Confusion matrix for de HMM generated using a Genetic Algorithm  
Figure 8: Structure of the HMM used in experiment 3