## 4 Data Analysis and Classification
Figure 9: (**A**) micro-Doppler section from free handed motion; (**B**) Singular Value Decomposition (SVD) \(u\) Array plotted as \(10\times log10\left(u\right)\) from micro-Doppler section; (**C**) SVD \(v\) Array plotted as \(10\times log10\left(v\right)\) from micro-Doppler section. The results from applying the classifier to the separate data from persons A, B, C and D can be seen in Table 2. The training percentage was varied from 20% to 40% in steps of 5% as real classifiers are typically trained with percentages comparable to this. The linear-diagonal DA result was shown to be slightly more effective than the quadratic version averaged across training levels, but by only ~2%. The classifier performance for person C produced the best results, 14% or 16% better than the worst performing result for the linear and quadratic classifier, respectively. This clearly shows that the challenge of assessing if an individual is carrying an item will be strongly dependent on the person being observed; agreeing closely with prior research which has already shown that micro-Doppler signatures can vary significantly between different individuals [45]. The DA classifier was then applied to the joint dataset from all individuals to evaluate the overall performance (Figure 11). The results show a classification probability that is approximately an average of the individual results seen in Table 2. Within this result it is worth noting that there is little variation in the performance with increase in train set size, indicating that little additional benefit is gained from training with 20% to 40%. This shows that the previous classifier processing on the individual person data was still statistically significant and not significantly affected by the sample set size. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Linear**} & \multicolumn{4}{c}{**Quadratic**} \\ \hline  & \multicolumn{4}{c}{**Training \%**} & \multicolumn{4}{c}{**Training \%**} \\ \hline
**Person** & **20** & **25** & **30** & **35** & **40** & **20** & **25** & **30** & **35** & **40** \\ \hline A & 59.7 & 60.9 & 60.6 & 63.6 & 62.1 & 58.6 & 58.0 & 58.1 & 59.1 & 61.3 \\ B & 64.6 & 62.3 & 63.4 & 61.9 & 66.0 & 59.4 & 58.4 & 59.0 & 58.2 & 58.7 \\ C & 76.2 & 75.3 & 77.0 & 76.3 & 76.1 & 74.4 & 75.7 & 75.2 & 75.3 & 74.3 \\ D & 64.0 & 66.0 & 65.1 & 64.9 & 65.3 & 65.2 & 65.5 & 65.4 & 66.6 & 65.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Discriminant Analysis (DA) classifier results from each individual person. Figure 10: Four example plots of different features plotted against each other. The free hand motion features are shown as blue crosses, while the bag carrying features are shown as red circles. For comparison the RF classification process was applied to the same data from the four individuals independently, shown in Table 3. These results use all five features for each individual and can be compared directly to Table 2. The RF classifier is shown to be more effective than the DA method, with the greatest difference found for Person D, who showed a 25% increase in classification success rate. On average the RF was found to be 13% better than the DA across all individuals, which is very significant. The trend of classification success against training set size was found to have a greater gradient for the RF method on the joint data compared to the DA classifier. This shows that the RF methodology is more sensitive to the training set size but is able to achieve higher overall classification performance. It was found to benefit by 6% when training with 40% data in comparison to 20%. The classifier results from the full dataset using features from all individuals is shown in Figure 12, which can be compared to the DA results in Figure 11. In this case, the RF classifier was tested using a range of input features from a single feature to all five features.