## 4 Data Analysis and Classification
The sectioning of the data was completed manually for this analysis, although it could be automated within further developed software. Each of these micro-Doppler sections have been analysed in order to evaluate the SVD components, for both the free handed and carrying case. For a real-time system this methodology would need to be streamlined by an automated computation method but for the offline processing that is being demonstrated within this work, an empirically manual selection was sufficient. An example micro-Doppler section, the SVD \(u\) array and \(v\) array from a free handed motion can all be seen in Figure 9A-C respectively. The two SVD output matrices are very different in their appearance, they have been plotted as \(10\times log10\left(u\right)\) and \(10\times log10\left(v\right)\) to best visually demonstrate the dynamic range of the values obtained. The u matrix has strong components visible at the top and left hand edge, while maintaining a strong diagonal component throughout. The \(v\) matrix is more noise like, although at the left hand edge clear non-Gaussian features are visible; hence the feature extraction from this matrix has been isolated to only the first 10 columns of this matrix. The evaluation of all the SVD matrices from each Doppler section away/towards was completed, and these matrices were then used to extract features that could be input into a classifier to evaluate how easily separable are the two different types of motion. The features that were extracted from the SVD profiles were as follows:  
1. Sum of all the values within the first 100 rows within of the \(u\) matrix
2. Mean of the diagonal of the \(u\) matrix
3. Standard deviation of the diagonal of the \(u\) matrix
4. Standard deviation of the first ten columns of the \(u\) array
5. Standard deviation of the first ten columns of the \(v\) array  
The numbering used here will continue through the remainder of the paper when referencing each individual feature. Example plots of four different paired combinations of the features listed above can be seen in Figure 10. This qualitatively demonstrates that some feature combinations are much more separable in the feature space than others. The feature pairs that were found to be more separable were features 3 vs. 2 and features 3 vs. 4, whereas features 1 vs. 4 were clearly the least separable. These obtained features were then used as inputs to a given classifier. These feature have been selected as prior research [31], demonstrated that these values can be successfully used to classify  
Figure 8: Example Doppler-time spectrogram from a person walking carrying a bag in both hands: (a) RTI micro-Doppler; (b) MTI micro-Doppler. different micro-Doppler motions in non-TTW scenarios. The total number of features extracted for all individuals was 1635 for the free hand walking case and 1470 for the bag carrying case, due to the reduced number of Doppler sections that could be extracted from the bag carrying case. The first classifier that has been selected for this work was the DA classifier applied in two different variants: the diagonal-linear and diagonal-quadratic. The training stage of the classifier was applied using a randomly selected sub-section percentage of the full dataset features. The classifier was then tested on the remaining samples that were not used in the training process. In order to represent an average training success rate, this process was repeated using 100 Monte-Carlo simulations; all results shown are the average value from these repetitions. The classifier success rate was defined by the output confusion matrix, by summing all correctly indicated classes and dividing by the total number of events, putting no emphasis on either false positive or false negative errors. Different real world scenarios may require emphasis of either avoiding false positives or false negatives, but for this analysis they have been treated equally.