# A Passive RF Testbed for Human Posture Classification in FM Radio Bands
## 3 Feature Engineering and Classification
### Feature Selection  
To select the best features to represent the acquired data, we computed various features, and their performance was first visually analyzed considering all collected datasets. From the multiple features initially identified as hypothetical candidates, we selected 15 features of interest. The selection of the features was based on a quantitative benchmark (variance of the samples) to evaluate their capacity to discriminate the three classes in the datasets. Let **r** be the matrix that contains the complex values collected by the reference antenna and **s** the matrix that contains the complex values collected by the surveillance antenna. Both **r** and **s** contain \(N\) columns and \(M\) rows, where \(N\) denotes the number of classes and \(M\) represents the number of samples per class. Table 10 identifies the 15 features adopted in the evaluation process. Note that when computing the Median Absolute Deviation (MAD), the central point used is the median. \begin{table}
\begin{tabular}{l l} \hline \hline
**Feature Label** & **Formula** \\ \hline Feature1 & max (\(|\textbf{r}|\)) \\ \hline Feature2 & max (\(|\textbf{s}|\)) \\ \hline Feature3 & max (\(|\textbf{r}{-}\textbf{s}|\)) \\ \hline Feature4 & std (\(|\textbf{r}|\)) \\ \hline Feature5 & std (\(|\textbf{s}|\)) \\ \hline Feature6 & std (\(|\textbf{r}{-}\textbf{s}|\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Description of the 15 features adopted in this work (max denotes the maximum value, std represents the standard deviation, and skew denotes the skewness). Note that **r** (for reference signal) and **s** (for surveillance signal) are the matrices heretofore mentioned. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **90 s Datasets** & **180 s Datasets** \\ \hline Class 0 & [1, 2, 3, 0] & [4, 6, 5, 2, 0, 1, 7, 3, 8] \\ \hline Class 1 & [0, 1, 2, 3] & [8, 0, 4, 6, 1, 7, 2, 5, 3] \\ \hline Class 2 & [1, 0, 2, 3] & [2, 1, 4, 0, 7, 6, 5, 3, 8] \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Description of the sequence of the slices of the calibration portions for datasets lasting 90 s and 180 s.  
Figure 7: Time division of Class 0 into 6 s slices for a 90 s dataset. Given the sample rate of 250 kS/s adopted in all datasets, we computed each feature for a sliding window of 25 kS. In each second of real-time acquisition, we were able to compute 10 feature outputs, which allowed 10 posture prediction outputs when neglecting the time required to compute each feature. The number of feature outputs for every dataset is described in Table 11.  
To decrease the overall computation time of the classification process, only 2 of the 15 features were dynamically selected and used in the classification algorithm. It is important to highlight that some features are strongly correlated with others (e.g., Feature1 and Feature9); thus, the selection of such features would not add much information. First, we visually tested different combinations of two features with the datasets in Table 5 by performing a scatter of the two chosen features for each class. The next step regarding feature selection relies on the identification of the two features that maximize the classification detection probability. In other words, the goal is to identify the two features that provide better separation between the sample clusters of the different classes. To evaluate the combinations of the features to be selected, we adopted the Analysis of Variance (ANOVA) method [18] for the calibration data from the 90 s and 180 s datasets. The ANOVA method is an efficient and simple feature selection technique that evaluates features through the variance between and within classes. The features achieving the highest F-statistic score can better discriminate the sampled data. Taking into consideration the datasets lasting 90 s and 180 s, Tables 12 and 13 present the mean, median, dissimilarity measure, and normalized variance of the 10 features obtaining the highest F-statistic values.