# Human Activity Recognition Based on Non-Contact Radar Data and Improved PCA Method
## 4 Experiments and Results
### Signal Preprocess: Improved PCA  
To convert the 1D raw radar data into 2D spectrograms, we first performed FFT (Fast Fourier transform) on the raw radar data and obtained the Range-Time images. Range FFT is used to derive the distance information of the target. The sampling data on each chirp is FFT and stored as a row vector of the matrix. We then transposed the \(X\)-axis with the \(Y\)-axis of the Range-Time images to obtain the Time-Velocity pattern of spectrograms which can better represent the characteristics of the movement. After the transposition, the \(X\)-axis represents Time and the \(Y\)-axis represents Range. Finally, we performed a second FFT on each range dimension using the Doppler FFT to obtain target speed information from the spectrogram (Time-Velocity pattern). The data conversion process is demonstrated in Figure 3. The typical spectrogram of each activity type is shown in Figure 4.  
To extract the features of the obtained 2D spectrograms, we processed the data using the PCA algorithm. Figure 5 shows the contribution rate of the first 10 components extracted from six types of radar spectrograms. As shown in Figure 5, the first two eigenvectors account for 70-80% of the sample information. Therefore, we set the parameter \(p=2\) in the improved PCA method and select these two eigenvectors for value enhancement. The other eigenvectors do not change their values. Figure 6 shows the spectrogram reconstructed from the principal components k = 1 to k = 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**Types of Activities** & **Number** \\ \hline Walking & 286 \\ Sitting & 289 \\ Standing & 287 \\ Picking up things & 287 \\ Drinking & 286 \\ Falling & 198 \\ Total & 1633 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of samples per activity type. Figure 3: Radar data process showing Time–Velocity patterns. Figure 4: Radar spectrograms of six activities. Figure 5: Contribution rates of the first 10 components of different activities. Figure 6 highlights that the first two principal components have reconstructed the main contours of the original spectrogram. After that, as the principal components increase, the information of the image gradually increases and the noise becomes smaller but still exists. Therefore, we only enhanced the first two values of the dimensions that contain most of the spectrogram information. In value enhancement, the size of the original radar spectrograms was \(256\times 256\) and the number of values in each dimension was \(256\). We selected the values of the first two dimensions for enhancement which accounted for most of the image information, with the number of selected values being \(2\times 256\). Each type of activity contained Q images. We calculated the mean value of data in these two dimensions of spectrograms. These values with the size of \(Q\times 1\) are normally distributed and the abnormal values were then selected and replaced with the mean values while the remaining normal values remained unchanged. The process of selecting and enhancing values is shown in Figure 7.  
In Figure 7, \(\mathbf{v}_{\text{normal}}\) denotes the normal values, \(\mathbf{v}_{\text{abnormal}}\) denotes the abnormal values, and \(\mathbf{\overline{V}}\) represents the mean values. The mean is not global. There are six activities in the  
Figure 6: Image Reconstruction in PCA method. Figure 7: Values’ selection and enhancement process. dataset and Q samples in each activity. The mean value is obtained according to each value of the enhanced eigenvector. The mean number of the enhanced eigenvectors is the sequence length of the eigenvectors. As can be seen in Figure 8, before the normal distribution, some of the values of the first two dimensions did not follow the \(2\sigma\) principle of normal distribution and were outside the \((\vec{x}-2\sigma,\vec{x}+2\sigma)\) range. Therefore, to enhance the values, we assigned these outlier values to the mean of the values.