## 2 Materials and Methods
### Data Pre-Processing
#### 2.3.2 Acoustic Signals  
The acoustic signal is collected by a microphone placed in the right ear. Firstly, we down-sample the acoustic signal from 44.1 kHz to 16 kHz [29]. Then, a spectrogram-based denoising method is utilized [30]. This method requires the original signal and a piece of pure noise signal as input. After converting the two into a spectrogram, the noise segment is used to calculate the threshold mask, and the similar noise in the original acoustic signal is removed with this mask. Since the microphone may receive continuous noise in the environment and the sound of breathing or heartbeat from the subjects. Thus, a segment collected when the subject is motionless is defined as noise. The denoising effect is shown in Figure 4.  
Figure 4: Denoising effect: (**a**) time domain signal diagram before denoising; (**b**) time domain signal diagram after denoising; (**c**) spectrogram transform by time domain signal before denoising; (**d**) spectrogram transform by time domain signal after denoising.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Feature Vector** & **Description** \\ \hline \(f_{67}^{M}\) & Correlation coefficient between \(a_{y}\) and \(a_{z}\) \\ \(f_{67}^{M}\) & Correlation coefficient between \(a_{x}\) and \(a_{z}\) \\ \(f_{68}^{M}\) & Correlation coefficient between \(\omega_{x}\) and \(\omega_{y}\) \\ \(f_{69}^{M}\) & Correlation coefficient between \(\omega_{y}\) and \(\omega_{z}\) \\ \(f_{70}^{M}\) & Correlation coefficient between \(\omega_{x}\) and \(\omega_{z}\) \\ \hline \hline \end{tabular}  
* M—motion signal; \(a_{norm}\)—Euclidean norm of acceleration; \(\omega_{norm}\)—Euclidean norm of angular velocity.  
\end{table}
Table 3: _Cont._The pre-processing of acoustic signals is similar to that of motion signals. The sliding window with a 5 s size and 75% overlapping is utilized. To avoid scale variance between different subjects and different activities, z-score standardization is used, as calculated by Equation (4):  
\[z=\frac{x-\mu}{\sigma}, \tag{4}\]  
where \(x\) is the time domain acoustic signal after processing the sliding window, \(\mu\) is the mean value of the signal amplitude, and \(\sigma\) is the standard deviation of the signal amplitude. In addition, a fast Fourier transform (FFT) is applied to obtain the power spectrum. Meanwhile, the Hamming window [31; 32] with zero padding is utilized in each window to improve computing ability. As features of acoustic data, four types of frequency-domain features are extracted from the segmented data, including total spectrum power [33], four sub-band powers [32; 33], brightness [32; 33], and spectral roll-off [32]. In addition, Mel-frequency cepstral coefficients, representing the characteristics of the general human ear's sensitivity to different frequencies, are commonly used in acoustic recognition. Hence, we also take 17 Mel-frequency cepstral coefficients as features. Finally, we obtained 24 acoustic features, as shown in Table 4, and a min-max normalization is utilized to scale features.  
Through the pre-processing stage, we acquire a motion feature matrix with size \(210\times n\) and an acoustic feature matrix with size \(24\times n\) from each trail, where \(n\) is the number of sliding windows. Thus, a size of \(234\times n\) feature matrix consisting of motion and acoustic features is obtained.