## 2 Materials and Methods
### Auditory Property-Based Features and Artificial Neural Network Classifiers  
We describe herein a new method based on the use of auditory model-based features wherein artificial neural network (ANN) classifiers were used to detect quickly low-intensity SBEs in the sleep sound records. Humans can distinguish small sound events and silence from sleep sounds. Therefore, in this study, we used the AIM of [PERSON] et al. [26], which simulated the processing mechanism of the auditory system. AIM consists of precochlear processing (PCP), basilar membrane motion (BMM), and the NAP and stabilized auditory image (SAI), which is converted using strobe temporal integration modules. However, given that (i) the calculation of SAI requires large computational and memory costs and (ii) the information on the detection of sound event is included prior to the strobe temporal integration processing [39], we used the PCP, BMM, and NAP modules of the AIM. Figures 1 and 2 show the flow charts of the automatic SBE detection system proposed in this study. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Exp-1** & **Exp-2** \\ \hline No. of patients & 25 & 15 \\ AHI & \(26.8\pm 22.9\) & \(24.1\pm 22.8\) \\ BMI & \(26.2\pm 6.2\) & \(25.5\pm 2.2\) \\ Age & \(56.6\pm 22.0\) & \(60.3\pm 12.3\) \\ Gender & 19 males/6 females & 9 males/6 females \\ SNR [dB] & \(-8.34\pm 1.40\)–\(0.88\pm 3.24\) & \(-13.84\pm 4.02\)–\(0.05\pm 3.22\) \\ Class & 18 OSAS/7 non-OSAS & 8 OSAS/7 non-OSAS \\ No. of SBEs & \(52.7\pm 13.2\) & \(54.1\pm 12.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Subject record database used in Exp-1. \begin{table}
\begin{tabular}{c c} \hline \hline  & **No. of Segments** \\ \hline SBEs & & \(963.4\pm 290.2\) \\  & Silence & \(502.7\pm 651.2\) \\  & Music & \(64.3\pm 193.2\) \\  & Alarm & \(93.3\pm 257.9\) \\  & Speech & \(52.9\pm 172.5\) \\ Non-SBEs & Footsteps & \(15.7\pm 30.0\) \\  & Mouth movement & \(2.5\pm 4.4\) \\  & Duvet noise & \(22.0\pm 59.9\) \\  & Fan & \(718.9\pm 785.9\) \\  & Tapping & \(46.0\pm 71.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of segments with snoring/breathing episodes (SBEs)/non-SBEs used in Exp-2. As shown in Figure 1, the 120 s recorded data segment first underwent preprocessing with a bandpass filter that simulated the characteristics of the outer and middle ears at the PCP stage of AIM (lower cutoff frequency: 1000 Hz, and upper cutoff frequency: 6000 Hz) [40]. After the recorded data passed through the PCP stage, the recorded data  
Figure 1: Flow chart of feature extraction based on the adopted auditory model. Figure 2: Flow chart of the automatic snoring/breathing event (SBE) detection system proposed in this study. were divided in windows with widths equal to 1024 samples and a shift width equal to 1 sample. Subsequently, at the BMM stage, filtering was conducted with an auditory filter bank that simulated the cochlear frequency analysis mechanism. In this study, we used a gamma chirp filter bank composed of 50 channel filters between the asymptotic frequencies of 100 Hz and 5000 Hz as an auditory filter bank. Given that the NAP stage simulates the phase fixing characteristics when converting BMM physical information into acoustic nerve information, the filter output obtained from the BMM stage was filtered by half-wave rectification and a low-pass filter. The output obtained from the NAP stage was framed with a frame size of 1024 samples and a shift size of 512 samples. Through this frame processing, a total number of 2582 frames for the 120 s recorded data were obtained. We applied power-law nonlinearity with an exponent of 1/15 on each NAP frame to derive cepstral features. Furthermore, DCT which has a property of energy compaction was also applied. The output extracted from the DCT generally needed to be normalized before the classification process. However, there is no optimal way of normalization or formal correction, as described in [41].