## 4 Results  
In this experiment, first, a respiratory signal was obtained from the PPG signal using the two datasets. These data were randomly separated into 80% of the training and 20% of the test data. In addition, to evaluate the performance of the proposed algorithm, reference RR was calculated from the oral-nasal pressure signal using a custom respiration detection algorithm [37].  
We summarized the main parameters of the proposed and conventional models when using the RRSYNTH dataset in Table 1. Using the BIDMC dataset, the main parameters are the same as in the RRSYNTH dataset, except for the dimensions of the features. This table adjusts the parameters for each process to achieve the best performance. Twenty total training and testing times were calculated using MATLAB \(\textregistered2022\)[42]. As shown in Table 2, the GBA models had a shorter execution time than the LSTM models and a higher total execution time than the SVR models. To evaluate the proposed method in comparison with the conventional methods, difference between the RR estimates is obtained experimentally. The reference RR values are summarized in Table 3 based on the mean absolute error (MAE) and standard deviation (SD) of the MAE. The MAE and SD results show the mean values from the 20 experiments. Lower SD and MAE values indicate a better performance than high SD and MAE values. Here, a new feature extraction process is also applied to SVR and LSTM methods, including the GBA model, which proposes a feature extraction method using the autocorrelation-based power spectral proposed for objective evaluation. As mentioned in the introduction, the proposed approach is called the CAGBA model. The results obtained using SVR with the multiphase feature extraction (SVRMF) and SVR with autocorrelation function-based power spectral feature (CASVR) models are listed in Table 3. The MAE result (2.89 bpm) of CASVR shows a higher performance than this (5.57 bpm) of SVRMF using the RRSYNTH dataset. Using the BIDMC, we see that the MAE results of the two models, SVRMF and CASVR, are very similar. The results obtained using LSTMs with multiphase feature extraction (LSTMMF) and LSTMs with autocorrelation function-based power spectral feature (CALSTM) [18] are shown in Table 3. The CALSTM (5.35) algorithm is shown to perform slightly better than the LSTMMF (5.63) using the RRSYNTH dataset. In addition, we check the MAE results (2.37 bpm vs. 2.54 bpm) of LSTMMF and CALSTM models when using the BIDMC data. The results obtained using a GBA with multiphase feature extraction (GBAMF) and the CAGBA model are suggested in Table 3. The MAE result (1.06 bpm) of CAGBA is compared with this (5.25) of GBAMF. We notice the MAE results (1.98 bpm) and (1.94 bpm) of GBAMF and CAGBA models using the BIDMC dataset.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Parameters** & **SVRMF** & **CASVR** & **LSTMMF** & **CALSTM** & **GBAMF** & **CAGBA** \\ \hline Dimension of Feature & 279 & 1542 & 279 & 1542 & 279 & 1542 \\ Dimension of Output & 1 & 1 & 1 & 1 & 1 & 1 \\ Epsilon & 3 & 3 & \(1.0\times 10^{-8}\) & \(1.0\times 10^{-8}\) & - & - \\ KernelFunction & Gau. & Gau. & - & - & Con. & Con. \\ KernelScale & auto & auto & - & - & - & - \\ Number of Hidden Unit & - & - & 200–300 & 200–300 & - & - \\ FullyConnectdLayer & - & - & 50 & 50 & - & - \\ Dropout & - & - & 0.2–0.5 & 0.2–0.6 & - & - \\ MaxEpoch & - & - & 300 & 300 & - & - \\ Solver & - & - & adam & adam & - & - \\ GrandientThreshold & - & - & 1 & 1 & - & - \\ ShrinkageFactor & - & - & - & - & 0.05–0.3 & 0.05–0.3 \\ SubsamplingFactor & - & - & - & - & 0.1–0.3 & 0.1–0.3 \\ MaxTreeDepth & - & - & - & - & 4–6 & 4–6 \\ Max Iterations & - & - & - & - & 2000 & 2000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The core parameters used in the proposed and conventional methods were summarized using the RRSYNTH dataset.