###### Abstract
In particular, several techniques such as autoregressive method [24], multiple fractal wavelet readers [25], wavelet packets [26], and maximum overlap discrete wavelet transform [27; 28] were used to extract features to compensate for insufficient data. However, it is difficult to determine which features should be used and which ones are needed to obtain the optimal estimation rate. Ensemble GBA based on multi-phase features also has the disadvantage that extracting the features required for RR estimation from the PPG signal is inconvenient and time-consuming. Another well-known machine learning (ML) model successfully used for estimation in the biomedical engineering field is support vector regression (SVR) [29; 30]. SVR is known to have the advantage of effectively approximating nonlinear effects even with a small number of training datasets. However, SVR is more complex to tune than the recent GBAs discussed in [31]. Nevertheless, significant progress has been made in developing new ML models over the past decade, and one of the most effective approaches to estimation accuracy is ensemble ML algorithms [32]. An ensemble algorithm composes a model by training several basic models such as a decision tree and then combining them to produce a model with a higher estimation probability [31]. Unlike methods based on simple averages of basic learners such as bagging [33], random forest [34], and boosting [35], the GBA is based on effective iteration strategies. This ensemble ML model has been successfully used in many areas and is just beginning to be used for RR estimation [22]. Based on these backgrounds, we propose a novel methodology combining an autocorrelation function-based power spectral feature extraction process with the GBA (CAGBA) model to estimate RR. Here, we can obtain the respiration frequency using the autocorrelation function-based power spectral feature extraction that finds the time axis's periodicity. Our input data have a small sample size, which is a challenge when using deep learning techniques. In general, a small number of samples cannot guarantee the successful performance of ML algorithms, such as LSTM, because the LSTM algorithms have several nonlinear features and require large datasets to train these features. In practice, we hope to develop a CAGBA that can perform well even with a small sample of PPG signals. We can solve the problem of small data by applying automatic autocorrelation function-based power spectral feature extraction [36]. The proposed CAGBA solves overfitting for the training datasets. In detail, we extend the data dimension by applying automated feature extraction technology, and we then split the long-resampled wave signal to increase the number of input data samples, which solves the overfitting problem caused by the small data sample problem. Furthermore, the proposed CAGBA is computationally inexpensive compared to the LSTM model. Furthermore, our research provides an accurate RR estimate using the CAGBA process and offers a solution to reduce the estimated uncertainty. This work is one of the first studies to use CAGBA for RR estimation with a limited sample. This study contributes to the RR estimation field as follows. * We propose a novel method for RR estimation using CAGBA from limited PPG signal data. The key to this method is to extend the dimension of the input data using the autocorrelation function-based power spectral feature extraction process;
* We split the long-resampled wave signal to increase the number of input data samples, which solves the overfitting problem caused by the small data sample problem;
* The proposed method uses an autocorrelation function-based power spectral feature extraction process from the PPG signals in the time domain, which automatically extracts relevant features from the power spectral, learns, and then estimates the RR.