{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T18:49:17Z","timestamp":1780080557923,"version":"3.54.0"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MSIT (Ministry of Science and ICT), Korea","award":["IITP-2024-RS-2024-00437191"],"award-info":[{"award-number":["IITP-2024-RS-2024-00437191"]}]},{"name":"IITP (Institute for Information &amp; Communications Technology Planning &amp; Evaluation)","award":["IITP-2024-RS-2024-00437191"],"award-info":[{"award-number":["IITP-2024-RS-2024-00437191"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Respiratory rate (RR) changes in the elderly can indicate serious diseases. Thus, accurate estimation of RRs for cardiopulmonary function is essential for home health monitoring systems. However, machine learning (ML) algorithm errors embedded in health monitoring systems can be problematic in medical decision-making because some data have much larger sample sizes in the training set than others. This difference in sample size implies biosignal data imbalance. Therefore, we propose a novel methodology that combines bootstrap-based imbalanced continuous power spectral generation (IPSG) with ML approaches to estimate RRs and uncertainty to address data imbalance. The sample differences between normal breathing (12\u201320 breaths per minute (brpm)), dyspnea (\u226520 brpm), and hypopnea (&lt;8 brpm) show significant data imbalance, which can affect the learning of ML algorithms. Hence, the normal breathing part with a large amount of data is well-trained. In contrast, the dyspnea and hypopnea parts with relatively fewer data are not well-trained, and this data imbalance makes it difficult to estimate the reference variables of the actual dyspnea and hypopnea data parts, thus generating significant errors. Hence, we apply ML models by mixing artificial feature curves generated using a bootstrap model with the original feature curves to estimate RRs and solve this problem. As a result, the nonparametric bootstrap approach significantly increases the number of artificial feature curves. The generated artificial feature curves are selectively utilized in the highly imbalanced parts. Therefore, we confirm that IPSG is efficiently trained to predict the complex nonlinear relationship between the feature vectors obtained from the photoplethysmography signal and the reference RR. The proposed methodology shows more accurate prediction performance and uncertainty. Combining the proposed Gaussian process regression (GPR) with IPSG based on the Beth Israel Deaconess Medical Center dataset, the mean absolute error of the RR is 0.79 and 1.47 brpm. Our approach achieves high stability and accuracy by randomly mixing original and artificial feature curves. The proposed GPR-IPSG model can improve the performance of clinical home-based monitoring systems and design a reliable framework.<\/jats:p>","DOI":"10.3390\/s25051437","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T11:22:12Z","timestamp":1740568932000},"page":"1437","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Imbalanced Power Spectral Generation for Respiratory Rate and Uncertainty Estimations Based on Photoplethysmography Signal"],"prefix":"10.3390","volume":"25","author":[{"given":"Soojeong","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4457-4407","authenticated-orcid":false,"given":"Mugahed A.","family":"Al-antari","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence and Data Science, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5446-288X","authenticated-orcid":false,"given":"Gyanendra Prasad","family":"Joshi","sequence":"additional","affiliation":[{"name":"Department of AI Software, Kangwon National University, Samcheok 10587, Kangwon State, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0002-9386","authenticated-orcid":false,"given":"Yeong Hyeon","family":"Gu","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence and Data Science, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1109\/TIM.2018.2805154","article-title":"Measuring uncertainty during respiratory rate estimation using pressure-sensitive mats","volume":"67","author":"Nizami","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1682","DOI":"10.1109\/JBHI.2014.2344679","article-title":"Breathsens: A continuous on-bed respiratory monitoring system with torso localization using an unobtrusive pressure sensing array","volume":"19","author":"Liu","year":"2014","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_3","unstructured":"Lacey, W., Hashmi, M.F., and Graham, D.D. (2024, December 01). Abnormal Respirations, StatPearls, Available online: https:\/\/pubmed.ncbi.nlm.nih.gov\/29262235\/."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1038\/jp.2015.173","article-title":"Monitoring the respiratory rate by miniature motion sensors in premature infants: A comparative study","volume":"36","author":"Kohn","year":"2016","journal-title":"J. Perinatol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1109\/TBME.2009.2019766","article-title":"Estimation of respiratory rate from photoplethysmogram data using time\u2013frequency spectral estimation","volume":"56","author":"Chon","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Du, J., Liu, S.Q., Zhang, B., and Yuen, P.C. (2021, January 10\u201317). Weakly Supervised rPPG Estimation for Respiratory Rate Estimation. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Montreal, QC, Canada.","DOI":"10.1109\/ICCVW54120.2021.00271"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2481","DOI":"10.1109\/JBHI.2022.3144990","article-title":"Respiratory Rate Estimation using U-Net-Based Cascaded Framework from Electrocardiogram and Seismocardiogram Signals","volume":"26","author":"Chan","year":"2022","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lee, S., Moon, H., Al-Antari, M.A., and Lee, G. (2022). Dual-Sensor Signals Based Exact Gaussian Process-Assisted Hybrid Feature Extraction and Weighted Feature Fusion for Respiratory Rate and Uncertainty Estimations. Sensors, 22.","DOI":"10.3390\/s22218386"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"99445","DOI":"10.1109\/ACCESS.2020.2998117","article-title":"Non-contact respiratory rate estimation in real-time with modified joint unscented Kalman filter","volume":"8","author":"Uysal","year":"2020","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2754","DOI":"10.1109\/ACCESS.2023.3234597","article-title":"Automatic Features Extraction Integrated with Exact Gaussian Process for Respiratory Rate and Uncertainty Estimations","volume":"11","author":"Lee","year":"2023","journal-title":"IEEE Access"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"125648","DOI":"10.1109\/ACCESS.2020.3007524","article-title":"Multi-phases and various feature extraction and selection methodology for ensemble gradient boosting in estimating respiratory rate","volume":"8","author":"Lee","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","unstructured":"Orfanidis, S.J. (1988). Optimum Signal Processing: An Introduction, Macmillan Publishing Company."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Leonarduzzi, R.F., Schlotthauer, G., and Torres, M.E. (September, January 31). Wavelet leader based multifractal analysis of heart rate variability during myocardial ischaemia. Proceedings of the 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, Buenos Aires, Argentina.","DOI":"10.1109\/IEMBS.2010.5626091"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, T., and Zhou, M. (2016). ECG classification using wavelet packet entropy and random forests. Entropy, 18.","DOI":"10.3390\/e18080285"},{"key":"ref_15","unstructured":"Zhao, Q., and Zhang, L. (2005, January 13\u201315). ECG feature extraction and classification using wavelet transform and support vector machines. Proceedings of the 2005 International Conference on Neural Networks and Brain, Beijing, China."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.csda.2013.09.006","article-title":"Discriminant analysis of multivariate time series: Application to diagnosis based on ECG signals","volume":"70","author":"Maharaj","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Liu, S., Yao, J., and Motani, M. (2019, January 18\u201321). Early prediction of vital signs using generative boosting via lstm networks. Proceedings of the 2019 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), San Diego, CA, USA.","DOI":"10.1109\/BIBM47256.2019.8983313"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kumar, A.K., Ritam, M., Han, L., Guo, S., and Chandra, R. (2022). Deep learning for predicting respiratory rate from biosignals. Comput. Biol. Med., 144.","DOI":"10.1016\/j.compbiomed.2022.105338"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"55245","DOI":"10.1109\/ACCESS.2018.2871091","article-title":"Automatic quantitative analysis of human respired carbon dioxide waveform for asthma and non-asthma classification using support vector machine","volume":"6","author":"Singh","year":"2018","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.artmed.2016.12.003","article-title":"Handling limited datasets with neural networks in medical applications: A small-data approach","volume":"75","author":"Shaikhina","year":"2017","journal-title":"Artif. Intell. Med."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.neunet.2007.12.031","article-title":"Training neural network classifiers for medical decision making: The effects of imbalanced datasets on classification performance","volume":"21","author":"Mazurowski","year":"2008","journal-title":"Neural Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neunet.2018.07.011","article-title":"A systematic study of the class imbalance problem in convolutional neural networks","volume":"106","author":"Buda","year":"2018","journal-title":"Neural Netw."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ward, M., Malmsten, K., Salamy, H., and Min, C.H. (2021, January 22\u201328). Data Balanced Bagging Ensemble of Convolutional-LSTM Neural Networks for Time Series Data Classification with an Imbalanced Dataset. Proceedings of the 2021 IEEE International Symposium on Circuits and Systems (ISCAS), Daegu, Republic of Korea.","DOI":"10.1109\/ISCAS51556.2021.9401389"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"429","DOI":"10.3233\/IDA-2002-6504","article-title":"The class imbalance problem: A systematic study","volume":"6","author":"Japkowicz","year":"2002","journal-title":"Intell. Data Anal."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kabra, A., Chopra, A., Puri, N., Badjatiya, P., Verma, S., Gupta, P., and Krishnamurthy, B. (2020, January 17\u201320). Mixboost: Synthetic oversampling using boosted mixup for handling extreme imbalance. Proceedings of the 2020 IEEE International Conference on Data Mining (ICDM), Sorrento, Italy.","DOI":"10.1109\/ICDM50108.2020.00129"},{"key":"ref_26","first-page":"5550","article-title":"A robust oversampling approach for class imbalance problem with small disjuncts","volume":"35","author":"Sun","year":"2022","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1109\/TBME.2002.802009","article-title":"A novel method for the detection of apnea and hypopnea events in respiration signals","volume":"49","author":"Micsik","year":"2002","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Efron, B. (1992). Bootstrap methods: Another look at the jackknife. Breakthroughs in Statistics, Springer.","DOI":"10.1007\/978-1-4612-4380-9_41"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Efron, B., and Tibshirani, R.J. (1994). An Introduction to the Bootstrap, Chapman and Hall\/CRC.","DOI":"10.1201\/9780429246593"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1088\/0967-3334\/37\/4\/610","article-title":"An assessment of algorithms to estimate respiratory rate from the electrocardiogram and photoplethysmogram","volume":"37","author":"Charlton","year":"2016","journal-title":"Physiol. Meas."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1111\/j.1469-8986.1993.tb01731.x","article-title":"Respiratory sinus arrhythmia: Autonomic origins, physiological mechanisms, and psychophysiological implications","volume":"30","author":"Berntson","year":"1993","journal-title":"Psychophysiology"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1109\/TBME.2013.2246160","article-title":"Multiparameter respiratory rate estimation from the photoplethysmogram","volume":"60","author":"Karlen","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Elgendi, M., Martinelli, I., and Menon, C. (2024). Optimal signal quality index for remote photoplethysmogram sensing. NPJ Biosens., 1.","DOI":"10.1038\/s44328-024-00002-1"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1109\/TII.2016.2612640","article-title":"Oscillometric blood pressure estimation based on deep learning","volume":"13","author":"Lee","year":"2016","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Vaseghi, S.V. (2008). Advanced Digital Signal Processing and Noise Reduction, John Wiley & Sons.","DOI":"10.1002\/9780470740156"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/79.647043","article-title":"The bootstrap and its application in signal processing","volume":"15","author":"Zoubir","year":"1998","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"96775","DOI":"10.1109\/ACCESS.2021.3095380","article-title":"A novel non-invasive estimation of respiration rate from motion corrupted photoplethysmograph signal using machine learning model","volume":"9","author":"Shuzan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","article-title":"Greedy function approximation: A gradient boosting machine","volume":"29","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"ref_40","unstructured":"(2024, December 02). Random Forest. Available online: https:\/\/www.ibm.com\/think\/topics\/random-forest."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Szalma, J., B\u00e1nhalmi, A., and Bilicki, V. (2018, January 23\u201326). Detection of Respiratory Effort-Related Arousals Using a Hidden Markov Model and Random Decision Forest. Proceedings of the 2018 Computing in Cardiology Conference (CinC), Maastricht, The Netherlands.","DOI":"10.22489\/CinC.2018.089"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Williams, C.K., and Rasmussen, C.E. (2006). Gaussian Processes for Machine Learning, MIT Press.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"41159","DOI":"10.1109\/JSEN.2024.3474050","article-title":"Confidence Interval and Respiratory Rate Estimations using Smart Feature Fusion based on Exact Gaussian Process","volume":"24","author":"Lee","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Tsai, Y.C., Lai, S.H., Ho, C.J., Wu, F.M., Henrickson, L., Wei, C.C., Chen, I., Wu, V., and Chen, J. (2020, January 20\u201324). High accuracy respiration and heart rate detection based on artificial neural network regression. Proceedings of the 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Montreal, QC, Canada.","DOI":"10.1109\/EMBC44109.2020.9175161"},{"key":"ref_45","unstructured":"Knapp-Cordes, M., and McKeeman, B. (2024, December 03). Improvements to tic and toc Functions for Measuring Absolute Elapsed Time Performance in MATLAB. Available online: https:\/\/www.mathworks.com\/company\/technical-articles\/improvements-to-tic-and-toc-functions-for-measuring-absolute-elapsed-time-performance-in-matlab.html."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4097\/kjae.2017.70.1.1","article-title":"Understanding one-way ANOVA using conceptual figures","volume":"70","author":"Kim","year":"2017","journal-title":"Korean J. Anesthesiol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.compbiomed.2015.04.015","article-title":"Estimated confidence interval from single blood pressure measurement based on algorithmic fusion","volume":"62","author":"Lee","year":"2015","journal-title":"Comput. Biol. Med."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/5\/1437\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:43:29Z","timestamp":1760028209000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/5\/1437"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,26]]},"references-count":47,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["s25051437"],"URL":"https:\/\/doi.org\/10.3390\/s25051437","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,26]]}}}