# SBNNR: Small-Size Bat-Optimized KNN Regression
## 7 Conclusions  
This study underscores the significance and effectiveness of the small-size bat-optimized nearest neighbor regression (SBNNR) framework, designed specifically to enhance prediction accuracy in small-dataset environments. In combination with KNN optimized by the bat algorithm, the SBNNR approach demonstrates improved model generalizability and robustness, as evidenced by significant gains in the \(R^{2}\) score across multiple real-world datasets. This improvement, observed in diverse fields with data limitations--such as medical diagnostics, environmental monitoring, and material sciences--affirms the method's adaptability and high performance. The framework achieves up to a 5% enhancement in \(R^{2}\) score when compared to traditional KNN optimized with grid search, highlighting its utility in scenarios where small datasets hinder model training and accuracy.  
This study paves the way for future research, particularly in the exploration of ensemble methods to further enhance model robustness. Integrating random forest (RF) into the SBNNR framework presents a promising avenue, especially as advancements in synthetic data generation continue to evolve. This integration could employ RF's ability to capture complex, non-linear relationships, potentially augmenting the predictive performance and resilience of the SBNNR framework in data-scarce environments. While KNN has shown substantial improvement through bat algorithm optimization, RF's ability to capture more complex, non-linear relationships may complement KNN by improving predictive accuracy and resilience against small-data limitations. Additionally, leveraging RF in conjunction with feature selection, instance selection, and hyperparameter optimization could further elevate performance, especially in complex domains where small datasets exhibit high variance. Future work may also focus on optimizing the GAN and DNN components to better support enhanced data augmentation and feature extraction, further bolstering the SBNNR framework's utility across fields that rely on small datasets.  
Conceptualization, R.S.; methodology, R.S.; software, R.S.; validation, R.S.; formal analysis, R.S.; investigation, R.S.; resources, J.G. and X.M.-B.; data curation, R.S.; writing original draft preparation, R.S.; writing--review and editing, J.G., [PERSON]B. and J.K.; visualization, R.S.; supervision, [PERSON] and X.M.-B.; project administration, J.G. and [PERSON]-[PERSON]; funding acquisition, R.S., J.G. and [PERSON]-B. All authors have read and agreed to the published version of the manuscript.  
This work has been supported by the Spanish Ministry of Science and Innovation under grant PID2021-124463 OB-100, funded by MCIN/AEI/10.13039/501100011033 and by ERDF \"A way of making Europe\", by the European Union's Horizon Europe under the HE ICOS project, Grant Agreement no. 101070177, and by the Catalan Government under contract 2021 SGR 00326. The corresponding author [PERSON] gratefully acknowledges the _Universitat Politecnica de Catalunya_ and _Banco Santander_ for the financial support of his predoctoral grant FPI-UPC 2021.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.