# SBNNR: Small-Size Bat-Optimized KNN Regression
## 5 Experimental Results
### Comparison with State of Art  
To gain deeper insights, we applied our proposed method to two datasets used in a recent study on small datasets by [PERSON] et al. (2018) and compared the results. This comparison allows for a direct evaluation of our approach's performance against established benchmarks in similar contexts. Table 3 shows the specifications of the datasets for our comparative analysis. Tables 4 and 5, along with Figures 3 and 4, provide a comprehensive analysis of the SBNNR method's performance compared to previous state-of-the-art methods for small-dataset regression. Table 4 presents the coefficient of determination (\(R^{2}\)) values for the SBNNR approach in comparison to methods developed by [PERSON] et al. (2018) across two specific datasets: BONE, which involves predicting trabecular bone strength, and FAT, which estimates body fat percentage in women. For the BONE dataset, the proposed SBNNR method achieved a total \(R^{2}\) score of 0.9285, which is a notable improvement over the score of 0.77 of the approach proposed by [PERSON] et al. (2018). This higher \(R^{2}\) indicates that the SBNNR framework better captures the variance within the BONE dataset, highlighting its improved accuracy and enhanced ability to generalize to new data points. Similarly, for the FAT dataset, SBNNR achieved a total \(R^{2}\) of 0.9835, compared to the value of 0.76 achieved by the method proposed by [PERSON] et al. (2018), showing that SBNNR provides a closer fit to the dataset's actual distribution, further reinforcing its effectiveness in small-data contexts. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Method** & **Train \(R^{2}\)** & **Test \(R^{2}\)** & **Total \(R^{2}\)** \\ \hline BONE & [PERSON] et al. (2018) & - & - & 0.77 \\  & Proposed Method & 0.9775 & 0.7681 & 0.9285 \\ \hline FAT & [PERSON] et al. (2018) & - & - & 0.86 \\  & Proposed Method & 0.9967 & 0.8351 & 0.9835 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of state-of-the-art methods with the proposed method (\(R^{2}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Instances** & **Features** & **Source** \\ \hline Prediction of trabecular bone strength in severe osteoarthritis (BONE) & 35 & 5 & [38] \\ Prediction of body fat percentage of women (FAT) & 24 & 7 & [39] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Datasets for comparative assessment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Method** & **RMSE** & **MAE** & **MAPE** \\ \hline BONE & [PERSON] et al. (2018) & 3.15 & 2.30 & 0.20 \\  & Proposed Method & 1.907 & 1.218 & 0.184 \\ \hline FAT & [PERSON] et al. (2018) & 1.04 & 1.00 & 0.07 \\  & Proposed Method & 0.635 & 0.389 & 0.032 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of state-of-the-art methods with the proposed method (error rates). The comparison presented in Table 5 focuses on error metrics--Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE)-- to assess prediction reliability across the same datasets. For the BONE dataset, SBNNR demonstrated substantial improvements, with an RMSE of 1.907, an MAE of 1.218, and an MAPE of 0.184, outperforming [PERSON] et al. 's corresponding values of 3.15, 2.30, and 0.20. These lower error rates suggest that SBNNR reduces prediction errors effectively, making it more robust and accurate for small datasets that often suffer from data irregularities. Similarly, the results on the FAT dataset underscore SBNNR's advantages, with RMSE, MAE, and mean absolute error (MAE). Figure 4: Predicted (red points for test data and blue points for train data) compared to actual values (green line) of the proposed method on the FAT dataset. Figure 3: Predicted (Red Points for test data and blue points for train data) compared to Actual values (Green line) Proposed method on BONE dataset. and MAPE values of 0.635, 0.389, and 0.032, respectively. These metrics are considerably lower than those reported for the method proposed by [PERSON] et al.