## 5 Experimental Results  
The experimental setup involves an optimized machine learning algorithm for performing horizontal fragmentation using the Red Fox Optimization-based Support Vector Machine (RFO-SVM) data fragmentation model. Prior to feeding the input database into the proposed model, pre-processing is performed to handle missing data and ensure data integrity. The implementation of RFO-SVM for data fragmentation and allocation was carried out using Python v3.10. The Python libraries used in the implementation were pandas v2.0.1, numpy v1.23.5, and sklearn v1.2.2. These libraries provide essential functionalities for data manipulation, numerical computations, and machine learning algorithms. The simulation setup for evaluating the performance of the implemented RFO-SVM algorithm is summarized in Table 3.  
The maximum number of iterations allowed for the RFO-SVM algorithm during the training process was set to 50, which controls the convergence of the algorithm and determines the number of iterations required to reach the optimal solution. The best model parameters are derived by the optimization process. The C range represents the regularization parameter of the SVM algorithm, which balances the trade-off between the training error and model complexity and it is set as 10. The \(\gamma\) range is a parameter specific to the radial basis function (RBF) kernel used in SVM that influences each training sample and determines the shape of the decision boundary. A \(\gamma\) range of 1.0 was employed in simulation, indicating the range of values considered for this parameter during the training process. The kernel function used in the SVM algorithm was the radial basis function (RBF) kernel for its ability to capture non-linear relationships between features. The air quality dataset was fragmented into four distinct subsets and the wine quality dataset was divided into six fragments. The evaluation measures are used to assess the performance of the proposed model, including accuracy, precision, recall, and F1-score. Accuracy measures the overall correctness of the model's predictions. It calculates the ratio of correct predictions to the total number of predictions. \[\text{Accuracy}=\left[\frac{\left(T_{p}+T_{n}\right)}{\left(T_{p}+T_{n} \right)+\left(F_{p}+F_{n}\right)}\right] \tag{32}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**S.NO.** & **Parameter** & **Value** \\ \hline
1. & Maximum iterations & 50 \\ \hline
2. & C range & 0.1–10 \\ \hline
3. & y range & 0.001–1.0 \\ \hline
4. & Kernel & Linear, polynomial, sigmoid rbf \\ \hline
5. & No. of fragments for air quality dataset & 4 \\ \hline
6. & No. of fragments for wine quality dataset & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation Setup. Precision measures the proportion of correctly predicted positive instances out of the total instances predicted as positive. \[Precision=\frac{T_{p}}{\left(T_{p}+F_{p}\right)} \tag{33}\]  
Recall, also known as sensitivity or true positive rate, measures the proportion of correctly predicted positive instances out of the total actual positive instances. \[Recall=\frac{T_{p}}{\left(T_{p}+F_{n}\right)} \tag{34}\]  
F1-score combines precision and recall into a single metric, providing a balanced measure of the model's performance. It is the harmonic mean of precision and recall. \[F1\text{-}score=2\times\left[\frac{Precision\times Recall}{Precision+Recall}\right] \tag{35}\]  
where \(T_{p},T_{n},F_{p},F_{n}\) are true positive, true negative, false positive, and false negative, respectively. Allocation Cost represents the cost associated with dividing the data into fragments. It is calculated based on the computational resources required for fragmentation and the complexity of the data distribution. \[Allocation\ Cost=f(Data,\ Fragmentation\ Criteria) \tag{36}\]  
where f () represents the function used to calculate the allocation cost based on the input data and the fragmentation criteria. The total cost of allocation is obtained by summing up the allocation cost of each fragment.