## 6 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**CNN**} & \multicolumn{4}{c}{**MLP**} \\ \cline{2-13}
**Dataset** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Validating**} & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Validating**} & \multicolumn{2}{c}{**Test**} \\ \cline{2-13}
**Accuracy** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Loss** & **F-Score** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Loss** & **F-Score** & **Time** \\ \hline MNIST & 98.9\% & 133.25 s & 99.0\% & 7.68 s & 99\% & 0.023 & 99.2\% & 80.7 s & 89.56\% & 118.4\% & 97.2\% & 53.3 s & 98\% & 0.056 & 98.15\% & 59.8 \\ Fashion-MNIST & 90.88\% & 133.37 s & 90.35\% & 83.4\% & 91\% & 0.26\% & 91.39\% & 9.3 s & 90.83\% & 109.86 s & 88.85\% & 5.78 s & 89\% & 0.315 & 98.45\% & 5.35 s \\ EMNIST-Letters & 86.19\% & 82.59 s & 89.13\% & 10.57 s & 93\% & 0.193 & 93.68\% & 10.62 s & 79.45\% & 25.65 s & 81.81\% & 3.35 s & 89\% & 0.344 & 89.29\% & 3.40 s \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The performance of CNN and MLP on MNIST, Fashion-MNIST, and EMNIST-Letters datasets in the conventional collaborative models experiments. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Training Data Size** & \multicolumn{2}{c}{**Percentage of the**} \\  & **Reduced Training Data** & **Test Data Size** \\ \hline
**MNIST** & 54,351 & 90.58\% & 10,000 \\
**Fashion-MNIST** & 41,355 & 68.92\% & 10,000 \\
**EMNIST-Letters** & 83,282 & 57.19\% & 20,800 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The sizes of the datasets used in the privacy-preserving collaborative models experiments. to the fact that CNN, as a deep learning method, can make better use of the training data. Consequently, any reduction in the training data has a more significant impact on the CNN models compared to the MLP models. However, this trade-off in accuracy may be considered acceptable in sensitive domains where privacy is a primary concern. Our results indicate that the MLP models were less impacted by the proposed framework, which uses subsets of data encoded using RBM. One possible explanation for this is that CNN incorporates a robust feature detection mechanism that generally requires large datasets to function effectively. While RBM does select features, its selection may not be as effective for classification tasks because it is not specifically oriented toward them. RBM focuses on identifying features that are necessary for data reconstruction, rather than those that are most relevant for classification. Consequently, when CNN is trained on only a subset of the data, it may fail to accurately identify all relevant features. It is worth noting that the proposed framework reduces training time. Table 9 also summarizes the training and testing times for the models across different datasets. For example, training the CNN model on the MNIST dataset with the proposed framework takes 99.391 s, down from the 133.25 s required by the conventional collaborative framework (see Tables 7 and 9). Similarly, training times for the CNN model on the Fashion-MNIST and EMNIST-Letters datasets are reduced to 68.51 and 35.24 s, respectively, down from 133.37 and 82.59 s in the conventional framework. Tables 7 and 9 also show a similar reduction in training time for the MLP models. Figures 6 and 7 show the percentage of training time using the reduced datasets in the proposed framework relative to the total time taken using the complete datasets in the conventional framework (which does not protect privacy). Through the experiments and the results, we found that our framework preserves privacy with some loss in classification accuracy. In addition to preserving accuracy, the proposed framework proved to significantly reduce the models' training time. Furthermore, it reduces the network overhead since it sends subsets of the data instead of the whole data.