# Communication-Efficient Vertical Federated Learning
## 5 Results
### Performance using Autoencoders  
Tables 6-9 provide a similar comparison to that shown in Section 5.1, but with an undercomplete autoencoder as a feature extraction technique. The table also provides an overview of how well the autoencoders perform when encoding local data of the clients. To gain a better understanding and observe the effect on overall performance, experiments were also carried out by varying the compression rates/encoding dimensions (25, 50, and 75 percent) of the autoencoders. A common observation across all datasets is that the performance of the aggregated model after applying the proposed method degrades as the compression rate of the autoencoder is reduced. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{2}{c}{**Accuracy (\%)**} & \multicolumn{2}{c}{**F1 Score (\%)**} \\ \hline Centralized Learning & \multicolumn{2}{c}{81.45} & \multicolumn{2}{c}{81.46} \\ Guest Party Performance & \multicolumn{2}{c}{68.88} & \multicolumn{2}{c}{68.87} \\ \hline  & \multicolumn{2}{c}{Autoencoder Performance} & \multicolumn{2}{c}{} \\  & Compression 25\% & \multicolumn{2}{c}{Compression 50\%} & \multicolumn{2}{c}{Compression 75\%} \\  & Training Loss & Validation Loss & Training Loss & Validation Loss & Training Loss & Validation Loss \\ \hline C1 & 74.27 & 75.69 & 76.72 & 77.15 & 80.14 & 80.66 \\ C2 & 0.0189 & 0.0194 & 0.0326 & 0.0340 & 0.0698 & 0.0699 \\ C3 & 9.84 & 10.06 & 36.14 & 37.22 & 45.15 & 46.61 \\ \hline  & \multicolumn{2}{c}{Performance on Aggregated Latent Data} & \multicolumn{2}{c}{} \\  & Compression 25\% & \multicolumn{2}{c}{Compression 50\%} & \multicolumn{2}{c}{Compression 75\%} \\  & Accuracy (\%) & F1 Score (\%) & Accuracy (\%) & F1 Score (\%) & Accuracy (\%) & F1 Score (\%) \\ \hline Encoding C1 & 77.88 & 77.89 & 75.19 & 75.20 & 75.72 & 75.73 \\ Without Encoding C1 & 80.83 & 80.84 & 79.79 & 79.79 & 79.31 & 79.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental Results on Adult Income Dataset. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Accuracy** & **F1 Score** \\ \hline Centralized Training with unpartitioned data & 75.10 & 74.29 \\ Guest party with local data & 66.10 & 58.95 \\ Performance after PCA at all clients & 74.79 & 72.18 \\ Performance after PCA at all clients except C1 & 74.79 & 72.08 \\ \hline \hline \multicolumn{2}{c}{**Overview of Feature Dimensions**} \\  & **Client 1** & **Client 2** & **Client 3** \\ \hline Feature dimension before PCA & 4 & 4 & 4 \\ Feature dimension after PCA & 3 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental Results on Wine Quality Dataset. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Accuracy** & **F1 Score** \\ \hline Centralized Training with unpartitioned data & 88.20 & 88.17 \\ Guest party with local data & 73.83 & 73.40 \\ Performance after PCA at all clients & 84.92 & 84.91 \\ Performance after PCA at all clients except C1 & 79.92 & 79.53 \\ \hline \hline \multicolumn{2}{c}{**Overview of Feature Dimensions**} \\  & **Client 1** & **Client 2** & **Client 3** \\ \hline Feature dimension before PCA & 26 & 42 & 38 \\ Feature dimension after PCA & 7 & 7 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental Results on Rice MSC Dataset. In the case of the _Adult Income Dataset_ in Table 6, it is seen that the autoencoder performs well during the compression of local data of other clients compared to the guest client. As the autoencoder becomes quite lossy when encoding the local data of the guest client, it stands to reason that the aggregated model's performance would be improved if the local data of the guest client were not encoded with the autoencoder. A similar trend is noticed in the case of the _Heart Disease Dataset_ as well (Table 7). However, it is only in this case that the autoencoders' training loss is greater than their corresponding testing losses, indicating overfitting. As autoencoders require a large number of samples to be trained, a small number of samples tends to overfit it.