# Distributed Online Multi-Label Learning with Privacy Protection in Internet of Things
## 7 Results
### Performance Analysis in a Large-Scale Distributed Environment
#### 7.2.1 Hamming Loss Evaluation  
Tables 5 and 6 show the Hamming loss of the DOML algorithm with different network connectivity for a network of 20 nodes and 100 nodes, respectively. This result is also summarized in Figure 5 for comparison. At the same time, we evaluate the performance of the traditional OML algorithm with the same number of datasets as a single node in the DOML algorithm as a reference.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Macro F1 Score**} & \multicolumn{3}{c}{**Micro F1 Score**} \\ \cline{2-7}  & **KNN** & **OML** & **DOML** & **KNN** & **OML** & **DOML** \\ \hline CAL500 & 0.0563 & 0.0490 & \(\mathbf{0.0614\pm 0.0035}\) & **0.3425** & 0.3370 & 0.3364 \(\pm\) 0.0157 \\ Corel5k & 0.0118 & 0.0000 & \(\mathbf{0.0174\pm 0.0066}\) & 0.0365 & 0.0000 & \(\mathbf{0.1524\pm 0.0246}\) \\ Emotions & **0.3853** & 0.2566 & \(0.3823\pm 0.0466\) & **0.4573** & 0.3722 & \(\mathbf{0.4415\pm 0.0661}\) \\ Enron & 0.0858 & 0.0173 & \(\mathbf{0.1054\pm 0.0082}\) & 0.4540 & 0.2693 & \(\mathbf{0.5483\pm 0.0161}\) \\ Medical & **0.1659** & 0.1111 & \(0.1599\pm 0.1037\) & 0.3217 & 0.1102 & \(\mathbf{0.3304\pm 0.2344}\) \\ scene & **0.6916** & 0.0029 & \(0.2028\pm 0.0857\) & **0.6986** & 0.0031 & 0.3297 \(\pm\) 0.0973 \\ yeast & **0.4840** & 0.4144 & \(0.4656\pm 0.0177\) & **0.8109** & 0.8034 & \(0.7861\pm 0.0050\) \\ \hline \hline \end{tabular}  
* The numbers in bold highlight the best performing of the three algorithms.  
\end{table}
Table 4: F1 Score of different algorithms with full benchmark datasets.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**DOML**} & \multicolumn{2}{c}{**OML**} \\ \cline{2-5}  & **25\%** & **50\%** & **100\%** & **-** \\ \hline CAL500 & 0.1511 \(\pm\) 0.0098 & \(\mathbf{0.1486\pm 0.0112}\) & 0.1489 \(\pm\) 0.0112 & 0.1499 \\ Corel5k & 0.0130 \(\pm\) 0.0015 & 0.0126 \(\pm\) 0.0015 & 0.0125 \(\pm\) 0.0015 & \(\mathbf{0.0110}\) \\ Emotions & 0.3556 \(\pm\) 0.0545 & \(\mathbf{0.3531\pm 0.0479}\) & 0.3886 \(\pm\) 0.0792 & 0.3564 \\ Enron & 0.0556 \(\pm\) 0.0034 & 0.0595 \(\pm\) 0.0035 & \(\mathbf{0.0539\pm 0.0032}\) & 0.0639 \\ Medical & 0.0306 \(\pm\) 0.0014 & 0.0311 \(\pm\) 0.0017 & 0.0314 \(\pm\) 0.0019 & \(\mathbf{0.0300}\) \\ scene & 0.2663 \(\pm\) 0.0259 & 0.2651 \(\pm\) 0.0272 & \(\mathbf{0.2647\pm 0.0275}\) & 0.2919 \\ yeast & 0.1687 \(\pm\) 0.0344 & 0.1609 \(\pm\) 0.0265 & 0.1605 \(\pm\) 0.0287 & \(\mathbf{0.1332}\) \\ \hline \hline \end{tabular}  
* The numbers in bold highlight the best performing of the three algorithms.  
\end{table}
Table 5: Hamming loss of DOML in a 20-node network with different connectivity and OML with the same amount of instances as each node.  
First, we can observe that the DOML algorithm obtains nearly the same Hamming loss results for various datasets with different network connectivity. Therefore, we can conclude that the Hamming loss of the DOML algorithm is not affected by the connectivity of the training network. However, as the size of the network increases, the number of training nodes increases, and the Hamming loss of the DOML algorithm increases. This means that the DOML algorithm loses accuracy when more nodes are involved in the training network. As the network size increases, the number of data assigned to each node is reduced, thus making each node have more difficulty with obtaining accurate results.