# Deep Image Clustering Based on Label Similarity and Maximizing Mutual Information across Views
## 4 Experiments
### Ablation Study  
In this section, to further verify the performance of our model, five additional ablation experiments are performed. The influence of different strategies to construct \(r_{i,j}\). The \(r_{i,j}\) constructed by the high threshold in DCCM and constructed by the K-means in this paper are used to guide the training of the two identical networks on Stl-10 datasets. The results are shown in Table 4. It can be seen that our strategy has enough advantages, indicating that K-means is a better alternative solution than the threshold. Impact of threshold. The clustering performance of STL-10 datasets under different thresholds in Equation (2) is displayed in Figure 3(a). For STL-10, the clustering performance increases gradually as the threshold increases. It indicates that the correct rate of the selected cluster-standard samples is also gradually increasing. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **ACC** & **NMI** & **ARI** \\ \hline OUR & 0.529 & 0.402 & 0.311 \\ DCCM & 0.391 & 0.297 & 0.213 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The influence of different strategies on constructing \(r_{i,j}\). Figure 3: Visualization of the class–level representations for different training stages of the proposed DCSM on the Imagenet10 datasets. (**a**) Initial stage of DCSM, (**b**) Middle stage of DCSM and (**c**) Final stage of DCSM. Figure 2: Confusion matrixes of the cluster results. (**a,b**) represent the clustering results on MNIST and Imagenet10 datasets, respectively. The dimensional impact of \(z\). As shown in Figure 4b, varying the dimension of \(z\) from 10 to 50 does not affect the clustering performance much. However, when the dimension of \(z\) becomes 0, which means that the network only learns class-level representations, the performance drops a lot. The reason is that class-level representation alone is not enough to describe the differences between images belonging to the same cluster. A good clustering model should assign data to clusters to keep inter-group similarity low while maintaining high intra-group similarity. The sensitivity of the model to mutual information. For convenience, the mutual information loss \(L_{MI}\) is divided into two parts: the global-local MI \(L_{ZC}=L_{LMI}+L_{LMIT}\) and the local-local MI \(L_{LMIC}\). To comprehensively examine the effect of global-local and local-local MI on the clustering performance of the model, \(L_{MI}\) was changed to \(L_{ZC}\) and \(L_{LMIC}\), respectively. The experimental results are shown in Table 5. From the results, the two parts of MI have similar performances in improving the clustering performance. It also proves our proposed extended mutual information is reasonable. The impact of each part. In the case of the combination of each part, the clustering performance is shown in Table 6. Due to the lack of \(L_{E}\) loss, the network will have unstable results, so the maximum entropy loss is not removed in this part. It can be found that it is very effective to use cluster-standard samples to correct the network parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**STL-10**} & \multicolumn{3}{c}{**ImageNet-10**} \\ \cline{2-7}  & **NMI** & **ACC** & **ARI** & **NMI** & **ACC** & **ARI** \\ \hline \(L_{DT}\) & 0.402 & 0.529 & 0.311 & 0.501 & 0.638 & 0.469 \\ \(L_{DT}+L_{FT}\) & 0.431 & 0.576 & 0.342 & 0.561 & 0.701 & 0.523 \\ \(L_{DT}+L_{FT}+L_{MI}\) & 0.483 & 0.625 & 0.410 & 0.623 & 0.769 & 0.581 \\ \hline \end{tabular}
\end{table} 
Table 6: The impact of each part. Figure 4: Clustering performance under different thresholds and \(z\). (**a**) Impact of threshold. (**b**) The dimensional impact of \(z\).