# Deep Subspace Clustering with Block Diagonal Constraint
## 3 Experiments
### Experimental Results and Analysis  
We employ three popular metrics to evaluate the clustering performance of all compared algorithms: Accuracy (ACC), Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI). With the block-diagonal representation \(Z\), we calculate the affinity matrix \(A=\frac{|Z|+|Z^{T}|}{2}\). Then, the clustering result is obtained by performing the spectral clustering method on affinity matrix \(A\). The experimental results of different methods on the Extended Yale B, ORL, PIE and COIL20 databases are shown in the Tables 2-5. The bold numbers in the table are the best results, and the short line means that some evaluation metrics of some methods are not shown. From the results in Tables 2-5, the following observations can be found: (1) Overall, DSC-BDC achieves competitive and stable performance compared to most baselines on all databases. Taking the Extended Yale B database as an example, DSC-BDC outperforms the other best method DSC-Net by 0.44%, 0.74% and 0.73% in terms of ACC, NMI and ARI, respectively. (2) Observing the experimental results of SSC and AE+SSC, it can be seen that, in most cases, the latter has higher accuracy, which indicates that deep networks can better extract nonlinear data features to improve the clustering effect. (3) Comparing BDR and DSC-Net, we can see that deep networks have powerful representation learning ability. Compared with the clustering results obtained by the BDR method (no network) with block diagonal structure constraints, DSC-Net does not strictly require the representation matrix structure and also obtained good clustering performance. (4) Our DSC-BDC framework achieves better performance than DSC-Net. The reason might be that a direct block diagonal regularizer is more effective than regularization using indirect structure priors in self-expression. For visually intuition, we show the corresponding derived representation matrix, as a clearer block diagonal structure of the representation matrix results in higher clustering performance. We show the three databases (Extended Yale B, ORL and COIL20) in Figure 2. Clearly, the representation matrix \(Z\) has apparent block diagonal structure. We next explore the advantages of the method using the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **ACC** & **NMI** & **ARI** \\ \hline LRR & 0.7392 \(\pm\) 0.0206 & 0.8808 \(\pm\) 0.0079 & 0.6041 \(\pm\) 0.0239 \\ LSR & 0.7484 \(\pm\) 0.0212 & 0.8812 \(\pm\) 0.0100 & 0.5799 \(\pm\) 0.0404 \\ SSC & 0.7652 \(\pm\) 0.0184 & 0.9060 \(\pm\) 0.0070 & 0.6510 \(\pm\) 0.0285 \\ AE+SSC & 0.7820 \(\pm\) 0.0234 & 0.9191 \(\pm\) 0.0066 & 0.6850 \(\pm\) 0.0204 \\ LR-kernel SC & 0.7520 \(\pm\) 0.0174 & 0.9341 \(\pm\) 0.0043 & 0.7238 \(\pm\) 0.0199 \\ EDSC & 0.8148 \(\pm\) 0.0143 & 0.9073 \(\pm\) 0.0060 & 0.6231 \(\pm\) 0.0641 \\ AE+EDSC & 0.8251 \(\pm\) 0.0184 & 0.9164 \(\pm\) 0.0062 & 0.6433 \(\pm\) 0.0545 \\ BDR & 0.8094 \(\pm\) 0.0200 & 0.9130 \(\pm\) 0.0086 & 0.5980 \(\pm\) 0.0712 \\ DSC-Net & 0.9686 \(\pm\) 0.0072 & 0.9911 \(\pm\) 0.0052 & 0.9620 \(\pm\) 0.0120 \\ ConvSCN-BD & 0.9732 \(\pm\) 0.0203 & 0.9890 \(\pm\) 0.0041 & 0.9723 \(\pm\) 0.0211 \\
**Ours** & **0.9760 \(\pm\) 0.0035** & **0.9960 \(\pm\) 0.0046** & **0.9807 \(\pm\) 0.0031** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Clustering performance of different algorithms on the PIE database.