# Deep Subspace Clustering with Block Diagonal Constraint
## 3 Experiments
### Experimental Results and Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **ACC** & **NMI** & **ARI** \\ \hline LRR & 0.5696 \(\pm\) 0.0104 & 0.5535 \(\pm\) 0.0060 & 0.2164 \(\pm\) 0.0149 \\ LSR & 0.5652 \(\pm\) 0.0100 & 0.5548 \(\pm\) 0.0052 & 0.2175 \(\pm\) 0.0092 \\ SSC & 0.5412 \(\pm\) 0.0103 & 0.5336 \(\pm\) 0.0036 & 0.2456 \(\pm\) 0.0162 \\ AE+SSC & 0.5778 \(\pm\) 0.0400 & 0.5793 \(\pm\) 0.0096 & 0.1751 \(\pm\) 0.0373 \\ LR-kernel SC & 0.8016 \(\pm\) 0.0101 & 0.8461 \(\pm\) 0.0013 & 0.7352 \(\pm\) 0.0108 \\ EDSC & 0.6138 \(\pm\) 0.0196 & 0.5868 \(\pm\) 0.0093 & 0.2722 \(\pm\) 0.0220 \\ AE+EDSC & 0.6061 \(\pm\) 0.0228 & 0.5910 \(\pm\) 0.0163 & 0.2694 \(\pm\) 0.0196 \\ BDR & 0.7253 \(\pm\) 0.0111 & 0.7103 \(\pm\) 0.0030 & 0.4927 \(\pm\) 0.0046 \\ DSC-Net & 0.9548 \(\pm\) 0.0003 & 0.9227 \(\pm\) 0.0004 & 0.8987 \(\pm\) 0.0008 \\ ConvSCN-BD & 0.9559 \(\pm\) 0.0010 & 0.9260 \(\pm\) 0.0008 & 0.9035 \(\pm\) 0.0012 \\
**Ours** & **0.9592 \(\pm\) 0.0008** & **0.9301 \(\pm\) 0.0010** & **0.9060 \(\pm\) 0.0018** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Clustering performance of different algorithms on the Extended Yale B database. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **ACC** & **NMI** & **ARI** \\ \hline LRR & 0.6755 \(\pm\) 0.0186 & 0.7881 \(\pm\) 0.0160 & 0.4305 \(\pm\) 0.0348 \\ LSR & 0.6800 \(\pm\) 0.0260 & 0.7940 \(\pm\) 0.0109 & 0.4288 \(\pm\) 0.0473 \\ SSC & 0.7504 \(\pm\) 0.0141 & 0.8578 \(\pm\) 0.0071 & 0.5988 \(\pm\) 0.0225 \\ AE+SSC & 0.7383 \(\pm\) 0.0215 & 0.8428 \(\pm\) 0.0088 & 0.5915 \(\pm\) 0.0252 \\ LR-kernel SC & 0.7185 \(\pm\) 0.0194 & 0.8540 \(\pm\) 0.0068 & 0.6088 \(\pm\) 0.0200 \\ EDSC & 0.6938 \(\pm\) 0.0255 & 0.8089 \(\pm\) 0.0126 & 0.5043 \(\pm\) 0.0305 \\ AE+EDSC & 0.6974 \(\pm\) 0.0171 & 0.8139 \(\pm\) 0.0109 & 0.5026 \(\pm\) 0.0365 \\ BDR & 0.7204 \(\pm\) 0.0192 & 0.8350 \(\pm\) 0.0117 & 0.4662 \(\pm\) 0.0471 \\ DSC-Net & 0.8463 \(\pm\) 0.0080 & 0.9172 \(\pm\) 0.0021 & 0.7878 \(\pm\) 0.0062 \\ ConvSCN-BD & 0.8360 \(\pm\) 0.0090 & 0.9149 \(\pm\) 0.0059 & 0.7791 \(\pm\) 0.0131 \\
**Ours** & **0.8505 \(\pm\) 0.0079** & **0.9182 \(\pm\) 0.0027** & **0.7932 \(\pm\) 0.0037** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Clustering performance of different algorithms on the ORL database. separation strategy (DSC-BDC) over the method without the separation strategy (ConvSCN-BD). We plot the accuracy of different databases in Figure 3. This implies the effectiveness of the separation strategy. We verify the convergence of DSC-BDC through the experiment of drawing convergence curves. The convergence curves of the four public databases are shown in Figure 4. In each subfigure, we define the horizontal axis to represent the number of iteration steps and the vertical axis to correspond to the value of termination criterion. It can be observed that DSC-BDC algorithm can converge with few iteration steps. Figure 3: The accuracy comparison of the method using the separation strategy (DSC-BDC) and the method without the separation strategy (ConvSCN-BD). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **ACC** & **NMI** & **ARI** \\ \hline LRR & 0.6887 \(\pm\) 0.0190 & 0.7714 \(\pm\) 0.0097 & 0.5873 \(\pm\) 0.0150 \\ LSR & 0.6871 \(\pm\) 0.0142 & 0.7683 \(\pm\) 0.0097 & 0.5927 \(\pm\) 0.0204 \\ SSC & 0.7898 \(\pm\) 0.0292 & 0.8917 \(\pm\) 0.0117 & 0.06546 \(\pm\) 0.0820 \\ AE+SSC & 0.8863 \(\pm\) 0.0113 & 0.9205 \(\pm\) 0.0074 & 0.7979 \(\pm\) 0.0278 \\ LR-kernel SC & 0.6268 \(\pm\) 0.0083 & 0.8056 \(\pm\) 0.0035 & 0.5568 \(\pm\) 0.0154 \\ EDSC & 0.8514 \(\pm\) 0.0000 & - & - \\ AE+EDSC & 0.8521 \(\pm\) 0.0000 & - & - \\ BDR & 0.7549 \(\pm\) 0.0000 & 0.8862 \(\pm\) 0.0000 & 0.6249 \(\pm\) 0.0000 \\ DSC-Net & 0.9004 \(\pm\) 0.0288 & 0.9562 \(\pm\) 0.0095 & 0.8765 \(\pm\) 0.0384 \\ ConvSCN-BD & 0.9160 \(\pm\) 0.0037 & 0.9613 \(\pm\) 0.0002 & **0.9899 \(\pm\) 0.0032** \\
**Ours** & **0.9174 \(\pm\) 0.0010** & **0.9632 \(\pm\) 0.0021** & 0.8944 \(\pm\) 0.0037 \\ \hline \hline \end{tabular}
\end{table}