# Deep Multi-View Clustering Based on Reconstructed Self-Expressive Matrix
## 4 Experiments
### Experimental Results
#### 4.5.3 Analysis on Time Complexity  
To further demonstrate the effectiveness and efficiency of our approach, we show the clustering accuracy and running time of our proposed method with various training samples \(N\) in Figure 4. We highlight the best results in red and the second best results in blue. We also compare the running time with the DMSC-UDL approach and all running \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Training Number \(N\)**} & \multicolumn{3}{c}{**YTF**} \\ \cline{3-5}  & & **ACC (\%)** & **NMI (\%)** & **ARI (\%)** \\ \hline DMSC-UDL & ALL & 68.25 & 83.14 & - \\ \hline \multirow{4}{*}{DCRSM} & 200 & 61.61 & 77.54 & 56.54 \\  & 500 & 60.28 & 77.76 & 60.19 \\ \cline{1-1}  & 1000 & 63.67 & 82.91 & 65.91 \\ \cline{1-1}  & 2000 & 67.24 & 83.33 & 66.93 \\ \cline{1-1}  & 5000 & 68.28 & 84.32 & 66.04 \\ \cline{1-1}  & 10000 & 70.69 & 86.55 & 70.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The clustering performance of YTF dataset with different training number. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Training Number \(N\)**} & \multicolumn{3}{c}{**COIL-20**} \\ \cline{3-5}  & & **ACC (\%)** & **NMI (\%)** & **ARI (\%)** \\ \hline DMSC-UDL & ALL & 79.24 & 89.00 & - \\ \hline \multirow{4}{*}{DCRSM} & 200 & 61.04 & 73.05 & 51.45 \\  & 500 & 68.20 & 80.72 & 62.62 \\ \cline{1-1}  & 1000 & 75.42 & 86.01 & 71.02 \\ \cline{1-1}  & 1440 & 81.18 & 89.15 & 77.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The clustering performance of COIL-20 dataset with different training number. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Training Number \(N\)**} & \multicolumn{3}{c}{**COIL-100**} \\ \cline{3-5}  & & **ACC (\%)** & **NMI (\%)** & **ARI (\%)** \\ \hline \multirow{4}{*}{DCRSM} & 200 & 61.61 & 77.54 & 56.54 \\  & 500 & 60.28 & 77.76 & 60.19 \\ \cline{1-1}  & 1000 & 63.67 & 82.91 & 65.91 \\ \cline{1-1}  & 2000 & 67.24 & 83.33 & 66.93 \\ \cline{1-1}  & 5000 & 68.28 & 84.32 & 66.04 \\ \cline{1-1}  & 1000 & 70.69 & 86.55 & 70.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The clustering performance of COIL-100 dataset with different training number. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Training Number \(N\)**} & \multicolumn{3}{c}{**Fashion-MNIST**} \\ \cline{3-5}  & & **ACC (\%)** & **NMI (\%)** & **ARI (\%)** \\ \hline DMSC-UDL & ALL & 65.45 & 68.34 & - \\ \hline \multirow{4}{*}{DCRSM} & 200 & 67.05 & 59.90 & 47.28 \\  & 500 & 68.50 & 64.88 & 52.22 \\ \cline{1-1}  & 1000 & 65.30 & 64.23 & 48.21 \\ \cline{1-1}  & 1500 & 66.35 & 64.26 & 49.21 \\ \cline{1-1}  & 2000 & 69.65 & 66.85 & 53.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The clustering performance of Fashion-MNIST dataset with different training number. time is calculated after pre-training. Compared with DMSC-UDL, our method effectively balances training time and clustering accuracy, delivering promising performance within a reasonable timeframe on all experimental datasets. For Fashion-MNIST, COIL-100 and YTF datasets, our approach can achieve comparable accuracy levels while reducing the running time by around 50%. For the COIL-20 dataset, we can obtain superior accuracy of 70.69% within a shorter timeframe. The results unequivocally display the superior performance and computational efficiency of our approach. For the time complexity, assuming that the resolution size of our input image is \(M\times M\) (all the images in the experimental dataset are square), the number of training samples is N and the training batch size is \(B\), then the size of input tensor is \(B\times 1\times m\times m\). We denote the numbers of channels of encoder as \([C_{1},C_{2},C_{3}]\). The size of output tensor after encoder can be represented as \(B\times C_{3}\times\frac{M}{4}\times\frac{M}{4}\).