# Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering
## 6 Experiments
### Results
#### 6.3.1 Clustering Results of Real Application Data Sets  
In this subsection, we assess the clustering performance of the baseline methods and MKSC. For each individual method, we tune its parameters as described in Section 6.2. In Table 11, we present the clustering performance of all methods on the StillDB data set. Compared to the baseline methods, the proposed method achieves the overall best performance across five metrics. Although the proposed algorithm takes second place in the PUR metric, it only lags behind the first-place SCLA by approximately 1%. Specifically, we analyze the evidence of the superiority of the proposed method as follows. The proposed method is compared with three types of algorithms. First, compared with traditional subspace clustering, the proposed method performs better, mainly due to the utilization of the fine-grained neighborhood matrix. The application of this matrix significantly improves the ability of the algorithm to preserve the latent information and handle nonlinear data. At the same time, the introduction of connectivity constraints also enhances the group structure of the affinity matrix. Second, when compared with tensor subspace clustering, the proposed method does not involve flattening or folding operations on the matrix, thus reducing the potential for information loss. Finally, deep subspace clustering algorithms often require a large amount of samples for learning. In this paper, the size of the data sets is relatively small, potentially resulting in the model not being fully utilized. Specifically, the EDESC algorithm, which deviates from the self-expressive framework, is more suitable for large data sets. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & **NSL-** & \multirow{2}{*}{**SSC**} & **SCLA** & **SSRSC** & **S-TLRR** & **R-TLRR** & **TLRSR** & **ETLRR** & **EDESC** & **PSSC** & **MKSC** \\ \hline Alphadigit & 0.4580 & 0.0349 & 0.4900 & 0.3796 & 0.3425 & 0.2184 & 0.3891 & 0.3711 & 0.3655 & 0.3141 & 0.5812 \\ Semeion & 0.6095 & 0.5267 & 0.6918 & 0.7219 & 0.4242 & 0.4242 & 0.4500 & 0.4313 & 0.4751 & 0.5286 & 0.8242 \\ MNIST & 0.5773 & 0.1547 & 0.5801 & 0.5994 & 0.4036 & 0.3329 & 0.4329 & 0.4166 & 0.4393 & 0.4650 & 0.6906 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Clustering ACC on handwritten digit and letter real application data sets. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & **NSL-** & \multirow{2}{*}{**SSC**} & **SCLA** & **SSRSC** & **S-TLRR** & **R-TLRR** & **TLRSR** & **ETLRR** & **EDESC** & **PSSC** & **MKSC** \\ \hline Alphadigit & 0.4950 & 0.0598 & 0.5192 & 0.4038 & 0.3645 & 0.2357 & 0.4114 & 0.3915 & 0.3878 & 0.3440 & 0.5962 \\ Semeion & 0.6585 & 0.5355 & 0.7094 & 0.7219 & 0.4395 & 0.4395 & 0.4570 & 0.4453 & 0.4480 & 0.5480 & 0.8242 \\ MNIST & 0.6326 & 0.1685 & 0.6354 & 0.6271 & 0.4511 & 0.3649 & 0.4881 & 0.4494 & 0.4775 & 0.5125 & 0.7293 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Clustering PUR on handwritten digit and letter real application data sets. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & **NSL-** & \multirow{2}{*}{**SSC**} & **SCLA** & **SSRSC** & **S-TLRR** & **R-TLRR** & **TLRSR** & **ETLRR** & **EDESC** & **PSSC** & **MKSC** \\ \hline Alphadigit & 0.4950 & 0.0598 & 0.5192 & 0.4038 & 0.3645 & 0.2357 & 0.4114 & 0.3915 & 0.3878 & 0.3440 & 0.5962 \\ Semeion & 0.6585 & 0.5355 & 0.7094 & 0.7219 & 0.4395 & 0.4395 & 0.4570 & 0.4453 & 0.4480 & 0.5480 & 0.8242 \\ MNIST & 0.6326 & 0.1685 & 0.6354 & 0.6271 & 0.4511 & 0.3649 & 0.4881 & 0.4494 & 0.4775 & 0.5125 & 0.7293 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Clustering FS on handwritten digit and letter real application data sets.