# RMRRASL: Robust Matrix Factorization with Robust Adaptive Structure Learning for Feature Selection
## 5 Experiments and Analysis
### Analysis of Experimental Results  
#### 5.5.1 Classification Performance Analysis  
In the first experiment, we tested the influence of parameter values on the classification performance of the proposed method. First, we analyzed the impact of each balance parameter (i.e., \(\alpha\) and \(\beta\)) on the accuracy of the RMFRASL method. From the experimental results shown in Figure 4, we can observe that (1) when the value of parameters is set to 0, the performance of the proposed RMFRASL method is relatively low. Thus, adding these two terms is necessary for feature selection. (2) With the parameter value increasing, the performance of the method also improves, which indicates that introducing the two terms can enhance the discriminatory capability of the selected features. (3) When the performance of the proposed method reaches the optimal value, it decreases or remains stable as the value of the parameter increases. This phenomenon may be due to the parameters being set as larger values such that the importance of the second and third terms of the objective function is overemphasized, while the first term is neglected. As a result, the proposed method is unable to extract the discriminatory features. Then, we evaluated the impact of the number of iterations on the performance of the proposed  
In the second experiment, we compared the performance of different feature selection methods. The classification accuracies of each unsupervised feature selection method on the five databases are given in Table 7. From the experimental results, we can find that, due to the LSFS computing the feature scores without considering the correlation of the selected feature, its performance was the worst. The RNEFS considers the feature self-representation capability; hence, its performance was better than LSFS. The performance of USFS was superior to RNEFS and LSFS since it incorporates soft label learning and constructs the regression relationships between the soft label matrix and features to guides feature selection. CNAFS and NNSAFS combine the geometric structure of the data or features and can select more discriminatory features to obtain slightly higher classification accuracy than RNEFS and USFS. Since RSR and SPNFSR exploit the feature self-representation capability and define the reconstruction error with \(L_{21}\)-norm to significantly improve robustness to noise, their performances are better than other compared methods. However, SPNFSR outperforms RSR due to it considering the geometric structure of features. By fully considering the feature self-representation, geometric structure, adaptive graph learning, and robustness together, our proposed RMFRASL achieved the best results among all compared methods. The classification accuracy rate curves of different feature selection methods with different numbers of selected features are shown in Figure 6. First, with the increase in the number of selected features, the classification accuracy rates of all methods improved. Then, the classification accuracy rates of most methods began to stabilize after achieving their best performances. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Databases** & **Accuracy Rate** & **Parameter \(\{\alpha,\beta\}\)** & **Dimension \(r\)** \\ \hline AR & \(69.77\pm 0.79\) & \(\{0.1,0.01\}\) & 260 \\ CMU PIE & \(89.17\pm 0.80\) & \(\{0.1,\,1\}\) & 360 \\ Extended YaleB & \(64.98\pm 0.75\) & \(\{0.1,\,0.01\}\) & 360 \\ ORL & \(93.92\pm 1.56\) & \(\{10000,\,0.01\}\) & 460 \\ COIL20 & \(95.93\pm 1.17\) & \(\{1000,\,0.1\}\) & 160 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The optimal combination of parameters and dimension on the classification task.