## 3 Results
### Classification Results
For mnist and Isolet datasets, when compared to the second-ranked algorithm, this algorithm has demonstrated an increase in clustering accuracy by 5.76% and 4.71%, respectively. In addition, the findings indicate that the DGA outperforms the baseline approach across all nine datasets, thereby affirming the indispensability of feature selection. The NMI results for the mnist dataset, while not exceptional, are moderate and surpass the baseline. This indicates that feature selection enhances its performance. Among the datasets analyzed, the performance of the SCFS algorithm was found to be comparable to that of the DGA in nine datasets. However, it was observed that the results obtained from SCFS were slightly inferior to those obtained from DGA. The reasons can be outlined as follows: (1) both approaches take into account the preservation of data structures, and (2) SCFS solely focuses on the manifold structure of the data; it disregards the manifold structure of the features. The ACC and NMI of the clustering outcomes when varying numbers of features are selected are presented in Figures 4 and 5, respectively. In accordance with Figure 4, it is evident that no matter how many features are selected, the performance of the DGA on datasets such as ORL (32*32), Isolet, Coll20, colon, Yale (32*32), and mnist is consistently \begin{table}
\begin{tabular}{c c c} \hline  & **Friedman Test (\(\tau_{\text{F}}\)) (1.9006)** & **Nemenyi Post Hoc Test (CD)** \\ \hline ACC & \(\tau_{\text{F}}\) = 8.192771084337322 & CD = 2.742416965892462 \\ NMI & \(\tau_{\text{F}}\) = 5.23896388179497 & CD = 2.742416965892462 \\ \hline \end{tabular}
\end{table} 
Table 4: [PERSON] and [PERSON] post hoc test (\(\alpha\) = 0.1, number of algorithms = 7, number of datasets = 9). Figure 3: [PERSON] post hoc test (Critical Difference diagram). \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**ACC**} & \multicolumn{2}{c}{**NMI**} \\ \hline  & **NLRL-LE** & **LLSRFS** & **DGA** & **NLRL-LE** & **LLSRFS** & **DGA** \\ Isolet & 0.7071 \(\pm\) 0.0201 & 0.6517 \(\pm\) 0.0067 & **0.7472 \(\pm\) 0.0114** & 0.7869 \(\pm\) 0.0104 & 0.7848 \(\pm\) 0.0052 & **0.812 \(\pm\) 0.004** \\ mnist & 0.5765 \(\pm\) 0.0142 & - & **0.6172 \(\pm\) 0.0042** & 0.4986 \(\pm\) 0.006 & - & **0.5004 \(\pm\) 0.0039** \\ Yale (32*32) & - & 0.4856 \(\pm\) 0.0040 & **0.5054 \(\pm\) 0.0124** & - & **0.5652 \(\pm\) 0.0062** & 0.5442 \(\pm\) 0.0061 \\ ORL (32*32) & - & 0.6113 \(\pm\) 0.0073 & **0.632 \(\pm\) 0.0154** & - & **0.7930 \(\pm\) 0.0056** & 0.7920 \(\pm\) 0.0071 \\ COIL20 & 0.6797 \(\pm\) 0.0406 & 0.7357 \(\pm\) 0.0053 & **0.743 \(\pm\) 0.021** & 0.7742 \(\pm\) 0.0180 & **0.8335 \(\pm\) 0.0024** & 0.8085 \(\pm\) 0.0036 \\ WarpER10P & - & - & 0.3785 \(\pm\) 0.0049 & - & - & 0.3645 \(\pm\) 0.0190 \\ WarpER10P & **0.5357 \(\pm\) 0.0256** & - & 0.4238 \(\pm\) 0.0158 & **0.5666 \(\pm\) 0.0235** & - & 0.3994 \(\pm\) 0.0173 \\ colon & - & - & 0.608 \(\pm\) 0.004 & - & - & 0.100 \(\pm\) 0.029 \\ TOX-171 & **0.5465 \(\pm\) 0.0150** & 0.5268 \(\pm\) 0.0174 & 0.468 \(\pm\) 0.062 & 0.2295 \(\pm\) 0.0157 & **0.3574 \(\pm\) 0.0076** & 0.206 \(\pm\) 0.027 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of accuracy (ACC) and normalized mutual information (NMI) between the two novel methods across all datasets presented as mean \(\pm\) standard deviation. (The best outcomes are indicated by bold). superior to that of other algorithms. On the remaining three datasets, the performance of DGA was slightly inferior compared to the other methods. Similarly, Figure 5 demonstrates that. In the majority of cases, the DGA algorithm outperforms other algorithms on datasets such as ORL (32*32), Isolet, Coll20, colon, and Yale (32*32). On the remaining four datasets, the DGA also achieved the second-best performance, falling slightly short of the optimal solution. Therefore, it can be inferred that DGA possesses certain advantages in comparison to alternative methods.