## 3 Experiment
### Performance on Different Datasets  
In order to study the performance of SSCMG under different number of labeled images per people, we conduct experiments on ORL with \(Ls\) rising from 1 to 5, and on the other three datasets with \(Ls\) increasing from 1 to 10. The corresponding results are revealed in Figure 1. Each class in the four datasets has an equal (or nearly equal) number of samples as other classes, so the classes are balanced. Each dataset has more than 30 classes and the accuracy per class cannot be visualized in Figure 1. Given these reasons, we report the average accuracy for all the classes on each dataset.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Means** \\ \hline \(n\) & Number of labeled and unlabeled samples \\ \(l\) & Number of labeled samples \\ \(C\) & Number of classes \\ \(k\) & Neighborhood size \\ \(T\) & Number of subspaces \\ \(d\) & Dimensionality of random subspace \\ \(Ls\) & Number of labeled samples per class \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations used in the experiments.  
From these four sub-figures, it is easy to observe that SSCMG achieves better performance than these comparing methods on all facial datasets and GFHF almost ranks second among these comparing methods. Although SSCMG, LGFHF and GFHF are based on the same objective function, SSCMG always outperforms the latter two. That is because SSCMG utilizes a mixture graph combined by multiple \(k\)NN graphs defined in the subspaces, whereas the latter two depend on a single \(k\)NN graph constructed in the PCA reduced space. This observation not only justifies the statement that graph determines the performance of GSSC methods, but also supports our motivation to utilize mixture graph for semi-supervised classification. LGFHF is slightly superior to GFHF. This fact indicates local scaling technique can only improve the \(k\)NN graph in a small scale. LGC often loses to other methods. The reason is that LGC utilizes a fully connected graph rather than a \(k\)NN graph, and this fully connected graph is more heavily distorted by noisy features. RMGT and LNP apply different techniques to optimize a \(k\)NN graph, but their accuracies are almost always lower than that of SSCMG. The cause is that optimizing a \(k\)NN graph that distorted by noisy features is rather difficult. CGSSL uses a compact \(l_{2}\) graph and it often outperforms LNP, which is based on a non-compact \(l_{2}\) graph, but CGSSL is always  
Figure 1: The performance of SSCMG on different \(Ls\) values. (**a**) Accuracy _vs._\(Ls\) (ORL); (**b**) Accuracy _vs._\(Ls\) (Pose27); (**c**) Accuracy _vs._\(Ls\) (AR); (**d**) Accuracy _vs._\(Ls\) (YaleB).  
outperformed by SSCMG. These facts suggest that optimizing an \(l_{2}\) graph alone can only improve the performance in a small range, and it may not result in an optimal graph for semi-supervised classification.  
As the number of labeled samples (\(Ls\)) increasing, the accuracy of SSCMG and other methods climbs steadily, for more labeled samples can often help to acquire a more accurate classifier. RMGT asks for a number of labeled samples to learn an optimized graph, but available labeled samples are not sufficient to optimize a good graph for RMGT. From these observations, we can conclude that mixture graphs can be used as a good alternative graph for GSSC methods on high dimensional data.