# Semi-Supervised Classification Based on Low Rank Representation
## 3 Experiments
### Accuracy with Respect to Different Number of Labeled Samples  
In order to study the influence of the number of labeled samples on the accuracy of semi-supervised classification, we conduct experiments on AR, PIE, and YaleB by varying \(m\) from 1 to 10, on ORL by varying \(m\) from 1 to 5. The recorded results are plotted in Figure 2.  
From Figure 2, we can observe that the accuracy of all methods increases with the number of labeled samples \(m\) rising and SSC-LRR always achieves better performance than other comparing methods. GFHF and LGC use a single \(k\)NN graph, while LGC outperforms GFHF. That is because LGC classifies samples based on the consistency assumption. This fact indicates that the consistency assumption can improve the performance of the algorithm in a small range. GFHF and LRR-GFHF use the same classifier, while the accuracy of GFHF is much lower than that of LRR-GFHF. This fact shows that LRR-based graph can better reflect the relationship between samples than \(k\)NN graph. The accuracy of LGC is lower than that of CGSSL and LNP, which utilize an optimized \(l_{2}\)-graph by different techniques. The cause is that LGC uses a single \(k\)NN graph, which can be easily destroyed by noisy featured. In contrast, \(l_{2}\)-graph is more effective than \(k\)NN graph in capturing the similarity relationship between samples. These observations also corroborate that graph determines the performance of GSSC methods.  
S-RLSC uses a single \(l_{1}\) graph, and achieves better performance than CGSSL and LNP on AR, PIE and YaleB. This fact coincides with previous study that \(l_{1}\)-graph is generally more effective than \(l_{2}\) graph based semi-supervised classification methods [12]. However, the accuracy of S-RLSC is lower than that of LNP on ORL, since ORL has a relative small number of training samples and \(l_{1}\)-graph asks for a large number of basic samples to optimize the sparse representation coefficients.  
Compared with GFHF, LGC, LNP and CGSSL, both the \(l_{1}\)-graph and LRR based graph demonstrate better ability to capture the relationship between high-dimensional samples. We want to remark that SSC-LRR achieves higher accuracy than S-RLSC, although both of them are inductive classifiers. The reason is that LRR graph has better capacity in exploiting the global data structure of samples than \(l_{1}\) graph. The performance margin between S-RLSC and SSC-LRR on AR is more obvious than that on other facial databases, since there are more noises in the images of AR than that of other datasets. This fact shows SSC-LRR is more robust to noise than \(l_{1}\) and \(l_{2}\) graphs. LRR-GFHF, LRR-MR and SSC-LRR employ LRR to construct a graph for semi-supervised classification, SSC-LRR and LRR-MR show improved accuracy than LRR-GFHF. This is principally because LRR-GFHF is extended to an inductive classifier by transferring the labels of labeled samples and pseudo labels of unlabeled samples to a new sample \(\mathbf{x}\), but the pseudo labels of unlabeled samples in the training set are not correctly predicted. In contrast, SSC-LRR does not predict the labels of unlabeled samples in the training set, it directly exploits \(\mathbf{W}\) and \(\mathbf{b}\) in Equation (6) to predict the label of \(\mathbf{x}\). LRR-MR is a non-linear inductive classifier, it often gets higher accuracy than other comparing methods, except SSC-LRR, although these adopted image datasets are not explicitly linear classifiable. This comparison shows that both linear classifiers and non-linear classifiers can achieve good performance by exploiting a LRR-based graph. These results support our motivation to use LRR for inductive semi-supervised classification.