# Semi-Supervised Classification Based on Low Rank Representation
## 3 Experiments  
### Experiments Setup  
In this section, we conduct experiments on four facial datasets AR [24], ORL [25], PIE [26] and YaleB [27] to validate the effectiveness of our proposed SSC-LRR with several related and representative graph-based semi-supervised classification methods: GFHF [2], LGC [3], LNP [5], CGSSL [9], LRR-GFHF [18], S-RLSC [11] and LRR-MR. LGC and GFHF use \(k\)NN graph, CGSSL and LNP employ \(l_{2}\) graph, S-RLSC uses \(l_{1}\)-graph. LRR-GFHF constructs a graph by utilizing coefficient matrix \(\mathbf{Z}\) in Equation (4), and then applies GFHF on this graph to classify unlabeled samples. LRR-MR uses the same graph as LRR-GFHF and SSC-LRR, but it employs a representative semi-supervised nonlinear classifier- manifold regularization (MR) [28] on the graph to predict the label of unlabeled samples. GFHF, LGC, CGSSL and LRR-GFHF are transductive classifiers that can not directly classify  
Figure 1: Flowchart of Semi-Supervised Classification based on Low-Rank Representation (SSC-LRR) algorithm.  
out-of-sample, which is currently not in the graph. We extend them for out-of-sample situations by setting the label of a new sample as the label of its nearest training sample, and the labels of unlabeled training samples are predicted by the respective transductive classifier in advance. Notably, S-RLSC, LRR-MR and SSC-LRR directly use all the labeled and unlabeled samples to predict the label of a new sample, without predicting the labels of unlabeled training samples in advance.  
AR contains 2600 images of 100 persons. These images are transformed into grayscale and cropped into 42 \(\times\) 30 pixels. Thus, each image can be viewed as a point in the 1260-dimensional space. For each person, we choose 13 images as training set, and set the rest ones as testing set. YaleB contains 2414 images of 38 people, and each image is cropped into 32 \(\times\) 32 pixels, and then transformed into grayscale images. For each person, we choose 20 images per person as training set, the remaining samples as testing set. ORL contains 400 face images of 40 people, and each image is cropped into 32 \(\times\) 32 pixels and transformed into a grayscale image. For each person, we select six images per person as training set, and remaining four images as testing set. PIE includes 41,368 face images of 68 individuals. In the experiment, we select the subset Pose27 (including 3329 images) for experiments and crop these images to 64 \(\times\) 64 pixels. For each person, we select 20 pictures of each person as training set and the rest images as testing set.  
For presentation, we introduce several symbols: \(N\)-the number of training samples, \(Nt\)-the number of testing samples, \(D\)-the dimensionality of samples, \(C\)-the number of classes, \(LU\)-the number of images per person in the training set, \(m\)-the number of labeled images per person in the training set, \(k\)-neighborhood size. In the experiments, unless extra specified, \(\lambda\) is set to 0.01, \(\alpha\) is set to 0.05, \(\beta\) is set to 0.05, \(k\) is set to 5. To reduce random effect, all the experimental results are the average of 20 independent runs. In each run, we randomly select a fixed number of samples from the training set as labeled samples, and the remaining samples of training set are used as unlabeled samples.