## 3 Experiment  
In this section, we conduct experiments on four publicly available face datasets to study the effectiveness of SSCMG. The face datasets used in the experiments are ORL [33], CMU PIE [34], AR [35], and extended YaleB [36]. ORL consists of 40 individuals with 10 images per person. We aligned and resized ORL images into 64 \(\times\) 64 pixels in grey scale, thus each image can be viewed as a point in the 4096-dimensional space. CMU PIE face dataset contains 41,368 face images from 68 individuals. The face images were captured under varying pose, illumination and expression conditions, and we chose a subset (Pose27) of CMU PIE as the second dataset. Pose27 includes 3329 face images from 68 individuals. Before the experiments, we resized the images to 64 \(\times\) 64 pixels and each image is an 8 bit grayscale image. AR face dataset includes over 4000 color face images from 126 people (70 men and 56 women). In the experiments, 2600 images of 100 people (50 men and 50 women) were used. We aligned and resized these images into 42 \(\times\) 30 pixels and then normalized them into 8 bit grayscale, thus each image is a point in the 1260-dimensional space. YaleB consists of 21,888 single light source images of 38 individuals each captured under 576 viewing conditions (9 \(\times\) 64 illumination conditions). We chose a subset that contains 2414 images and resized these images into 32 \(\times\) 32 pixels, with 256 gray level per pixel, so each image is a 1024-dimensional vector. ORL and extended yaleB can be downloaded from the link in reference [37].  
To comparatively study the performance of SSCMG, we take several representative methods as comparing methods, which include GFHF [4], LNP [11], RMGT [7], LGC [5], CGSSL [10]. We regard the classification accuracy on testing samples as the comparative index, and the higher the accuracy, the better the performance. Gaussian kernel used for graph construction can often be improved upon by using the 'local scaling' method [31,38]. We utilize local scaling to adjust the graph defined in Equation (1) and name GFHF on the adjusted graph as LGFHF. The diffuse interfaces model in [31] is proposed for binary classification and it is not so straightforward for multi-class datasets. Since the target of this study is to investigate the effectiveness of mixture graph for semi-supervised classification and the proposed SSCMG is a special case of \(p\)-Laplacian with \(p=2\), we do not compare SSCMG with the diffuse interfaces model and \(p\)-Laplacian with different \(p\) values. In the following experiments, we firstly apply principal component analysis (PCA) [3] to project each facial image into a 100-dimensional vector, and then use different methods to predict the labels of unlabeled images. For convenience, notations used in the experiments are listed in Table 1.  
In the experiments, if without extra specification, \(\alpha\) in LGC [5] is set to 0.01, \(\sigma\) in Equation (1) is set to the average Euclidean distance between \(n\) samples, and \(k\) is fixed as 3 for all the methods that based on a \(k\)NN graph. \(T\) and \(d\) are set to 70 and 40, respectively. Other parameters of these comparing methods are kept the same as reported in the original papers. The sensitivity of these input parameters will be studied later. To reduce random effect, all reported results are the average of 20 independent runs. In each run, the training set and testing set are randomly partitioned.