# Semi-Supervised Ridge Regression with Adaptive Graph-Based Label Propagation
## 4 Experiment and Analysis
### Experimental Results and Analysis  
To fairly compare the performances of our approach and other algorithms, the average accuracy rates and standard deviations over 10 random training sample selection procedures of different algorithms are listed in Table 4. From Table 4, we can get the following observations: (1) KNN is sensitive to noise; its accuracy rate is lower than other methods. (2) The performance of RR is better than that of LSR, which indicates that RR can avoid the over-fitting problem effectively. (3) The accuracy rate of ICS_DLSR is higher than that of LSR and RR. This is because that the inter-class sparsity regularization term can improve discriminative ability of transformation matrix adequately. (4) By exploring the locality structure of the learned dictionary, the performance of LCLE_DL is better than that of RR and ICS_DLSR in most cases, which implies that the locality of data can improve the performance effectively. (5) The performance of the proposed SSRR-AGLP is consistently superior to other algorithms for five face image databases. It is because SSRR-AGLP not only employs both the labeled and unlabeled data to train the classifiers, but also takes advantage of the locality and sparsity of data for adaptive graph construction. In the second experiment, to verify the performances of the proposed SSRR-AGLP under different numbers of labeled samples, we select 50% samples as the training set for each facial database, i which different numbers of samples are selected as labeled samples for each training set. Table 5 lists the best average accuracy rates obtained by SSRR-AGLP with varied numbers of labeled samples. We can see that with the increase in labeled samples, the performance of the proposed SSRR-AGLP is improved gradually. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Yale** & **ORL** & **Extended YaleB** & **AR** & **CMU PIE** \\ \hline KNN & 84.93 \(\pm\) 7.20 & 73.05 \(\pm\) 2.68 & 75.42 \(\pm\) 6.98 & 69.04 \(\pm\) 6.93 & 90.07 \(\pm\) 6.51 \\ LSR & 88.27 \(\pm\) 7.97 & 84.75 \(\pm\) 1.60 & 87.51 \(\pm\) 7.22 & 82.66 \(\pm\) 6.70 & 91.57 \(\pm\) 5.41 \\ RR & 89.07 \(\pm\) 7.82 & 85.75 \(\pm\) 2.30 & 88.33 \(\pm\) 9.23 & 86.77 \(\pm\) 4.72 & 92.44 \(\pm\) 5.03 \\ ICS\_DLSR & 90.00 \(\pm\) 2.45 & 87.60 \(\pm\) 1.98 & 92.04 \(\pm\) 0.81 & 90.93 \(\pm\) 1.44 & 92.71 \(\pm\) 0.75 \\ LCLE\_DL & 90.40 \(\pm\) 3.00 & 87.65 \(\pm\) 3.11 & 91.93 \(\pm\) 0.62 & 90.91 \(\pm\) 1.14 & 93.91 \(\pm\) 1.34 \\ SSRR-AGLP & 91.60 \(\pm\) 5.83 & 90.25 \(\pm\) 3.75 & 94.40 \(\pm\) 6.87 & 92.73 \(\pm\) 5.06 & 95.88 \(\pm\) 3.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average accuracy (%) and standard deviation (%) of different methods for different databases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Database** & **Yale** & **ORL** & **Extended YaleB** & **AR** & **CMU PIE** \\ \hline \(\gamma=0.0001\) & 89.61 \(\pm\) 5.20 & 88.73 \(\pm\) 4.68 & 92.08 \(\pm\) 5.69 & 91.00 \(\pm\) 4.39 & 92.96 \(\pm\) 3.57 \\ \(\gamma=0.001\) & 91.27 \(\pm\) 5.79 & 90.00 \(\pm\) 3.16 & 94.22 \(\pm\) 6.72 & 92.66 \(\pm\) 5.45 & 95.51 \(\pm\) 3.41 \\ \(\gamma=0.01\) & 91.60 \(\pm\) 5.83 & 90.25 \(\pm\) 3.75 & 94.40 \(\pm\) 6.87 & 92.73 \(\pm\) 5.06 & 95.88 \(\pm\) 3.55 \\ \(\gamma=0.1\) & 91.00 \(\pm\) 4.80 & 89.95 \(\pm\) 3.18 & 94.24 \(\pm\) 5.18 & 91.93 \(\pm\) 4.86 & 95.37 \(\pm\) 3.87 \\ \(\gamma=1\) & 90.52 \(\pm\) 4.69 & 88.76 \(\pm\) 3.87 & 93.13 \(\pm\) 5.60 & 91.00 \(\pm\) 4.24 & 94.19 \(\pm\) 3.46 \\ \(\gamma=10\) & 89.87 \(\pm\) 5.64 & 87.54 \(\pm\) 3.25 & 92.16 \(\pm\) 5.09 & 90.54 \(\pm\) 3.69 & 93.27 \(\pm\) 3.23 \\ \(\gamma=100\) & 88.76 \(\pm\) 5.78 & 86.90 \(\pm\) 3.63 & 91.40 \(\pm\) 4.28 & 89.79 \(\pm\) 4.50 & 92.35 \(\pm\) 3.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average accuracy (%) and standard deviation (%) of different values of parameter \(\gamma\) for different databases.