# Semi-Supervised Ridge Regression with Adaptive Graph-Based Label Propagation
## 4 Experiment and Analysis
### Experimental Results and Analysis
In the third experiment, the predicted labels of SSRR-AGLP are compared with the traditional label propagation algorithms to evaluate the performance of SSRR-AGLP. Specifically, the number of the selected label samples for each database is set as the same as in the first experiment, and the accuracy of the predicted labels by SSRR-AGLP and LP is listed in Table 6. It can be seen that the performance of SSRR-AGLP is superior to that of LP due to the cooperation of adaptive graph leaning and label propagation in it. In other words, compared with the traditional LP which predicts the labels by constructing a graph in advance, adaptive graph learning in SSRR-AGLP can improve the predicted performance of SSRR-AGLP. Besides, according to the predicted labels of traditional LP algorithm, we utilize the ridge regression (RR) algorithm (denoted as LP + RR) for classification and the results for the five databases are listed Table 7. From Table 7, we can see that the performance of LP + RR is better than that of the RR algorithm, but still worse than that of SSRR-AGLP. This indicates that combining both of the LP and RR algorithms into a uniform framework can provide a benefit for classification tasks. Finally, Figure 4 displays the convergence curves of SSRR-AGLP for five facial image databases. In this figure, the x-axis and y-axis denote the number of iterations and the value of the objective function, respectively. We can see that the proposed iterative updating algorithm converges very fast (usually within 20 iterations). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Database** & **LP** & **SSRR-AGLP** \\ \hline Yale & 89.56 \(\pm\) 5.89 & 97.33 \(\pm\) 2.30 \\ ORL & 88.13 \(\pm\) 2.38 & 90.25 \(\pm\) 3.81 \\ Extended YaleB & 77.39 \(\pm\) 8.30 & 95.55 \(\pm\) 5.15 \\ AR & 78.00 \(\pm\) 9.27 & 97.63 \(\pm\) 3.40 \\ CMU PIE & 88.55 \(\pm\) 9.75 & 91.74 \(\pm\) 6.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The label propagation accuracies (%) and standard deviations (%) of the proposed SSRR-AGLP and traditional LP for five facial image databases. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Database** & **RR** & **LP + RR** & **SSRR-AGLP** \\ \hline Yale & 89.07 \(\pm\) 7.82 & 89.20 \(\pm\) 6.89 & 91.60 \(\pm\) 5.83 \\ ORL & 85.75 \(\pm\) 2.30 & 87.55 \(\pm\) 2.34 & 90.25 \(\pm\) 3.75 \\ Extended YaleB & 88.33 \(\pm\) 9.23 & 91.89 \(\pm\) 7.89 & 94.40 \(\pm\) 6.87 \\ AR & 86.77 \(\pm\) 4.72 & 88.44 \(\pm\) 4.07 & 92.73 \(\pm\) 5.06 \\ CMU PIE & 92.44 \(\pm\) 5.03 & 92.95 \(\pm\) 5.18 & 95.88 \(\pm\) 3.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The average classification accuracies (%) and standard deviations (%) of RR, RR based on the predicted labels of traditional LP and SSRR-AGLP for five facial image databases. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Database** & \multicolumn{3}{c}{**Accuracy (\%)**} \\ \hline Yale & 88.80 \(\pm\) 5.56(2/4) & 91.60 \(\pm\) 5.83(3/3) & 95.20 \(\pm\) 4.88(4/2) \\ ORL & 83.25\(\pm\)2.92(2/3) & 90.25 \(\pm\) 3.75(3/2) & 92.35 \(\pm\) 2.16(4/1) \\ Extended YaleB & 92.07 \(\pm\) 4.20(12/20) & 92.38 \(\pm\) 4.23(16/16) & 94.40 \(\pm\) 6.87(18/14) \\ AR & 90.37 \(\pm\) 8.07(3/4) & 92.73 \(\pm\) 5.06(4/3) & 94.27 \(\pm\) 4.93(5/2) \\ CMU PIE & 85.78 \(\pm\) 7.95(4/8) & 95.88 \(\pm\) 3.55(6/6) & 93.82 \(\pm\) 4.58(8/4) \\ \hline \hline \end{tabular} Note that the two numbers in parentheses are the corresponding the quantities of labeled samples and unlabeled samples in training set.  
\end{table} 
Table 5: The average results of the proposed SSRR-AGLP with different numbers of labeled samples for five facial image databases.