## 5 Experiments
### Parameter Sensitivity  
In the proposed LPLC-HDL method, there are three key parameters, i.e., \(\lambda\), \(\gamma\) and \(\eta\), which are used to balance the importance of the label-aware constraint, the group regularization and the locality constraint. To analyze the sensitivity of the parameters, we define a candidate set \(\{10^{-5},10^{-4},10^{-3},10^{-2},10^{-1},10^{0},10^{1},10^{2},10^{3},10^{4}, 10^{5}\}\) for them and then perform LPLC-HDL with different combinations of the parameters on the Yale face dataset and the Caltech 101 dataset. By fixing the parameter \(\eta\), the classification accuracy versus \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Acc. (\%)** & **Method** & **Acc. (\%)** \\ \hline Softmax & 87.3 & LC-KSVD (1020) [6] & 93.60 \\ SVM [38] & 90.9 & DL-COPAR (1025) [16] & 91.62 \\ SRC [33] & 93.2 & JBDC (1002) [15] & 93.12 \\ NSC [48] & 90.10 & CLSDDL-LC (1018) [19] & 94.01 \\ CRC [34] & 93.0 & CLSDDL-GC (1018) [19] & 94.47 \\ ProCRC [35] & 94.8 & OverFeat [41] & 86.8 \\ K-SVD (1020) [39] & 92.41 & NAC [49] & 95.3 \\ D-KSVD (1020) [5] & 93.55 & DAS [50] & 80.66 \\ FDDL (1020) [13] & 94.60 & **LPLC-HDL (1018)** & **95.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The classification results (%) on the Oxford 102 Flowers dataset. Figure 5: Example images from the Oxford 102 Flowers dataset. different values of the parameters \(\lambda\) and \(\gamma\) are shown in Figures 5(a) and 6(a). As can be seen in the figures, the best classification result can be obtained when the parameters \(\lambda\) and \(\gamma\) locate in a feasible range. When \(\gamma\) is very small, the effect of the group regularization is limited, leading to weak discrimination of the class-specific dictionary. On the other hand, when \(\gamma\) becomes very large, the classification accuracy drops as the remaining terms in (4) become less important, which decreases the representation ability of the hybrid dictionary. By fixing the parameters \(\lambda\) and \(\gamma\), the classification accuracy versus different values of the parameter \(\eta\) are shown in Figures 5(b) and 6(b). From them we can see that the classification accuracy is insensitive to the parameter \(\eta\) when its value located in a certain range, e.g., \(10^{-5}\leq\eta\leq 10^{-1}\) on the Yale face dataset. It should be noted that the incoherence between the shared and class-specific dictionaries is increased with increasing parameter \(\eta\), which influences the reconstruction of the test data and decreases the classification accuracy. Due to the diversity of the datasets, it is still an open problem to adaptively select the optimal parameters for the different datasets. In the experiments, we use an effective and simple way to find the optimal values for the parameters \(\lambda\), \(\gamma\) and \(\eta\). Based on the previous analysis, we first fix the parameter \(\eta\) to a small value such as 0.01, then search the candidate combination of the parameters \(\lambda\) and \(\beta\) from the coarse set of \(\{10^{-5}\), \(10^{-4}\), \(10^{-3}\), \(10^{-2}\), \(10^{-1}\), \(10^{0}\), \(10^{1}\), \(10^{2}\), \(10^{3}\), \(10^{4}\), \(10^{5}\}\). According to the best coarse combination of them, we can further define a fine candidate set where their optimal values may exist. Then we perform the proposed LPLC-HDL again with different combinations of the parameters \(\lambda\) and \(\beta\) selected from the fine candidate set. This way, we can obtain the optimal values of the parameters for all the experimental datasets: hence, the best classification results are guaranteed. Besides the key parameters \(\lambda\), \(\gamma\) and \(\eta\) in our LPLC-HDL method, there are also the parameters \(\delta\) and \(k\) in the proposed locality constraint. In the experiments, we find that these two parameters have stable values on the experimental datasets.