## 6 Parameters Initialization
Consequently, this reduced the training time by a factor of 65 on average. We visually show the comparative training times in Figure 7 \begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **Accuracy (\%)** & **Test Time (ms)** \\ \hline LC-KSVD [8] & 89.73 \(\pm\) 0.59 & 0.60 \\ D-KSVD [23] & 89.77 \(\pm\) 0.57 & 0.61 \\ SRC [9] & 89.71 \(\pm\) **0.45** & 50.19 \\ FDDL [12] & 90.01 \(\pm\) 0.69 & 42.82 \\ ADDL [19] & 80.88 \(\pm\) 1.07 & — \\ LC-PDL [20] & 80.90 \(\pm\) 1.06 & — \\ SLatDPL [21] & 91.90 \(\pm\) 0.72 & — \\ DBDL [25] & 91.09 \(\pm\) 0.59 & 1.07 \\ \hline JBDC [24] & 92.32 \(\pm\) 0.64 & **0.16** \\ Training Time (min) & 38.40 & \\ \hline Our Method & **93.25**\(\pm\) 0.72 & **0.16** \\ Training Time (min) & **36.60** & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Face recognition for Extended YaleB database [54]. Results are based on 10 experiments. for JBDC and our method. Although we do not show the classification time per sample, we observed that it behaves the same way as in previous experiments. We tested that sparsity in the range of 40 to 70 produces acceptable results. However, lowering the value from 40 degrades the classification accuracy, and increasing the value beyond 70 does not increase the accuracy. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Training Samples** & **5** & **10** & **15** & **20** & **25** & **30** \\  & & \multicolumn{4}{c}{**Accuracy (\%)**} & \\ \hline SRC [9] & 76.23 & 79.99 & 81.27 & 83.48 & 84.00 & 84.51 \\ FDDL [12] & 78.31 & 81.37 & 83.37 & 84.76 & 85.66 & 85.98 \\ D-KSVD [23] & 79.69 & 83.11 & 84.99 & 86.01 & 86.80 & 87.72 \\ LC-KSVD [8] & 79.74 & 83.13 & 85.20 & 85.98 & 86.77 & 87.81 \\ DBDL [25] & 80.11 & 84.03 & 85.99 & 86.71 & 87.97 & 88.81 \\ \hline JBDC [24] & 82.92 & 89.60 & 91.65 & 92.81 & 93.98 & 93.82 \\ Training Time (min) & 44.13 & 125.53 & 222.57 & 362.38 & 512 & 622.44 \\ \hline Our Method & **83.80** & **90.25** & **92.09** & **93.16** & **94.66** & **94.81** \\ Training Time (min) & **14.28** & **43.02** & **73.67** & **117.61** & **166.96** & **237.05** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Object classification for the Caltech-101 database [55] with six stages consisting of randomly selected 5, 10, 15, 20, 25, and 30 data points from each class for training sets, respectively. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Methods/Examples Per Class**} & \multicolumn{2}{c}{**7**} & \multicolumn{2}{c}{**20**} \\ \cline{2-5}  & **Accuracy (\%)** & **Test Time (ms)** & **Accuracy (\%)** \\ \hline SRC [9] & 84.60 \(\pm\) 1.37 & 59.91 & 96.65 \(\pm\) 1.37 \\ LC-KSVD [8] & 85.37 \(\pm\) 1.34 & 0.91 & 96.13 \(\pm\) 0.64 \\ D-KSVD [23] & 85.41 \(\pm\) 1.49 & 0.92 & 96.02 \(\pm\) 0.58 \\ FDDL [12] & 85.97 \(\pm\) 1.23 & 50.03 & 96.22 \(\pm\) 1.03 \\ ADDL [19] & - & - & 96.37 \(\pm\) 0.78 \\ LC-PDL [20] & - & - & - & 96.38 \(\pm\) 0.79 \\ SLatDPL [21] & - & - & 98.13 \(\pm\) 0.53 \\ DBDL [25] & 86.15 \(\pm\) 1.19 & 1.20 & 97.47 \(\pm\) 0.99 \\ \hline JBDC [24] & 88.90 \(\pm\) 0.75 & 0.19 & 96.70 \(\pm\) 0.83 \\ Training Time (min) & 51.83 & & & \\ \hline Our Method & **89.27 \(\pm\) 0.61** & **0.18** & **98.20 \(\pm\) 0.31** \\ Training Time (min) & **47.26** & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Face recognition for AR database [38]. The results are based on two sets of 10 experiments each. In each experiment of the two sets of experiments, 7 and 20 examples were randomly selected for training sets, and the rest of the examples were used as test sets, respectively

Figure 7: Comparison of the computational cost of JBDC and our approach for the Caltech-101 database

### Scene Categorization

We performed two sets of 10 experiments, each consisting of 50 samples and 20 samples per category, respectively, for training sets and the rest for test sets.