## 6 Parameters Initialization
We report the results of two sets of 10 experiments each in Table 5. Our approach increases the accuracy by 0.7% in the experiment with 50 samples per class and increases it by 0.3% in the experiment with 20 samples per class when compared with the best accuracy approaches. Although our approach beats LatDPL with a lesser percentage of increase in accuracy, while comparing with the nearest approaches (Bayesian approaches), i.e., DBDL and JBDC, the increase in accuracy is more than 1%. This gain in accuracy is attributed to our idea of learning the same representations for the training data and the corresponding labels over the dictionary and the dictionary classifier, respectively, in the Bayesian setting. Our approach truly exploits the sparse representation and the reconstruction power of a dictionary and tailors a linear classifier to behave like a dictionary classifier. We observed that the learned dictionaries and the dictionary classifiers sizes are 300 and 740 atoms in two experiments for both approaches, i.e., JBDC (the nearest one) and ours, respectively. Despite the same size of the dictionary and the dictionary classifier in both these approaches for 50 samples per class experiment, our approach's test time of 0.66 ms is significantly less than that of JBDC. This clearly shows the efficiency of the learned dictionary of our approach during computing sparse representations of test samples. These representations are ultimately mapped to the corresponding labels as the reconstructions computed by the dictionary classifier. Likewise, the dictionary also performs efficiently in terms of standard deviation, training time, and classification time per test sample. We did not report the test times for 20 samples per class experiments, as the test times follow the trend of the dictionary size, like in the other experiments. ### Action Recognition

Our experiment consists of five fivefold group-wise cross-validations with different seed values for each cross-validation. The model was trained and tested on 25 partitions, and the mean recognition rates and the standard deviation values are reported in Table 6. We reported the results of JBDC and our model. The proposed approach outperformed the other approach in terms of recognition accuracy, standard deviation, training time, and test time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods/Examples** & \multicolumn{2}{c}{**50**} & \multicolumn{1}{c}{**20**} \\ \cline{2-4}
**Per Class** & **Accuracy (\%)** & **Test Time (ms)** & **Accuracy (\%)** \\ \hline SRC [9] & 95.41 \(\pm\) 0.13 & 78.33 & \\ LC-KSVD [8] & 95.37 \(\pm\) 0.28 & 0.59 & 93.93 \(\pm\) 0.45 \\ D-KSVD [23] & 95.12 \(\pm\) 0.18 & **0.58** & 93.76 \(\pm\) 0.48 \\ FDDL [12] & 94.08 \(\pm\) 0.43 & 57.99 & — \\ ADDL [19] & - & - & 93.45 \(\pm\) 0.44 \\ LC-PDL [20] & - & - & 93.40 \(\pm\) 0.45 \\ SLatDPL [21] & - & - & 94.63 \(\pm\) 0.59 \\ DBDL [25] & 96.98 \(\pm\) 0.28 & 0.71 & - \\ \hline JBDC [24] & 97.45 \(\pm\) 0.28 & 1.33 & 93.73 \(\pm\) 0.41 \\ Training Time (min) & 170 & & 37.22 \\ \hline Our Method & **98.10 \(\pm\) 0.08** & 0.66 & **94.90 \(\pm\) 0.54** \\ Training Time (min) & **160** & & **30.11** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Scene categorization for the Fifteen Scene Category database [57]. The results are based on two sets of 10 experiments each. In each experiment of the two sets of experiments, 20 and 50 examples were randomly selected for training sets, and the rest of the examples were used as test sets, respectively. ## 10 Statistical Analysis

In conjunction with the performance evaluations based on classification accuracies, standard deviations, test times, and training times presented in this paper, here, we present a statistical analysis to obtain deep insight into the method by presenting a comparison with the most relevant method (Bayesian), i.e., JBDC. Although numerous metrics are available to gauge the performance, we present two metrics, i.e., confidence interval and AUC-ROC metrics to evaluate the performance of the methods.