## 6 Parameters Initialization
In our approach, the sparse weights of a test sample over the learned dictionary are computed using orthogonal matching pursuit (OMP). Efficient optimization of the atoms of the dictionary determines how quickly OMP computes the sparse weights. Accordingly, the test time is either large or small, depending on the efficiency of the learned dictionary. 7. **Critical model parameters:** A few of the model parameters, like dictionary size and sparsity, along with other parameters, also play a crucial role in determining the efficiency of the model. Figure 6: Action images from UCF actions dataset clips. ## 9 Experiments

We performed experiments for face recognition, object and scene categorization, and action recognition on standard datasets, i.e., the Extended YaleB [54] and AR [38] datasets, the Caltech-101 [55] and Fifteen Scene Category [57] datasets, and the UCF sports actions dataset [59], and we compared the results with the state-of-the-art methods, discriminative Bayesian dictionary learning (DBDL) [25], the joint Bayesian discriminative classifier (JBDC) [24], the sparse-representation-based classification (SRC) [9], the label-consistent K-SVD (LC-KSVD) [8], the discriminative K-SVD (D-KSVD) [23], the fisher discrimination dictionary learning (FDDL) [12], the joint analysis discriminative dictionary learning (ADDL) [19], the locality-constrained projective dictionary learning (LC-PDL) [20], and the twin-incoherent self-expressive latent dictionary pair learning (SLatDPL) [21]. These are the state-of-the-art approaches in the area of discriminative dictionary learning/sparse-representation-based classification. We reported the results for these approaches with the same protocols of experimentation followed for our approach. In conjunction with reporting the classification accuracy, standard deviation, and training and testing times for all these methods in general, we also carried out a detailed statistical analysis of our approach with the nearest Bayesian approach (JBDC). In this analysis, we computed confidence intervals, computational efficiency, and AUC/ROC scores to establish the effectiveness of our approach. We report the outcomes of this analysis in Section 10. In our approach, we set \(a_{0}\) and \(b_{0}=min_{c}|I_{c}|\), \(\forall c\in\{1,2,\dots,C\}\), and \(K=1.25N\)[24]. We set noninformative hyperparameters \(c_{0},d_{0},e_{0}\), and \(f_{0}=10^{-6}\). We initialized precision parameters, i.e., \(\lambda_{a}\) and \(\lambda_{h}\), with the value \(10^{9}\), except for the UCF sports dataset, where we used the value \(10^{12}\) due to the small size of the training data. We initialized \(\lambda_{s}^{c}\) with 1 and set the values \(M\) and \(C\) for \(\lambda_{\phi_{0}}\) and \(\lambda_{h_{0}}\). A discussion on the parameter values selection of the proposed approach is provided in Section 13. We performed the experiments on an Intel Core i5 Processor with 16 GB RAM. The results of the experiments for face recognition, object and scene classification, and action recognition experiments are discussed in the following sections. ### Face Recognition for Extended Yaleb Database

We randomly selected fifteen examples from each class, and the rest of the data were used as test data. We conducted 10 experiments by randomly selecting the training and testing samples in each experiment. We report mean recognition accuracy, mean standard deviation, and test time in Table 2. The accuracy of our approach, i.e., 93.25, is the highest among all the listed methods. The improvement in the accuracy is attributed to the use of the same representations for learning of dictionary and the classifier. Improvement in the training time is attributed to a reduction in the overall number of the model parameters due to learning only a single set of representations. It is also noted that on using the dictionary pruning option, the dictionary size is adaptively reduced to 570 atoms starting from 712 atoms, i.e., 1.25 times the size of the training data, without degrading the accuracy.