# Manifolds-Based Low-Rank Dictionary Pair Learning for Efficient Set-Based Video Recognition
## 4 Experimental Results and Analysis
### Experiments on Set-Based Object Classification Task  
In this part of the study, the ETH-80 [28] dataset was used to verify the performance of the proposed method on a set-based object classification task. As shown in Figure 3c, this dataset contains 80 image sets of 8 different categories including apples, cars, cows, cups, dogs, horses, pears, and tomatoes; each category contains 10 image sets, and each image set includes 41 different views images. Each image was resized to \(20\times 20\) pixels. For fair comparison, five image sets were randomly selected from each category for training (i.e., used as gallery sets), and the remaining image sets were selected for testing (i.e., used as probe sets). We repeated this process 10 times, and we report the average experimental results. The finally recognition rates and computing time of different methods are shown in Figure 4.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Accuracy** \\ \hline D-KSVD & 59.20 \\ ADDL & 62.30 \\ DDL & 60.10 \\ SLatDPL & 61.90 \\ CEBSR & 66.31 \\ \hline MbLRDPL-SPD & 72.16 \\ MbLRDPL-GM & 71.85 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Classification accuracy (%) of different dictionary learning methods on the YTC dataset.  
Figure 4: _Cont._  
As shown in Figure 3(a), we found that the classification accuracy of MbLRDPL was the highest, demonstrating that our proposed method can effectively deal with the object classification task. Specifically, MbLRDPL reduced the classification error of dynamic modeling methods by at least 75.61% (ISCRC) and reduced the error of static modeling methods by at least 33.33% (MMFML). These results indicate that our proposed MbLRDPL combines the advantages of both static and dynamic modeling methods, which is an observation consistent with our previous theoretical analysis. Additionally, we found that the static modeling methods performed better than the dynamic modeling methods, demonstrating that the static modeling methods are more suitable for object classification tasks. Compared with dictionary learning methods, we found that our MbLRDPL outperformed these methods by at least 6.25%, indicating that our LRDPL classifier has a more powerful classification ability. Figure 3(b) again shows that MbLRDPL runs much faster than the methods used for comparison, likely because the static modeling strategy can substantially reduce the number of samples, and the subsequent LRDPL classifier runs quickly by avoiding the \(L_{1}\)-norm optimization problem.  
In conclusion, compared with the state-of-the-art (SOTA) methods, we observe that (a) on Honda dataset, the MbLRDPL and SOTA method JMLC both achieve 100% accuracy. However, our MbLRDPL runs much faster (about 900 times) than JMLC in terms of testing time; (b) on the YTC dataset, our MbLRDPL achieves 72.16% accuracy, reducing the errors of SOTA methods JMLC, DML and CEBSR by 0.96%, 4.36%, and 17.36%, respectively. MbLRDPL runs much faster than these SOTA methods; (c) on the ETH-80 dataset, our MbLRDPL achieves 95% accuracy, reducing the errors of SOTA methods JMLC and CEBSR by 75.69% and 55.56%, respectively. We find again that MbLRDPL runs much faster than the comparison SOTA methods.