## 2 Background Fundamentals
### Randomized Low-Rank Approximations
The training performance with the various batch sizes and iteration processes is shown in Figure 8.2 Here, with a batch size of 32, the approximated dataset (AP) requires the lowest number of iterations to achieve the best training performance with respect to _Ac_, _Pr_, _Rc_, and _Fs_ compared with the non-approximated dataset. Additionally, it is observed that the proposed DEM produces better performance with a batch size of 32, as represented in Figure 8.3

Based on the classification accuracy obtained using the approximated and non-approximated data, along with the evaluation of the performance analysis, we had the confidence to select the approximated dataset with a batch size of 32 to obtain the prediction accuracy. The obtained prediction accuracy is listed in Figure 8.4

Figure 8.5 Training performance with a batch size of 32. \begin{table}
\begin{tabular}{r r r r r r r r r r r} \hline \hline \multirow{2}{*}{**Batch Size**} & \multicolumn{2}{c}{**Iteration**} & \multicolumn{2}{c}{**Accuracy**} & \multicolumn{2}{c}{**Precision**} & \multicolumn{2}{c}{**Recall**} & \multicolumn{2}{c}{**F\({}_{\text{1}}\)-Score**} \\  & **NAP** & **AP** & **NAP** & **AP** & **NAP** & **AP** & **NAP** & **AP** & **NAP** & **AP** \\ \hline
64 & 210 & 160 & 69.2 & 76.9 & 33.33 & 43.75 & 44.4 & 5 & 34.37 & 46.43 \\
32 & 190 & 130 & 89.26 & 91.26 & 82.49 & 91.67 & 62.5 & 97.22 & 71.12 & 94.36 \\
20 & 250 & 140 & 78.4 & 84.6 & 56.25 & 83.33 & 59.72 & 84.72 & 50.2 & 77.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Training iteration for approximated and non-approximated datasets. From Table 10, batch-32 produced 96.1% accuracy for the approximated dataset, where as 93.76% accuracy for the non-approximated dataset. The 12 splits provide the best classification accuracy. Thus, there is an increase in prediction accuracy of 2.34% for the simulated approximated dataset. For the approximated dataset the evaluation metrics such as \(Pr\), \(Rc\), and \(Fs\) show their values as 93.87, 85.14, and 89.29 respectively, which is shown in Figure 16.

## 6 Comparative Analysis with Existing Research Methods

A comparative analysis has been carried out with the proposed model against the model designed by [35] using LSTM, also compared to a model proposed by [20] using Bagging-ensemble, and compared by ensemble model proposed by [18]. Table 11 has given the justification regarding the choice of the proposed model and demonstrated the prediction analysis with the approximated dataset where the proposed DEM model achieved the highest \(Pr=93.87\), \(Rc=85.14\), and \(Fs=89.29\) comparing with the existing deep learning, and an ensemble model. Here, the ensemble model [18] is designed with the conventional machine learning techniques so while the data size is huge and the model is working over the varieties of data characteristics, prediction performance is reduced. Among LSTM [35], and Bagging-ensemble [20], the prediction performance shows better in the case of the bagging-ensemble process because the prediction process is suppressed with the conventional LSTM for the overfitting problem. Figure 16: Testing performance with batch size 32. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Split**} & \multicolumn{3}{c}{**Approximated Dataset**} & \multicolumn{3}{c}{**Non-Approximated Dataset**} \\  & **Batch-64** & **Batch-32** & **Batch-20** & **Batch-64** & **Batch-32** & **Batch-20** \\ \hline
1 & 84.77 & 89.14 & 78.96 & 80.47 & 86.31 & 77.26 \\
2 & 85.37 & 89.64 & 79.25 & 80.72 & 87.53 & 78.1 \\
3 & 86.48 & 90.27 & 80.76 & 82.25 & 89.03 & 78.59 \\
4 & 87.13 & 92.96 & 83.31 & 83.39 & 89.86 & 80.73 \\
5 & 87.79 & 93.57 & 84.7 & 84.67 & 90.7 & 82.91 \\
6 & 88.18 & 94.81 & 86.24 & 85.11 & 91.48 & 83.63 \\
7 & 89.57 & 95.73 & 86.59 & 86.52 & 92.89 & 84.47 \\
8 & 90.28 & 96.1 & 87.66 & 87.41 & 93.76 & 85.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Prediction accuracy for approximated and non-approximated dataset. Figure 17 demonstrates a comparative analysis using the accuracy with a split of 8.