# hLSTM-Aging: A Hybrid LSTM Model for Software Aging Forecast
## 6 Results Analysis
### Metrics  
For the CPU utilization, Table 1 shows a clear difference between the accuracy of the LSTM networks and the probabilistic methods according to the metrics used. While the LSTM-based methods were superior to MSE results, the probabilistic methods showed slightly better MAPE values. Among the LSTM models, the Conv-LSTM had better results but was not very far from the other LSTM models. The SARIMA model had the best results among the statistical methods compared to the rest of the methods. The proposed combination (moving average + Conv-LSTM) had better results when compared to the individual methods in almost all of the evaluation metrics. Concerning the disk usage (Table 2), the results show similar behavior to the previous time series evaluated (CPU utilization). In addition, the moving average technique presented better results than the rest of the probabilistic methods and better MAPE results concerning LSTM-based methods. Once again, the LSTM models had similar results, but the BI-LSTM had better performance when compared to the others. Here, the proposed combination (moving average + Conv-LSTM) method had better performance in training than the individual methods and had a close result in the test data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Architecture** & **MSE-Train/Test** & **MAPE-Train/Test** & **MAE-Train/Test** \\ \hline Vanilla-LSTM & \(5\times 10^{-6}/3\times 10^{-5}\) & \(1.01\times 10^{-1}/1.95\times 10^{-1}\) & \(1.6\times 10^{-3}/6.1\times 10^{-3}\) \\ Stacked-LSTM & \(1\times 10^{-5}/2\times 10^{-4}\) & \(1.36\times 10^{-1}/5.06\times 10^{-1}\) & \(2\times 10^{-3}/1.5\times 10^{-2}\) \\ Bi-LSTM & \(6\times 10^{-6}/2\times 10^{-6}\) & \(1.09\times 10^{-1}/1.8\times 10^{-2}\) & \(1\times 10^{-3}/5\times 10^{-4}\) \\ CNN-LSTM & \(6\times 10^{-6}/5\times 10^{-5}\) & \(1.11\times 10^{-1}/2.24\times 10^{-1}\) & \(1\times 10^{-3}/7\times 10^{-3}\) \\
**Conv-LSTM** & \(6\times 10^{-6}/3\times 10^{-5}\) & \(1.04\times 10^{-1}/1.43\times 10^{-1}\) & \(1\times 10^{-3}/4\times 10^{-3}\) \\ AR & \(1.548\times 10^{0}/5\times 10^{-4}\) & \(2\times 10^{-4}/5\times 10^{-3}\) & \(3\times 10^{-4}/1.84\times 10^{-2}\) \\ MA & \(1.140\times 10^{0}/1.841\times 10^{0}\) & \(3.03\times 10^{-1}/4.31\times 10^{-1}\) & \(3.25\times 10^{-1}/1.350\times 10^{0}\) \\ ARMA & \(1.845\times 10^{0}/7\times 10^{-3}\) & div by zero/\(7.8\times 10^{-2}\) & \(7.643\times 10^{0}/7.4\times 10^{-2}\) \\ ARIMA & \(1.649\times 10^{0}/1.1\times 10^{-2}\) & \(2\times 10^{-4}/2.9\times 10^{-2}\) & \(3\times 10^{-4}/9.5\times 10^{-2}\) \\
**SARIMA** & \(1.739\times 10^{0}/6.8\times 10^{-2}\) & \(1\times 10^{-4}/7.0\times 10^{-2}\) & \(1\times 10^{-4}/2.25\times 10^{-1}\) \\ \hline
**hLSTM** & \(5\times 10^{-6}/2\times 10^{-5}\) & \(8.6\times 10^{-2}/1.37\times 10^{-1}\) & \(2\times 10^{-5}/4\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of evaluation metrics for CPU utilization data. For the VmRSS time series (Table 3), the test results followed the same pattern we observed for the disk usage measure. The Vanilla-LSTM showed better results in the test experiments concerning the other LSTM-based models. For the probabilistic methods, the moving average technique had a better performance. The hybrid combination (moving average + Conv-LSTM) achieved better results in all the evaluation metrics. In the one VM memory used table (Table 4), all the LSTM methods showed similar results, but the Conv-LSTM still demonstrated an advantage in the testing experiments, while for the statistical models, once again the moving average had a better performance when compared with the other methods. The results were better for the proposed combination (moving average + Conv-LSTM) than those from the training set's methods. The hybrid combination had slightly worse results in both MSE and MAE metrics but surpassed the individual methods in the MAPE metric in the test set.