# ML-Empowered Microservice Workload Prediction by Dual-Regularized Matrix Factorization
## 4 Performance Evaluation
### Ablation Study (Rq2)  
This experiment aims to validate the independent contributions of the core components in the proposed TDDRMF framework, including trend regularization, periodic regularization, nuclear norm constraints, and the dynamic error detection mechanism. An incremental modeling approach is adopted, where components are progressively added to analyze their impact on multi-step prediction performance. The experiment includes the following four model configurations (with abbreviations):  
1. Matrix Factorization + Trend Regularization (MF + T): Captures short-term changes and long-term trends.  
2. Matrix Factorization + Trend Regularization + Periodic Regularization (MF + T + P): Adds periodic modeling on top of trend modeling.  
3. Matrix Factorization + Trend Regularization + Periodic Regularization + Nuclear Norm Constraints (MF + T + P + N): Introduces low-rank constraints to model inter-service dependencies.  
4. Full model (TDDRMF): Incorporates all components to evaluate the combined effect of dynamic updates and regularizations.  
The results are summarized in Table 4, demonstrating that prediction accuracy improves significantly with the gradual integration of these components, while computational  
\begin{table}
\begin{tabular}{l c c c c c c} \hline
**Metric** & **TDDRMF** & **TAMF** & **TRMF** & **ARIMA** & **RF** & **LSTM** \\ \hline
**RMSE** & 0.3353 & 0.3368 & 0.4391 & 0.4101 & 0.2773 & **0.2319** \\
**R\({}^{2}\)** & 0.9808 & 0.9808 & 0.9730 & \(-\)6.3680 & 0.9989 & **0.9992** \\
**Train Time (s)** & 2.33 & 1.12 & **1.11** & 580.96 & 9890.77 & 44,451.21 \\
**Pred Time (s)** & **0.001** & 0.002 & **0.001** & 3.14 & 5.07 & 0.29 \\ \hline \end{tabular}
\end{table}
Table 2: Performance comparison across models (1-step).  
\begin{table}
\begin{tabular}{l c c c c c c} \hline
**Metric** & **TDDRMF** & **TAMF** & **TRMF** & **ARIMA** & **RF** & **LSTM** \\ \hline
**RMSE** & 0.3784 & 0.4645 & 0.5782 & 0.4311 & 0.3548 & **0.3192** \\
**\(R^{2}\)** & 0.9771 & 0.9715 & 0.9612 & \(-\)3.2 \(\times\) 10\({}^{34}\) & 0.9983 & **0.9986** \\
**Train Time (s)** & **2.24** & 12.95 & 12.31 & 675.29 & 9890.77 & 44,451.21 \\
**Pred Time (s)** & **0.009** & 0.011 & 0.011 & 3.90 & 14.62 & 1.61 \\ \hline \end{tabular}
\end{table}
Table 3: Performance comparison across models (10-step).  
efficiency is also enhanced. The baseline matrix factorization model captures only the low-dimensional structure of workloads, resulting in lower accuracy and longer training time. By incorporating temporal regularization (MF + T + P), the model significantly improves its ability to capture short-term trends and periodic patterns, reducing prediction error. The nuclear norm constraints (MF + T + P + N) optimize the low-rank representation of microservice dependencies, enhancing the accuracy of multi-step prediction tasks. However, due to the necessity of retraining the model for each prediction and the inability to fully leverage historical errors for timely adjustments, its performance does not reach the optimal level. In contrast, the complete model incorporating the dynamic error detection and update mechanism (TDDRMF) achieves real-time error correction, maintaining the continuity and stability of predictions, significantly reducing both training and prediction times, while simultaneously improving accuracy.  
In summary, the Q2 experimental results validate the rational design of the TDDRMF framework. The integration of temporal regularization, nuclear norm constraints, and the dynamic error detection mechanism significantly enhances prediction accuracy and computational efficiency. The synergistic effect of these components enables TDDRMF to excel in dynamic and complex environments, offering an efficient and accurate solution for workload prediction tasks.