# ML-Empowered Microservice Workload Prediction by Dual-Regularized Matrix Factorization
## 2 Related Work
[16] compares the prediction effects of LSTM, AR, and HTM and dynamically selects the best performing model; [PERSON]. [15] proposes an ensemble approachbased on metaheuristics combined with an Extreme Learning Machine (ELM) in order to reduce the training time and improve the prediction performance. [PERSON]. [17] further integrates multiple models (e.g., ARIMA, multilayer perceptron, support vector regression, Random Forest, and LSTM) and dynamically adjusts the model configurations to adapt to changes in the workload environment. These methods solve the problem of unstable performance of a single model to a certain extent, while improving the adaptability in complex workload scenarios. However, they inherit the disadvantage of single-model ML and are unable to fully capture the underlying structure of the workload data and the dynamic and collaborative relationships between microservices. Matrix factorization has been widely applied in time series forecasting due to its advantages in capturing latent features and temporal dynamics. For example, [PERSON]. [30] proposes a spatio-temporal modeling framework (MF-STN) that combines matrix factorization with neural networks to capture regional characteristics and correlations through latent embeddings, thereby improving the accuracy of urban flow prediction. Similarly, Ref. [31] develops a non-stationary time matrix factorization model (NoTMF), which integrates matrix factorization with vector autoregression (VAR) to address high-dimensional time series forecasting problems. Furthermore, Ref. [22] introduces a matrix factorization method incorporating temporal regularization and autoregressive processes to model nonlinear dynamics and detailed properties in time series. Ref. [23] designs the Temporal Autoregressive Matrix Factorization (TAMF) framework, which uses trend and periodic regularization to uncover latent characteristics of time series while handling data sparsity issues. Then, BTAMF [32] splits the direct variables in the traditional decomposition into two parts--a trend component and a periodic component--and then uses an autoregressive model over the target series' preceding time steps to capture trend fluctuations, alongside a second autoregressive model built on strongly correlated historical segments to characterize periodic patterns. This design enables both the accurate imputation of missing values and effective forecasting of future observations without sacrificing the original time series characteristics. These studies demonstrate the potential of matrix factorization in capturing complex data change trends and handling sparse data. However, most of the current matrix factorization approaches focus mainly on modeling temporal dynamics of datasets and ignore their dynamic relationships existing in many applications such as microservice workload scheduling. In summary, existing approaches to microservice workload prediction have their strengths and limitations: statistical methods are efficient in linear, stable scenarios but struggle with nonlinearity and sparse data; machine learning and deep learning models with the attention mechanism can capture complex temporal dynamics and dependencies but rely on large, complete datasets and incur heavy training and computing overheads; ensemble learning improves robustness by combining multiple models but inherits the high costs and structural blind spots of its base learners; and traditional matrix factorization excels at imputing missing values and denoising but typically focuses only on temporal patterns and overlooks the critical collaborative dependencies that drive load propagation among microservices. In contrast to existing methods, our TDDRMF employs matrix factorization with temporal and nuclear-norm regularization to jointly model multi-scale workload dynamics and low-rank service dependencies. Its convex optimization backbone ensures fast convergence, and its low-rank design naturally denoises and handles missing data.