# Proactive Service Caching in a MEC System by Using Spatio-Temporal Correlation among MEC Servers
## 2 Related Works
### Time Series Prediction Methods  
Time series data analysis and prediction have been extensively researched for a long time and have found applications in various industries, including finance, climate, health \begin{table}
\begin{tabular}{c c c} \hline
**Ref.** & **Control** & **Objective** & **Algorithm** \\ \hline
[19] & pricing & maximize MECS Profit & Stakelberg game, knapsack \\
[20] & cost function & optimize distributed caching & Mean-Field Game \\
[21] & virtual queue & minimize completed task delay & Lyapunov Opt. with DRL \\
[22] & graph among contents & minimize service delay & Knowledge graph with DRL \\
[23] & admission probability & maximize cache hit rate & Model-free RL \\
[24] & spatio-temporal correlation & maximize cache hit rate & Multi-Agent RL \\
[25] & temporal correlation & boost cache hit rate & LSTM model \\
[26] & temporal correlation & improve cache hit rate & LSTM model \\
[27] & temporal correlation & maximize cache hit rate & LSTM model with BPSO \\
[28] & temporal attention & predict top-K popular contents & ViT model \\
[29] & temporal attention & predict content popularity & LSTM with CL \\
[30] & spatio-temporal correlation & predict content popularity & ViT with cross attention \\
[31] & fake data & high cache hit rate & FL with GAN \\ proposed & spatio-temporal correlation & predict top-K popular services & ConvLSTM \\ \hline \end{tabular}
\end{table} 
Table 2: Cross-comparison of caching methods in a MEC system (DRL: Deep Reinforcement Learning, LSTM: Long Short-Term Memory, ConvLSTM: Convolutional LSTM, ViT: Vision Transformer, BPSO: Binary Particle Swarm Optimization, CL: Contrastive Learning, FL: Federated Learning, GAN: Generative Adversarial Network). care, transportation, and more. Research endeavors to analyze or predict time series data through traditional statistical models have been actively conducted. The drawback of the traditional statistical models lies in their application of regression to certain fixed factors using the most recent historical data. Therefore, the prediction performance tends to decrease when they are applied to volatile time series. Time series analysis techniques employing deep learning technologies demonstrate superior performance by overcoming these challenges. These methods are categorized into RNN-based, Transformer-based, and MLP-based techniques. The RNN-based approaches [32; 33; 34] enable effective representation of the dynamic characteristics inherent in time series data. However, the RNN-based approach requires the computation and management of hidden states at every time step, leading to an increased computational cost and prolonged training times, particularly when dealing with extensive datasets. The Transformer-based method improves the performance by addressing the structural limitations of the RNN-based method. Unlike RNN-based techniques that utilize recurrent networks, the Transformer-based technique employs positional encoding to indicate the temporal sequence of the data [35; 36]. Through selectively assigning weights to crucial information from the past, the Transformer-based method learns to focus on significant features and past trends. However, since the Transformer-based model is characterized by its intricate architecture, it presents challenges in terms of configuration complexity and result interpretation. MLP-based models, such as N-BEATS [37] and NHITS [38], revolve around the challenges faced by the Transformer-based method. Since they use a simple MLP architecture, they are simple, flexible, and make it easy to interpret the learned time series features. These methods exhibit excellent performance in a single variate and a multi-variate time series data prediction. However, they predict solely based on the temporal correlations within the given time series data. In our service popularity prediction problem, the time series data in each MECS have a relationship not only in the time domain but also in the space domain.