Network Traffic Modeling and Prediction Using Graph Gaussian Processes

[2nazero]

Network Traffic Modeling and Prediction Using Graph Gaussian Processes

@article{mehrizi2022network,
  title={Network Traffic Modeling and Prediction Using Graph Gaussian Processes},
  author={Mehrizi, Sajad and Chatzinotas, Symeon},
  journal={IEEE Access},
  volume={10},
  pages={132644--132655},
  year={2022},
  publisher={IEEE}
}

[kyungheee]

1. problem definition

Since traffic data follows a graph-structured topology, this paper addresses the traffic prediction problem modeled as a graph. The graph $\mathcal{G}$ consists of nodes $\mathcal{V}$ and edges $\mathcal{E}$, with traffic data $y_t$ at time $t$. The goal of this problem is to predict the traffic at a future time based on observed traffic data. However, the challenge arises from the presence of both observed and missing nodes.

2. GP for network traffic data.

This paper presents traffic data as a Bayesian model based on Gaussian Processes (GP). The model includes both observed and missing nodes, and assumes that the traffic data is generated according to a Gaussian likelihood. The mathematical formulation is given as follows:

$$ y_t = Wf_t + b + n_t $$

• $y_t$ : the traffic data at time $t$ for each node.
• $W$ : factor loading matrix, which captures the specific characteristics of each node
• $f_t$ : latent variable vector that captures common temporal patterns among the nodes
• $b$ : bias vector that represents the overall traffic volume at each node
• $n_t$ : additive white noise at time $t$

[2nazero]

Can you give a more precise explanation of how the formula above solve the problem of observed and missing nodes? And also the results after applying the formula?