Bayesian Kernelized Matrix Factorization for Spatiotemporal Traffic Data Imputation and Kriging

Missingness and corruption are common problems for real-world traffic data. How to accurately perform imputation and prediction based on incomplete or even sparse traffic data becomes a critical research question in intelligent transportation systems. Low-rank matrix factorization (MF) is a common solution for the general missing value imputation problem. To better characterize and encode the strong spatial and temporal consistency in traffic data, existing work has introduced flexible spatial/temporal Gaussian process (GP) priors to model the latent factors in MF framework, which also allows us to perform kriging for unseen locations and virtual sensors. However, learning the hyperparameters in GP kernels remains a challenging task. In this paper, we present a Bayesian kernelized matrix factorization (BKMF) model with an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for model inference. By learning the kernel hyperparameters from their marginal posteriors through a slice sampling treatment and updating the latent factors alternatively with Gibbs sampling, we achieve a fully Bayesian model for the spatiotemporally kernelized (i.e., GP prior regularized) MF framework. We apply BKMF on both imputation and kriging tasks, and our results demonstrate the superiority of BKMF compared with state-of-the-art spatiotemporal models. In addition, we also explore the effects of different GP kernels in characterizing networked spatiotemporal traffic state data.