Large-scale Traffic Data Imputation Using Matrix Completion on Graphs

Incomplete data is common and unavoidable in the data-driven intelligence transportation system. There are several studies on traffic data imputation, while how to utilize temporal-spatial information is still under discussion. In this paper, we propose an imputation algorithm based on matrix completion on graphs. To derive an appropriate estimation matrix, the temporal and spatial dependencies are considered as graphs. The smoothness of graphs is added to the objective function as regularization terms. Then, a heuristic method is proposed to solve optimization in case of large-scale traffic data. Through the iterations, the low rank, the observed error and the smoothness of temporal and spatial graphs are minimized. The missing in the incomplete data could be recovered by corresponding entries in the estimation matrix. In the numerical experiment, we apply our method to the expressway detector data of Tokyo Metropolitan. The proposed method is shown to be applicable in both speed and volume data. Moreover, we discussed the imputation performance in different missing patterns. Compared with the baseline matrix completion method and the tensor-based method, our method achieved higher overall accuracy.