Ensemble correlation-based low-rank matrix completion with applications to traffic data imputation

Low-rank matrix completion (LRMC) is a recently emerging technique which has achieved promising performance in many real-world applications, such as traffic data imputation. In order to estimate missing values, the current LRMC based methods optimize the rank of the matrix comprising the whole traffic data, potentially assuming that all traffic data is equally important. As a result, it puts more emphasis on the commonality of traffic data while ignoring its subtle but crucial difference due to different locations of loop detectors as well as dates of sampling. To handle this problem and further improve imputation performance, a novel correlation-based LRMC method is proposed in this paper. Firstly, LRMC is applied to get initial estimations of missing values. Then, a distance matrix containing pairwise distance between samples is built based on a weighted Pearson's correlation which strikes a balance between observed values and imputed values. For a specific sample, its most similar samples based on the distance matrix constructed are chosen by using an adaptive K-nearest neighboring (KNN) search. LRMC is then applied on these samples with much stronger correlation to obtain refined estimations of missing values. Finally, we also propose a simple but effective ensemble learning strategy to integrate multiple imputed values for a specific sample for further improving imputation performance. Extensive numerical experiments are performed on both traffic flow volume data as well as standard benchmark datasets. The results confirm that the proposed correlation-based LRMC and its ensemble learning version achieve better imputation performance than competing methods.