Functional clustering and missing value imputation of traffic flow trajectories

Patterns of traffic flow trajectories play an essential role in analysing traffic monitoring data in transportation studies. This research presents a data-adaptive clustering approach to explore traffic flow patterns and a unified algorithm to impute missing values for incomplete traffic flow trajectories. We recommend using subspace-projected functional data clustering with the assumption that each observed daily traffic flow trajectory is a realization of a random function sampled from a mixture of stochastic processes, and each subprocess represents a cluster subspace spanned by the mean function and eigenfunctions of the covariance kernel of the random trajectories. The unified algorithm combines probabilistic functional clustering with functional principal component analysis to propose a mixture prediction for missing value imputation. The proposed methods effectively unravel distinctive daily traffic flow patterns and improve the accuracy of missing value imputation. The advantage of the proposed approaches is demonstrated through numerical studies of a real traffic flow data application.