Application of Principal Component Analysis to Predict Dynamic Origin–Destination Matrices

Abstract

Prediction of the time evolution of origin–destination (O-D) matrices is important for many applications in the traffic domain. These applications range from ex ante evaluation to real-time prediction and control. Since O-D matrices are high-dimensional multivariate data structures, both the specification and the estimation of O-D prediction models are methodologically and computationally cumbersome. This paper demonstrates that a significant reduction of the dimensionality of the O-D data that preserves structural patterns can dramatically reduce computational costs without a significant loss of accuracy. This paper explores the application of principal component analysis (PCA) for this purpose. PCA shows that the dimensionality of the time series of O-D demand can be reduced significantly. This paper also shows how the results from the PCA method can be used to reveal the structure in the underlying temporal variability patterns in dynamic O-D matrices. The results indicate three main patterns that can be distinguished in dynamic O-D matrices: structural, structural deviation, and stochastic trend patterns. Insight into how these trends contribute to each O-D pair and how this information can be further used to predict dynamic O-D matrices on the basis of a set of dynamic O-D matrices obtained from real data is provided.