CUR decomposition for compression and compressed sensing of large-scale traffic data

Intelligent Transportation Systems (ITS) often operate on large road networks, and typically collect traffic data with high temporal resolution. Consequently, ITS need to handle massive volumes of data, and methods to represent that data in more compact representations are sorely needed. Subspace methods such as Principal Component Analysis (PCA) can create accurate low-dimensional models. However, such models are not readily interpretable, as the principal components usually involve a large number of links in the traffic network. In contrast, the CUR matrix decomposition leads to low-dimensional models where the components correspond to individual links in the network; the resulting models can be easily interpreted, and can also be used for compressed sensing of the traffic network. In this paper, the CUR matrix decomposition is applied for two purposes: (1) compression of traffic data; (2) compressed sensing of traffic data. In the former, only data from a “random” subset of links and time instances is stored. In the latter, data for the entire traffic network is inferred from measurements at a “random” subset of links. Numerical results for a large traffic network in Singapore demonstrate the feasibility of the proposed approach.