Spatiotemporal Analysis of Traffic Data: Correspondence Analysis with Fuzzified Variables vs. Principal Component Analysis Using Weather and Gas Price as Extra Data

Study of large rail traffic databases presents formidable challenges for transport system specialists, more particularly while keeping both space and time factors together with the possibility of showing influencing factors related to the users and the transport network environment. To perform such a study, a bibliographic analysis in both statistics and transport revealed that geometrical methods for feature extraction and dimension reduction can be seen as suitable. Since there are several methods/options with, in principle, required input data, this article aims at comparing Principal Component Analysis (PCA) and Correspondence Analysis (CA) for traffic frequency data, both methods being actually used with such data. The procedure stands as follows. First a grand matrix is built where the rows correspond to time windows and the columns to all the possible origin-destination links. Then this large frequency matrix is studied using PCA and CA. The next part of the procedure consists in studying the effects of influencing factors with the possibility of keeping the quantitative scales with PCA or using fuzzy segmentation with CA, the corresponding data being considered as supplementary column points. The procedure is applied on a rail transport network including 10 stations (one corresponding to the airport) and one-hour time windows for 4 months, the available influencing factors being the temperature, rain level and gas price. The comparative analysis shows that CA graphical outputs are more complicated than PCA ones, but reveal more specific results, e.g. the network user behavior related to the airport, while PCA mainly opposes link clusters with low vs. high frequencies. Fuzzy windowing performed using actual and simulated data reduces the loss of information when averaging, e.g. over time, and can show non-linear relational phenomena. The possibility of displaying new traffic data in real time is also considered.