Geographical window based structural similarity index for origin-destination matrices comparison

Most traditional metrics compare origin-destination (OD) matrices based on the deviations of individual OD flows and often neglect OD matrix structural information within their formulations. Limited metrics exist in literature for the structural comparison of OD matrices. One such metric is mean structural similarity index (MSSIM) that computes statistics on groups of OD pairs defined by local sliding windows. However, MSSIM can result in different values based on the choice of the size of the window. In literature, no clear consensus has been reported on the level of acceptability of the window size and the resulting MSSIM values. Addressing this need, we propose the concept of geographical window, and develop geographical window based structural similarity index (GSSI) that exploits OD matrix structure by computing statistics on the group of OD pairs that are geographically correlated. Compared to traditional sliding window based MSSIM, the advantages of GSSI technique identified from real case study application are (a) it preserves geographical integrity; (b) it compares results with physical significance; (c) it captures local travel patterns; (d) it compares large-scale sparse OD matrices; and (e) it is computationally efficient. A thorough sensitivity analyses suggest that GSSI is a robust statistical metric and has potential for practical applications such as, benchmarking different OD estimation methods; improving the quality of solution by maintaining structural consistency in the OD estimation process; and identifying gaps in the transit service by comparing local (within a geographical window) travel patterns of car and public transit.