Geographical window based structural similarity index for OD matrices comparison

Most traditional metrics compare OD matrices based on the deviations of individual OD flows and often neglect OD matrix structural information within their formulations. Very few metrics exist in literature for 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 windows. However, MSSIM can result in different values based on the choice of local window size. In literature, no clear consensus has been reported on the level of acceptability of sliding window size and the resulting MSSIM values. To overcome the afore-mentioned problems, this study proposes the concept of geographical window, and develops geographical window based structural similarity index (GSSI) that exploits OD matrix structure by computing statistics on group of OD pairs that are geographically correlated. Compared to traditional sliding window-based SSIM, the GSSI technique preserves geographical integrity, compares results with physical significance, can capture local travel patterns, captures correlation distortions as effective as a small sized sliding window, and is computationally very efficient. The robustness of the GSSI is further tested through sensitivity analysis. The findings of the study suggest that GSSI is a robust statistical metric and has potential for practical applications that involve OD matrices comparison.