The origin-destination (OD) matrices express the number and the pattern of trips distributed between OD pairs. OD matrix structural comparison can be used to identify different mobility patterns in the cities. A comparison of two OD matrices could express their difference from both numerical and structural aspects. Limited methods, such as the mean structural similarity (MSSIM) index and geographical window-based structural similarity index (GSSI), have been developed to compare the structural similarity (SSIM) of two matrices. These methods calculate the structural similarities of two OD matrices by grouping the OD pairs into local windows. The obtained results from the MSSIM entirely depend on the dimensions of the chosen windows. Meanwhile, the GSSI method only focuses on the geographical adjacency and correlation of zones while selecting local windows. Accordingly, this paper developed a novel method named Socioeconomy, Land-use, and Population Structural Similarity Index (SLPSSI) in which local windows are selected according to socioeconomic, land-use, and population properties for SSIM comparison of OD matrices. The proposed method was tested on Tehran’s OD matrix extracted from cell phone Geographic Position System (GPS) data. The advantage of this method over two previous ones was observed in determining the new pattern of trips on local windows and more precise detection of SSIM of the weekdays. The SLPSSI approach is up to 10 percent more accurate than the MSSIM method and up to 5.5 percent more accurate than the GSSI method. The proposed method also had a better performance on sparse OD matrices. It is capable of better determining the SSIM of sparse OD matrices by up to 8% compared with the GSSI method. Finally, the sensitivity analysis results indicate that the suggested method is robust and reliable since it is sensitive to applying both constant and random coefficients.

中文翻译：

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具有社会经济、土地利用和人口特征的基于局部窗口的起点-终点矩阵之间的结构比较

起点-终点 (OD) 矩阵表示分布在 OD 对之间的出行次数和模式。OD 矩阵结构比较可用于识别城市中的不同流动模式。两个 OD 矩阵的比较可以从数值和结构方面表达它们的差异。已经开发了有限的方法，例如平均结构相似性 (MSSIM) 指数和基于地理窗口的结构相似性指数 (GSSI)，以比较两个矩阵的结构相似性 (SSIM)。这些方法通过将 OD 对分组到局部窗口来计算两个 OD 矩阵的结构相似性。从 MSSIM 获得的结果完全取决于所选窗口的尺寸。同时，GSSI方法在选择本地窗口时只关注区域的地理相邻性和相关性。因此，本文开发了一种名为社会经济、土地利用和人口结构相似性指数 (SLPSSI) 的新方法，其中根据社会经济、土地利用和人口特性选择局部窗口，用于 OD 矩阵的 SSIM 比较。所提出的方法在从手机地理定位系统 (GPS) 数据中提取的德黑兰 OD 矩阵上进行了测试。在确定本地窗口上的新出行模式和更精确地检测工作日的 SSIM 方面，观察到该方法优于前两种方法的优势。SLPSSI 方法的准确度比 MSSIM 方法高 10%，比 GSSI 方法高 5.5%。所提出的方法在稀疏OD矩阵上也有更好的性能。与 GSSI 方法相比，它能够更好地确定稀疏 OD 矩阵的 SSIM，最高可达 8%。最后，敏感性分析结果表明所建议的方法稳健可靠，因为它对应用常数和随机系数都很敏感。