Gravity models, popular for estimating spatial interactions, assume independent spatial interactions from locations to all other locations and, therefore, overlook potential latent multilateral influences in play. This research combines self-organizing map (SOM) and trajectory analysis to classify patterns of spatial interactions and trace changes in the patterns simultaneously across all locations and decipher the development and dependence of multilateral interactions in space and time. We use international trading among 207 countries from 1900 to 2014 to demonstrate the proposed SOM–trajectory analysis. We create SOMs of annual international trade for all countries, trace each country's changes in trading patterns over 115 years, and compare the trajectories for countries. The combined SOM–trajectory analysis elicits the hidden trading development and geographic influences brought into play. The proposed method is adaptable to other domains of spatial interactions (e.g., immigration) to characterize the temporal patterns of multilateral spatial interactions at locations individually or contextually.

中文翻译：

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识别多边空间相互作用的时间模式：以国际贸易为例

重力模型，流行于估计空间相互作用，假设从位置到所有其他位置的独立空间相互作用，因此忽略了潜在的潜在多边影响。该研究结合自组织地图 (SOM) 和轨迹分析，对空间相互作用模式进行分类，并同时跟踪所有位置的模式变化，并破译多方相互作用在空间和时间上的发展和依赖性。我们使用 1900 年至 2014 年间 207 个国家/地区之间的国际贸易来证明所提出的 SOM 轨迹分析。我们为所有国家创建年度国际贸易的 SOM，追踪每个国家 115 年来贸易模式的变化，并比较各国的轨迹。组合的 SOM 轨迹分析引发了隐藏的交易发展和地理影响。所提出的方法适用于其他空间交互领域（例如，移民），以单独或上下文地表征位置处多边空间交互的时间模式。