Interaction in large-scale outdoor space has been extensively studied due to its importance in understanding the human-land relationship. Models such as the gravity have been proven to be able to quantify the interaction between two places. However, interaction in indoor space still remains unclear even though humans spend over 70% of their time indoors. Few studies attempt to construct an indoor interaction model. In this study, we analyze the interaction between stores in shopping malls via customer flow to determine whether indoor mobility interaction follows the gravity law and what are its influencing factors. Based on indoor positioning data, two customer flow measures (connectivity flow, indicating the direct connection between stores, and association flow, indicating the association relationship between stores) and two distance measures (path distance, indicating the minimum travel cost, and store distance, indicating the mean travel cost) are defined to fit the traditional and extended gravity models (considering store floor and type). We find that 1) interaction between stores follows a power law distribution, indicating that only a small fraction of store pairs is closely related; 2) customer mobility is governed by the gravity law, where the distance decay exponent is 1-2 for the connectivity flow and 0-1 for the association flow; and 3) store floor and type are two important factors that affect the interaction between stores. These findings provide insights for modeling indoor interactions and can support indoor settings to optimize their layout, estimate the customer flow and promote sales.
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