Variable-Specific Classification of Zones, Pairs of Zones, and Clusters of a Spatial System via Modified Gravity Model

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Research Article

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IEEE Transactions on Emerging Topics in Computing


Hierarchical structures include spatial systems (e.g., a continent), clusters of a spatial system (e.g., countries of a continent), zones of a cluster (e.g., states of a country), and so on. Variable-specific classification of the zones (Xi) of a cluster of zones (X) within a spatial system is the main focus of this paper. Variable-specific (e.g., GDP, population, trade, resources, economic activity etc) classification of zones is done by computing the levels of interaction between the ith and jth zones. Based on a heuristic argument, we proposed a modified gravity model for the computation of levels of interaction between the zones. This argument is based on the following two facts: (i) the level of interaction between the zones Xi and Xj, with masses mXi and mXj is direction-dependent, and (ii) the level of interactions between the zones Xi and Xj, with masses mXi and mXj, situated at strategically insignificant locations would be much different (lesser) from that of the zones Xi and Xj with similar masses mXi and mXj but situated at strategically highly significant locations. Based on this argument, we provide a modified gravity model by incorporating the dXij ≠ dXji, and the product of location significance indexes (φXiφXj) of the corresponding zones. This modified gravity model yields the level of interaction between the two zones that satisfies FXij ≠ FXji. We demonstrate this modified gravity model on the 28 states of India, whereby the areal extents (land resources) of each state is considered as a parameter mass. The levels of interactions are presented for all pairs of states.

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