MNCD-KE: a novel framework for simultaneous attribute- and interaction-based geographical regionalization

Existing regionalization methods tend to be either spatial attribute- or spatial interaction-based, while real-world tasks usually involve both considerations to satisfy multiple objectives simultaneously. In this research, we propose Multilayer Network Community Detection and Kernel Extension (MNCD-KE), a two-step regionalization framework, as a feasible solution for such tasks. First, spatial attributes are embedded into attributes of nodes in a spatial interaction-defined multilayer network, and the kernel and marginal parts of the regions are determined by giving the membership value of the regionalization units to network communities. Second, the final result is obtained through a kernel extension process considering geographical constraints, including spatial contiguity, size balance, morphological regularity, and existing boundary consistency of the regions. Empirical experiments show that the proposed method yields outcomes that, in maintaining comparable performances with most baseline algorithms with either 'attribute' or 'interaction' objectives as measured by the respective criteria, simultaneously meet the dual objectives with results intuitively comprehensible. Its low computing costs and parameter adjustment flexibility make the proposed framework a convenient approach for real-world multi-objective regionalization tasks. We conclude the research with discussions on the boundary conditions for the framework to work and their relevance to city science theories, along with practical implications.