The Moran Spectrum as a Geoinformatic Tupu: implications for the First Law of Geography

Geoinformatic Tupu, or Geoinformatic graph spectrum, is a theoretical as well as a technical framework for generalizing geographic knowledge and solving real world problems. Geoinformatic Tupu is a promising platform for capitalizing on the technical advances of Geographic Information Systems, and to integrate the Chinese traditional way of thinking with modern information technology. It has been one of the major research topics in the Chinese GIScience community in recent decades, with an evolving epistemological development. A core objective of Geoinformatic Tupu is to recover and represent geographic principles with the Tupu approach, which is adopted in this paper to formulate the First Law of Geography (FLG) [i.e. the law of spatial autocorrelation] as the Moran Spectrum–a combination of sequential diagrams, graphs, and numeric components. Using the Moran Spectrum as a conduit, we present the theory of Moran Eigenvector Spatial Filtering (MESF), a distinct branch of spatial statistics that has demonstrable advantages in statistical modelling and machine learning, but has yet to be widely disseminated due to its conceptual and computational complexity. This paper demonstrates the effectiveness of the Tupu approach in enriching the representation of the FLG as well as deepening its applications. It also suggests inclusion of the Moran Spectrum as a core component in Geoinformatic Tupu.