Evaluation on the Prominences of Irregular Areas Based on Spatial Weight Matrices

Abstract

In regional science, an area that has special geometric attributes and maintains significant spatial correlation and spatial interaction close to adjacent zones is called a prominent area. The prominence of irregular areas can be measured using a prominence index, which is a stationary distribution of a Markov chain transition matrix identical to a spatial weight matrix. In this paper, to identify the relationship between the prominence of an area and its geometric attributes, an expanded definition for measuring geometric attributes such as size, shape, and location in irregular areas is presented. The expanded definition involves identifying size with area, location with number of adjacent areas, and shape with edge roughness or smoothness and compactness. In this approach, spatial clusters composed of prominent areas are extracted using K-means cluster analysis. A very different relationship between prominence and the geometric attributes of areas is shown by spatial correlation analysis when the prominences are derived from different spatial weight matrices. The results of this analysis are as follows: 1) Although different prominences can be obtained from different weight matrices, generalized weight matrices are more appropriate to measure the prominence of areas than distance decay and k-order. 2) The prominence measured using the distance-decay matrix is only negatively correlated with the size of areas, but the prominence derived from the generalized matrix is more strongly correlated with the size, location, and shape of areas.