关键词: 点模式, Voronoi邻近关系, 相关性, 趋同假设, 拉普拉斯平滑

Abstract: Point pattern convergence exerts a fundamental way in quantifying similar spatial patterns, which plays an essential function in revealing geographical phenomena emergence, development and evolution. Nevertheless, the independence test for traditional unary point pattern was based on a given frequency or random distribution. Moreover, the local correlation analysis for binary point pattern was focused on single observation and the surroundings were measured by Euclidean distance. Hereto, the issues on correlation in clustering, comprehensive convergence quantization for the point pattern under multiple observations and topological adjacency and non-adjacency relations need to be addressed. In facets of adjacency clustering and local convergence values over the criteria of spatial pattern, an extraction method for point pattern convergence under Voronoi adjacency relation was proposed. Firstly, independent spatial point patterns were tessellated using a clustering algorithm based on the Voronoi Adjacency Correlation Table, abbr. VACT. Secondly, the Nearest Neighbor Index was calculated through the Voronoi Adjacency Index algorithm, VAI for short, and in combination with the hypothesis testing results including mean distance and variance, the comprehensive convergence hypothesis was quantified via Laplace smoothing. Thirdly, according to λ truncated matrix, the strong convergent point patterns were extracted under the support of Voronoi adjacency and non-adjacency relations. Last but not least, taking the resident point set of Tengchong Yunnan for example, through point pattern construction and comparison, convergence calculation and strong convergence extraction, this method was evaluated to be promising.

Key words: point pattern, Voronoi adjacency relation, correlation, convergence hypothesis, Laplace smoothing