Voronoi邻近关系支持下的点模式趋同提取方法

An Extraction Method for Point Pattern Convergence under Voronoi Adjacency Relation

点模式及其趋同研究是揭示地学现象的产生、发展与演变,量化空间相似性分布、诠释空间分布成因的重要方式。目前,点模式研究侧重于已知频率与随机分布的一元独立性检验、距离测度下单观测值的二元相关性分析,而针对集聚过程相关性,空间拓扑与非拓扑邻近、综合多观测值的点模式趋同量化研究顾及不足。据此,以空间邻近性聚类、局部相关的多指标评价为切入点,本文提出了一种Voronoi邻近关系支持下的点模式趋同提取方法。首先,以Voronoi邻近相关表集聚算法剖分出空间独立性点模式;其次,依据Voronoi邻近关系指数测度、样本分布均值与分布方差的趋同假设,使用拉普拉斯平滑算子评价趋同度;最后,依据λ截矩阵,提取出Voronoi邻近、非Voronoi邻近关系支持下的强趋同点模式。试验以云南省腾冲市居民点数据为算例,经与点模式构建的聚类方法对比、趋同度计算与强趋同提取,验证了该方法的可行性与有效性。

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,ab br.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 toλtruncated 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.