Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for...Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.展开更多
Dual clustering performs object clustering in both spatial and non-spatial domains that cannot be dealt with well by traditional clustering methods.However,recent dual clustering research has often omitted spatial out...Dual clustering performs object clustering in both spatial and non-spatial domains that cannot be dealt with well by traditional clustering methods.However,recent dual clustering research has often omitted spatial outliers,subjectively determined the weights of hybrid distance measures,and produced diverse clustering results.In this study,we first redefined the dual clustering problem and related concepts to highlight the clustering criteria.We then presented a self-organizing dual clustering algorithm (SDC) based on the self-organizing feature map and certain spatial analysis operations,including the Voronoi diagram and polygon aggregation and amalgamation.The algorithm employs a hybrid distance measure that combines geometric distance and non-spatial similarity,while the clustering spectrum analysis helps to determine the weight of non-spatial similarity in the measure.A case study was conducted on a spatial database of urban land price samples in Wuhan,China.SDC detected spatial outliers and clustered the points into spatially connective and attributively homogenous sub-groups.In particular,SDC revealed zonal areas that describe the actual distribution of land prices but were not demonstrated by other methods.SDC reduced the subjectivity in dual clustering.展开更多
文摘Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.
基金supported by the National Natural Science Foundation of China(Grant No.40901188)the Key Laboratory of Geo-informatics of the State Bureau of Surveying and Mapping(Grant No.200906)the Fundamental Research Funds for the Central Universities(Grant No.4082002)
文摘Dual clustering performs object clustering in both spatial and non-spatial domains that cannot be dealt with well by traditional clustering methods.However,recent dual clustering research has often omitted spatial outliers,subjectively determined the weights of hybrid distance measures,and produced diverse clustering results.In this study,we first redefined the dual clustering problem and related concepts to highlight the clustering criteria.We then presented a self-organizing dual clustering algorithm (SDC) based on the self-organizing feature map and certain spatial analysis operations,including the Voronoi diagram and polygon aggregation and amalgamation.The algorithm employs a hybrid distance measure that combines geometric distance and non-spatial similarity,while the clustering spectrum analysis helps to determine the weight of non-spatial similarity in the measure.A case study was conducted on a spatial database of urban land price samples in Wuhan,China.SDC detected spatial outliers and clustered the points into spatially connective and attributively homogenous sub-groups.In particular,SDC revealed zonal areas that describe the actual distribution of land prices but were not demonstrated by other methods.SDC reduced the subjectivity in dual clustering.
