Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive latt...Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and展开更多
Many classical clustering algorithms do good jobs on their prerequisite but do not scale well when being applied to deal with very large data sets(VLDS).In this work,a novel division and partition clustering method(DP...Many classical clustering algorithms do good jobs on their prerequisite but do not scale well when being applied to deal with very large data sets(VLDS).In this work,a novel division and partition clustering method(DP) was proposed to solve the problem.DP cut the source data set into data blocks,and extracted the eigenvector for each data block to form the local feature set.The local feature set was used in the second round of the characteristics polymerization process for the source data to find the global eigenvector.Ultimately according to the global eigenvector,the data set was assigned by criterion of minimum distance.The experimental results show that it is more robust than the conventional clusterings.Characteristics of not sensitive to data dimensions,distribution and number of nature clustering make it have a wide range of applications in clustering VLDS.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Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and
基金Projects(60903082,60975042)supported by the National Natural Science Foundation of ChinaProject(20070217043)supported by the Research Fund for the Doctoral Program of Higher Education of China
文摘Many classical clustering algorithms do good jobs on their prerequisite but do not scale well when being applied to deal with very large data sets(VLDS).In this work,a novel division and partition clustering method(DP) was proposed to solve the problem.DP cut the source data set into data blocks,and extracted the eigenvector for each data block to form the local feature set.The local feature set was used in the second round of the characteristics polymerization process for the source data to find the global eigenvector.Ultimately according to the global eigenvector,the data set was assigned by criterion of minimum distance.The experimental results show that it is more robust than the conventional clusterings.Characteristics of not sensitive to data dimensions,distribution and number of nature clustering make it have a wide range of applications in clustering VLDS.
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.
