In data mining from transaction DB, the relationships between the attributes have been focused, but the relationships between the tuples have not been taken into account. In spatial database, there are relationships b...In data mining from transaction DB, the relationships between the attributes have been focused, but the relationships between the tuples have not been taken into account. In spatial database, there are relationships between the attributes and the tuples, and most of the associations occur between the tuples, such as adjacent, intersection, overlap and other topological relationships. So the tasks of spatial data association rules mining include mining the relationships between attributes of spatial objects, which are called as vertical direction DM, and the relationships between the tuples, which are called as horizontal direction DM. This paper analyzes the storage models of spatial data, uses for reference the technologies of data mining in transaction DB, defines the spatial data association rule, including vertical direction association rule, horizontal direction association rule and two-direction association rule, discusses the measurement of spatial association rule interestingness, and puts forward the work flows of spatial association rule data mining. During two-direction spatial association rules mining, an algorithm is proposed to get non-spatial itemsets. By virtue of spatial analysis, the spatial relations were transferred into non-spatial associations and the non-spatial itemsets were gotten. Based on the non-spatial itemsets, the Apriori algorithm or other algorithms could be used to get the frequent itemsets and then the spatial association rules come into being. Using spatial DB, the spatial association rules were gotten to validate the algorithm, and the test results show that this algorithm is efficient and can mine the interesting spatial rules.展开更多
In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided...In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.展开更多
基金The work is supported by Natural Science Foundatiion of Chongqing (No .CSTC 2005BB2065)
文摘In data mining from transaction DB, the relationships between the attributes have been focused, but the relationships between the tuples have not been taken into account. In spatial database, there are relationships between the attributes and the tuples, and most of the associations occur between the tuples, such as adjacent, intersection, overlap and other topological relationships. So the tasks of spatial data association rules mining include mining the relationships between attributes of spatial objects, which are called as vertical direction DM, and the relationships between the tuples, which are called as horizontal direction DM. This paper analyzes the storage models of spatial data, uses for reference the technologies of data mining in transaction DB, defines the spatial data association rule, including vertical direction association rule, horizontal direction association rule and two-direction association rule, discusses the measurement of spatial association rule interestingness, and puts forward the work flows of spatial association rule data mining. During two-direction spatial association rules mining, an algorithm is proposed to get non-spatial itemsets. By virtue of spatial analysis, the spatial relations were transferred into non-spatial associations and the non-spatial itemsets were gotten. Based on the non-spatial itemsets, the Apriori algorithm or other algorithms could be used to get the frequent itemsets and then the spatial association rules come into being. Using spatial DB, the spatial association rules were gotten to validate the algorithm, and the test results show that this algorithm is efficient and can mine the interesting spatial rules.
文摘In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.
