Granular Computing Based On Quotient Space And Its Application In KDD

With the advent of information era, research of the methods of information processing is becoming much more important. As a kind of information processing method, granular computing technique has been deepened into different subject areas. When compared with other granular computing methods, the problem to be solved can be abstracted from different granularity world under the method of quotient space which is based on quotient set. The problem can be solved not only from its inner or local part, but also can be analyzed and processed from its outline or overall by this method.In this thesis, both the method of granular computing in quotient space and the problem of clustering analysis in fuzzy quotient space are studied, the application problem of granular computing idea in data mining is also discussed, such as bipartite graph matching and multi-dimensional clustering.The main contents of the thesis are as follows:1. Based on discussion of the theory of quotient space and fuzzy quotient space, an important property associated the cross-sectional relationship and quotient space is proved. When this property is used, fuzzy granularity concept can be extended into generalized granularity, a hierarchical structure of a problem can be defined by the measure of distance to construct fuzzy quotient space.2. Based on the research of quotient space model, the property of algorithm about the network-coverage has been summarized when the completely maximum sub-net (or sub-graph) being searched as a cover. And even more, a weak condition of the algorithm has been analyzed and proved in the view of running. Based on this, the shortest network path algorithm based on coverage model of quotient space network has been researched by the using of the chain of hierarchical quotient space, the idea of its computing procedure in hierarchy and the idea of the computing of Yang-hui triangle are compared. 3. Based on the maximal tree method of fuzzy clustering with idea of Kruskal algorithm and the clustering algorithm based on the relation of similarity, the clustering algorithm based on fuzzy quotient space is studied and three clustering methods are analyzed and compared.4. On the algorithm problem of bipartite graph match, the Hungarian algorithm is deeply researched which is used to find the perfect match of bipartite graph by matrix method. The bipartite graph match problem is studied under the tool of auxiliary graph, the Hungarian algorithm is improved and the essence of the optimal solution for assignment problem of Hungarian algorithm is summarized. And then, the application problem of granular computing idea in bipartite graph is studied.5. Based on quotient space theory, three multi-dimensional aggregation algorithms of clustering based on data cube are researched. These three classic and high effective algorithms are analyzed and compared. At last, the application problem of granular computing idea in multi-dimensional aggregation is studied.