Clusteirng Structuarl Invairant Research Based On Granular Space

In this paper, fuzzy proximity relations are focused on as main objects based on the granular space theory, and the clustering structural analysis is proposed and discussed. The structure of a fuzzy relation is the essential characteristic. This paper penetrates the key point and emphasizes on the research whether the clustering structure is preserved under a mapping. The problems of isomorphism and similarity are obtained relative to fuzzy proximity relations. This paper is organized as follows:In chapter one, the developments of bioinformatics, granular compute, cluster analysis and fuzzy proximity relation are briefly outlined both at home and abroad. Besides, the main work and innovations of this paper are given.In chapter two, the representation of the granular space, an improving algorithm to compute the clustering structure and the corresponding min-transitive closure of a fuzzy proximity relation based on granular space are firstly given. Besides, the measure about the degree of granulation is shown. Secondly, the minimum dynamic connected graph is built to explain the generation process of the granular space. At the same time, the concept of key point sequence is introduced and other concepts are defined. Finally, the relationship between key point sequence and clustering structural is provided.In chapter three, the clustering structural analysis on protein sequences is given based on the granular space of a fuzzy proximity relation. Firstly, by using the MEGA software and introducing the inner product, the alignment distances of xylanse sequences are transformed into a fuzzy proximity relation. Secondly, its granular space is obtained by applying an algorithm. Finally, the clustering structural analysis on protein sequences and the method for determining optimal number of clusters are given. These researches provide a quantitative tool for analyzing protein sequences.In chapter four, the concept of isomorphism is firstly introduced into fuzzy proximity relations. At the same time, the two clustering structure invariance principles of fuzzy proximity relations by using the key point sequence set are given. Secondly, the clustering structure of a fuzzy proximity relation is illustrated under three typical triangular norms by example. And for given a fuzzy proximity relation, an optimization model is established to obtain the optimal approximation for keeping its clustering structure by the linear combination between its minimum fuzzy proximity relation and min-transitive closure. Thirdly, the concept of ?-similarity is added into fuzzy proximity relations and associative properties are given. Finally, by introducing the concept of the strong ?-similarity, the relationship between the isomorphism and strong ?-similarity of two fuzzy proximity relations is studied. These results provide research tools for the general analysis of clustering structure. These results help us better understand fuzzy proximity relations and clustering structure, and provide theories and methodologies for managing data information.In chapter five, the whole work is summarized and reported. Besides, the ideas and thoughts of further research are pointed out.