The Study Of Mutual Transformation Between Attribute Topology And Concept Lattice

Based on mathematical concepts and conceptual hierarchies, formal concept analysis(FCA), a discipline which focuses on the research of attributes, is a powerful tool for data analysis and knowledge processing. As a core data structure of FCA, concept lattice shows the generalization-specialization relationship between concepts. As a new method to represent the formal context, attribute topology shows the relationships between concepts intuitively and has attracted widespread attention. To ensure the comprehensive compatibility between attribute topology and FCA, this paper carries out the following studies:Firstly, this paper researches attribute topology further and presents some new notions such as Pseudo-parent attribute pairs. Then, global formal concepts searching of attribute topology algorithm is proposed with the basic idea of Depth First Search. This method, firstly constructs the attribute topology into a hierarchized topology, with four levels and fixed start and end points. Then, according to certain rules, all attributes of the hierarchized topology are sorted. Finally, limited by the constraints and calculation rules, this method explores and backtracks the sorted vertices, repetitively, completing the traversal of all paths between the global start and end points. The global formal concepts searching of attribute topology algorithm, an important step of mutual transformation between attribute topology and concept lattice, is a prerequisite for transformation.Secondly, Beyond the theory that attribute topology and formal lattice are uniquely correspond, each vertex, in which path from global formal concepts searching of attribute topology algorithm, can be treated as a formal concept, completing a concept tree. Different sorted vertices can be generated beyond above rules, leading to different concept trees, and based on this, the transformation feasibility from concept tree to concept lattice is been demonstrated by mathematical methods. Based on the concept tree, the transformation relationship between attribute topology and concept lattice has been proved and transformation algorithm has been advanced.Finally, based on the mutual transformation between attribute topology and concept lattice, the evaluation sheet of accomplishment degree on the graduation requirements of Electronic and Information Engineering of Yanshan University is selected as the test da-taset. The pretreated formal context and hierarchized attribute topology are generated, then concept lattice is generated, according to the global formal concepts searching of attribute topology algorithm. According to the comprehensive analysis of the experimental process and results, the feasibility of the transformation between attribute topology and concept lattice is been demonstrated, and the significance of dataset is been evaluated objectively.