Research On 3D Concept Lattice Reconstruction From 2D Concept Lattice

As the main data structure in Formal Concept Analysis, the concept lattices is a powerful instrument of data analyse. Concept lattice visualization provides an intuitionist method for analyzing and observing the internal relationship of knowledge components, but concept lattice visualization with computer is quite difficult. Currently a lot of lattice layout are based on planar graphics. However, while we observe and analyse the internal relationship of knowledge components, it is obvious that 2-D layout will bring the problems of crossing segment and the nodes landscape orientation expanding immoderately. What's more, due to inherent characteristics of concept lattices in expanding in space, 3-D concept lattice not only can avoid the problems, but also should be the more suitable solution for concept lattices visualization. So it becomes a novel research topic how to reconstruction the 2-D concept lattice to 3-D concept lattice and allow convenient interoperation in 3-D space.According to analyzing the model of concept lattice and researching its characteristics of mathematics, a more logical policy of 2-D concept lattice reconstructed to 3-D space is proposed, which is the main purpose of this paper. In this thesis, the definition of formal concept analysis and the algorithm of constructing concept lattice are introduced, it also discusses the modality of lattice visualization nodes layout in 3-D space and the insufficiency. This thesis particularly dissertates the policy of 2-D concept lattice reconstructing to 3-D concept lattice by analyzing the characteristics of concept lattice and layout, and presents the algorithm of 3-D reconstruction, and performs the implementation.The main content of the dissertation includes:1. Brief introduction of fundamental notions including definitions relevant to concept lattices construction and visualization.2. Some processing forms for visualization of concept lattices.3. For the sake of overcoming the shortcomings of 2-D concept lattice graph, this paper particularly discusses the policy of 2-D lattice reconstructing to 3-D lattice, and presents the algorithm of 3-D reconstruction.According to analyzing the algorithm and results of the experiments, the structure of 3-D concept lattice is much better and more beautiful after reconstruction. At the same time, it also solves the disadvantages of 2-D concept lattice graph effectively. Finally, by way of increasing implement speed and improving the readability of concept lattice graph, how to improve and optimize the policy and the algorithm is discussed in this paper.