The Study Of Concept Lattices And Visualization

Concept Lattices was put forward by Professor Wille of Germany at first in 1982. Because concept lattices have a good mathematic nature and the characteristics is suitable for batch processing, so it has been developing rapidly. At the present, the theory is applied in variety of fields including machine learning, information retrieval, digital library, software engineering and knowledge discovery, etc.As the central data structure in Formal Concept Analysis, the concept lattices describes the connection between objects and attributes in essence, and performs conceptual connections between generalization and specialization of formal concepts. The Hasse diagram of a concept lattice implements knowledge visualization.Concept lattice visualization provides an intuitionist method for analyzing and observing the internal relation of knowledge components. But the automatic layout of the concept lattice is quite difficult. There are two kinds of main layout means, one is the manual, and another one is the automatic. The advantage of the layout of manual method can revise each node position according to people's aesthetic opinion so as to obtain a high quality diagram of concept lattices. But the manual method takes too much time; therefore, how to utilize the computer to carry on the automatic layout of the concept lattice is paid close attention by researchers.The greatest difficulty is how to draw an arbitrary lattice as elegantly as possible. There are many studies on layout of concept lattice. However, they adopt in common plane diagram to display the result. Due to inherent characteristics of concept lattices in expanding in space, 3-D display and interoperation should be themore suitable solution for concept lattices visualization. It becomes a novel research topic how to not only display concept lattice elegantly but also allow convenient interoperation in three-dimensions space.This dissertation presents a 3-D visualization policy of concept lattices. This paper discusses the problems and solutions by analyzing the procedure of 3-D display and process, and performs the implementation.The main contents of the dissertation includes,1. Brief introduction of fundamental notions including definitions relevant to concept lattices and visualization.2. Some processing forms for visualization of concept lattices.3. The Methodology of the automatic layout of the concept lattice and corresponding mathematic model.4. 3-D visualization policy and implementation.