【作者】 马骏；

【导师】 沈夏炯；

【作者基本信息】 河南大学 ， 应用数学， 2005， 硕士

【摘要】 概念格是由德国的Wille教授于1982年首先提出的,由于概念格具有良好的数学性质和适合批处理等特点,因此发展非常迅速,目前已经在机器学习、信息检索、数字图书馆、软件工程和知识发现等方面得到了广泛应用。 概念格作为形式概念分析中核心的数据结构,本质上描述了对象和特征之间的联系,表明了概念之间的泛化与例化关系,其相应的布局图(Hasse图)则实现了对数据的可视化。 概念格的可视化给人们提供了直观的分析与观察知识单元内在关系的方法,然而概念格的布局却是相当困难的。在概念格的图形表示中,有两种主要的布局手段,一种是手工布局,另一种是利用计算机自动布局。手工布局的优点是能够根据人们的审美观去修改每个节点的位置,从而得到一种高质量的概念格图形。然而手工布局费时费力,效率不高。因此如何利用计算机进行概念格的自动布局自然受到了人们的高度重视。 自动布局的最大困难在于如何尽可能“美观”地显示任意给定的概念格。目前概念格的自动布局研究有很多,然而,它们共同的特点是都采用了平面成像的策略。由于概念格的结构决定了它的空间伸展特性,因此,三维显示和互操作应该是概念格可视化更加合适的解决方案。在三维空间中,如何既能“美观”地显示概念格又能方便地实现概念格的人机交互操作,成为一个新的研究课题。 本文提出了概念格的三维可视化策略,文中主要讨论了相关概念和几种常用可视化表示形式,并通过对概念格三维可视化的分析,着重论述了三维空间中的层次布局与层内节点布局问题及解决方案,并加以实现。 论文主要内容包括: 1、概念格的理论基础简介,包括与概念格及其可视化相关的一些定义。 2、概念格可视化处理的各种形式。 3、概念格自动布局的方法和相关的数学描述。 4、概念格的三维可视化策略及其实现问题。更多还原

【Abstract】 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.更多还原