概念三元格渐进式构造算法研究

发布时间：2018-05-15 23:23

本文选题：三元概念分析 + 构造算法　；参考：《郑州大学》2017年硕士论文

【摘要】：当今时代科技迅猛发展,互联网上出现了越来越多的三维数据,而形式概念分析是以二维数据为基础的,不能满足对此类数据进行挖掘研究的需求,因此无法从中获取到有价值的信息。随着形式概念分析发展逐渐成熟,三元概念分析作为一种分析三维数据的理论体系,在近几年逐渐受到了许多研究人员的关注。通过对三元概念分析理论研究,可以实现对三维数据中有价值信息的获取,因此对该理论的研究是一个有实用意义的研究课题,这一领域中概念三元格构造算法是实现三元概念分析能够应用到实际工作中的重要基础。从三元概念分析的基本理论入手,本文的主要工作有:(1)提出并证明概念三元格构造算法相关定理。关于定理证明部分,首先提出非三元概念排除定理,在生成三元概念的同时排除非三元概念,同时也证明结合操作能够获得所有的三元概念。其次是三元概念集合完备性的证明,此定理是证明理论的核心内容。最后给出了三元概念之间关系的定理。(2)运用相关定理提出以渐进式方式实现的概念三元格构造算法。在概念格构造算法中,Godin算法是一个重要的渐进式构造算法,本文是在此基础上提出概念三元格渐进式构造算法。该算法首先按照条件集合将三元背景进行分解,每个条件下的所有三元关系为一个单独子表,将此看作一个特殊的形式背景,利用概念格构造算法求每个形式背景下的所有概念,增加方式为对应的条件将概念转换为三元概念,通过给出特定的结合操作逐步地构造多条件下的三元概念集合,最后运用预序关系的定义实现并建立三元概念之间的关系。对已生成三元概念集合的三元背景,在对象集和属性集不变的条件下,增加条件后的新三元背景,利用已生成的三元概念集合经过结合操作来获得新三元背景下的三元概念集合。(3)通过实验对提出的概念三元格渐进式构造算法进行完备性证明及性能分析。本文提出的构造算法经过理论证明和实验分析表明概念三元格是完备的,在论文的最后一部分提出算法中有待改进之处,这些将成为未来工作的重要部分进行深入研究。
[Abstract]:Nowadays, with the rapid development of science and technology, more and more 3D data appear on the Internet, and the formal conceptual analysis is based on two-dimensional data, which can not meet the needs of mining such data. Therefore, no valuable information can be obtained from it. With the development of formal conceptual analysis, ternary conceptual analysis, as a theoretical system for analyzing 3D data, has been paid more and more attention by many researchers in recent years. By studying the theory of ternary conceptual analysis, we can obtain valuable information from three-dimensional data, so the research of this theory is a practical research topic. In this field, the algorithm of constructing concept triples is an important basis for the application of trivariate concept analysis to practical work. Starting with the basic theory of three dimensional concept analysis, the main work of this paper is to propose and prove the relevant theorems of the algorithm for constructing concept triple lattice. In the part of theorem proof, we first put forward the exclusion theorem of non-ternary concept. We also prove that all the ternary concepts can be obtained by combining operation with the generation of ternary concept and the exclusion of non-ternary concept at the same time. The second is the proof of the completeness of the triple concept set, which is the core of the proof theory. Finally, we give the theorem of the relationship between ternary concepts. 2) by using the correlation theorem, we propose an algorithm for constructing concept triples in a progressive way. The Godin algorithm is an important incremental construction algorithm in the concept lattice construction algorithm. The algorithm firstly decomposes the ternary background according to the conditional set, and all the ternary relations under each condition are treated as a special formal background. By using the concept lattice construction algorithm, all the concepts in each formal background are obtained, and the concept is transformed into a ternary concept by the corresponding conditions, and the triple concept set under multiple conditions is constructed step by a specific combined operation. Finally, the relationship between three concepts is realized and established by the definition of preorder relation. For the ternary background of the generated triple concept set, under the condition that the object set and the attribute set are invariant, the new ternary background after the condition is added. The ternary concept set under the new ternary background is obtained by combining operation with the generated triple concept set. The proposed algorithm is proved to be complete and its performance is analyzed by experiments. Through theoretical proof and experimental analysis, the proposed algorithm is proved to be complete. In the last part of this paper, the algorithm needs to be improved, which will become an important part of the future work for further study.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP301.6

【相似文献】