基于离散Morse方法的分类规则研究

Classification Rules Based on Discrete Morse Theory

摘要: 随着离散Morse方法的出现和发展，其应用也越来越广泛，主要领域有拓扑学、计算机图形学和几何建模等。分类规则挖掘则是通过对训练样本数据集的学习构造分类规则的过程，是数据挖掘、知识发现的一个重要方面。分类规则挖掘的实质是希望得到高准确性、有趣的和易于理解的分类规则。本文利用离散Morse方法构造分类器，从大量数据中选出人们感兴趣的有用信息。首先综述了数据挖掘和离散Morse方法的相关理论知识，描述了Hasse图、离散梯度向量域和离散Morse函数三者之间的关系，并介绍了构建离散梯度向量域和离散Morse函数的算法。最后针对分类的挖掘问题，构造了关于分类规则的单纯复形，并利用离散Morse方法分析解决了关于分类规则的问题，并通过例证表明了该方法的可行性和高效性。

Abstract: With the emergence and development of discrete Morse theory, it has been widely applied, such as Topology, Computer Graphics and geometric modeling. Classification mining is the process of learning through the training sample data set to construct classification rules, and is an important aspect of data mining, knowledge discovery. The essence of the classification mining is to get high accuracy, interesting and easy to understand classification rules. In this paper, discrete Morse Theory is used to construct classifier, Purpose is to elect the useful information which people interested in from large amounts of data. First we summarizes the relevant theoretical knowledge about data mining and discrete Morse theory, describes the relationship between the Hasse diagram, discrete gradient vector field and discrete Morse function, and describes the algorithm to build a discrete gradient vector field and discrete Morse function. Finally, for the problem of classification mining, we construct the simplicial complex about the classification rules, use the discrete Morse theory to solve the problem of classification rules, and show the feasibility and efficiency of the method through the example.