﻿ 基于离散Morse方法的分类规则研究

# 基于离散Morse方法的分类规则研究Classification Rules Based on Discrete Morse Theory

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.

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