面向重尾噪声的模糊规则模型

doi:10.13232/j.cnki.jnju.2019.01.006

南京大学学报(自然科学版) ›› 2019, Vol. 55 ›› Issue (1): 61–72.doi: 10.13232/j.cnki.jnju.2019.01.006

面向重尾噪声的模糊规则模型

贾海宁^1,2*，王士同^1,2

1.江南大学数字媒体学院，无锡，214122；2.江苏省媒体设计与软件技术重点实验室，江南大学，无锡，214122

接受日期:2018-12-07 出版日期:2019-02-01 发布日期:2019-01-26
通讯作者: 贾海宁, E－mail：jayazle@163.com E-mail:jayazle@163.com
基金资助:
国家自然科学基金(61772198)

Rule－based fuzzy model for heavy－tailed noisy data

Jia Haining^1,2*，Wang Shitong^1,2

1.School of Digital Media，Jiangnan University，Wuxi，214122，China；2.Key Laboratory of Media Design and Software Technology of Jiangsu Province，Jiangnan University，Wuxi，214122，China

Accepted:2018-12-07 Online:2019-02-01 Published:2019-01-26
Contact: Jia Haining, E－mail：jayazle@163.com E-mail:jayazle@163.com

摘要/Abstract

摘要： 针对一般模糊规则模型对含有重尾噪声的数据集鲁棒性较差的问题，提出了面向重尾噪声的模糊规则(Rule－based Fuzzy Model for Heavy－tailed Noisy Data，HtRbF)模型. 该模型使用了两种新的聚类方法，学生t分布均值聚类算法(Student’s t－distribution C－Means，StCM)和学生t分布下的背景模糊聚类方法(Student’s t－distribution Context Fuzzy C－Means，StCFCM)，并将其应用在初始规则和新规则的生成中，使模型在重尾噪声场景下生成更为准确的规则，有效减少了模型的输出误差，使其更接近真实输出. HtRbF模型具有良好的抗噪能力，通过对数据集添加不同类型的重尾噪声进行系统性实验，实验结果证明了HtRbF模型的有效性．

关键词: 重尾噪声, 学生t分布, 模糊规则, 学生t分布模糊聚类, 学生t分布背景模糊聚类

Abstract: Based on student’s t－distribution，a novel rule－based fuzzy model called Rule－based Fuzzy Model for Heavy－tailed Noisy Data(HtRbF)with strong robustness to heavy－tailed noisy data is proposed in this paper. In the proposed model HtRbF，both Student’s t－distribution C－Means(StCM)and Student’s t－distribution Context Fuzzy C－Means(StCFCM)are designed to generate initial fuzzy rules and their refined fuzzy rules so as to make the proposed model more accurate for heavy tailed noisy scenes. In the inference part，the proposed model HtRbF estimates the error of each initial fuzzy rule and then refines these fuzzy rules by removing a rule with the maximal error among all initial fuzzy rules. Such a refinement procedure provides a better insight into the design of fuzzy models. The coefficients of the local linear function in the then－part of each fuzzy rule are estimated by the Weighted Least Square Estimation(WLS)method. These linear functions can also be substituted for the quadratic functions in order to improve the accuracy of the proposed model. By adding different heavy－tailed noises to the data sets，our experimental results indicate the effectiveness of the proposed model HtRbF in the sense of both promising performance and satisfactory anti－noise effect.

Key words: heavy－tailed noise, Student’s t－distribution, fuzzy rules, Student’s t－distribution C－Means, Student’s t－distribution Context Fuzzy C－Means

中图分类号:

TP181

贾海宁, 王士同. 面向重尾噪声的模糊规则模型[J]. 南京大学学报(自然科学版), 2019, 55(1): 61–72.

Jia Haining, Wang Shitong. Rule－based fuzzy model for heavy－tailed noisy data[J]. Journal of Nanjing University(Natural Sciences), 2019, 55(1): 61–72.

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面向重尾噪声的模糊规则模型

Rule－based fuzzy model for heavy－tailed noisy data

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