Quantitative analyses and development of a q -incrementation algorithm for FCM with tsallis entropy maximization

IF 1.4 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
M. Yasuda
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引用次数: 2

Abstract

Tsallis entropy is a q-parameter extension of Shannon entropy. By extremizing the Tsallis entropy within the framework of fuzzy c-means clustering (FCM), a membership function similar to the statistical mechanical distribution function is obtained. The Tsallis entropy-based DA-FCM algorithm was developed by combining it with the deterministic annealing (DA) method. One of the challenges of this method is to determine an appropriate initial annealing temperature and a q value, according to the data distribution. This is complex, because the membership function changes its shape by decreasing the temperature or by increasing q. Quantitative relationships between the temperature and q are examined, and the results showthat, in order to change uikq equally, inverse changes must be made to the temperature and q. Accordingly, in this paper, we propose and investigate two kinds of combinatorial methods for q-incrementation and the reduction of temperature for use in the Tsallis entropy-based FCM. In the proposed methods, q is defined as a function of the temperature. Experiments are performed using Fisher's iris dataset, and the proposed methods are confirmed to determine an appropriate q value in many cases.
基于tsallis熵最大化的FCM q增量算法的定量分析与开发
Tsallis熵是Shannon熵的q参数扩展。通过在模糊c均值聚类(FCM)框架内对Tsallis熵进行极化,得到一个类似于统计力学分布函数的隶属函数。将基于Tsallis熵的DA- fcm算法与确定性退火(DA)方法相结合,提出了基于Tsallis熵的DA- fcm算法。该方法的挑战之一是根据数据分布确定合适的初始退火温度和q值。这是很复杂的,因为隶属函数通过降低温度或增加q来改变其形状。研究了温度和q之间的定量关系,结果表明,为了使ukq相等地变化,温度和q必须反向变化。因此,本文提出并研究了两种用于基于Tsallis熵的FCM的q增量和温度降低的组合方法。在提出的方法中,q被定义为温度的函数。使用Fisher的虹膜数据集进行了实验,并在许多情况下证实了所提出的方法可以确定适当的q值。
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来源期刊
Advances in Fuzzy Systems
Advances in Fuzzy Systems MATHEMATICS, APPLIED-
CiteScore
4.10
自引率
7.70%
发文量
15
审稿时长
21 weeks
期刊介绍: Advances in Fuzzy Systems is an international journal which aims to provide a forum for original research articles in the theory and applications of fuzzy subsets and systems. The goal of the journal is to help promote the advances in the development and practice of fuzzy system technologies in the areas of engineering, management, medical, economic, environmental, and societal problems. Advances in Fuzzy Systems is intended to provide a rapid communication of fully refereed papers through the open access publication model, which will enable the journal to reach a far greater audience than traditional subscription-based journals.
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