A New Criterion for Improving Convergence of Fuzzy C-Means Clustering

IF 1.9 3区 数学 Q1 MATHEMATICS, APPLIED
Axioms Pub Date : 2024-01-02 DOI:10.3390/axioms13010035
J. Pérez-Ortega, Carlos Fernando Moreno-Calderón, Sandra Silvia Roblero-Aguilar, N. N. Almanza-Ortega, J. Frausto-Solís, Rodolfo Pazos-Rangel, J. M. Rodríguez-Lelis
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Abstract

One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.
提高模糊 C-Means 聚类收敛性的新标准
模糊 C-Means 算法是解决模糊聚类问题最常用的算法之一,但其主要局限性之一是计算复杂度较高。众所周知,算法的效率取决于初始化和收敛策略等因素。本研究提出了一种新的收敛策略,该策略基于连续两次迭代中目标函数值的差值,用下一次到最后一次迭代中目标函数值的百分比表示。此外,还提出了一种新方法来优化算法收敛或停止阈值的选择,该方法基于帕累托原则。为了验证我们的方法,我们对一系列真实数据集进行了求解,结果发现迭代次数显著减少,而求解质量没有受到明显影响。根据所提出的方法和所进行的实验,我们发现,如果希望迭代次数分别减少约 75.2% 和 64.56%,而解决方案的质量分别降低 2% 和 1%,那么使用等于 0.73 和 0.35 的阈值是比较方便的。值得一提的是,随着数据集规模的扩大,所提出的方法往往能获得更好的结果,因此建议将其用于大数据和数据科学中的数据集。
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来源期刊
Axioms
Axioms Mathematics-Algebra and Number Theory
自引率
10.00%
发文量
604
审稿时长
11 weeks
期刊介绍: Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.
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