用于识别不同模糊度聚类的模糊聚类：一种进化多目标优化方法
Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness: An Evolutionary Multi-Objective Optimization Approach
AI总结：
针对模糊聚类模糊度参数需适配应用的问题，提出熵c均值方法，通过NSGA-II和MOEA/D优化两个矛盾目标以生成不同模糊度聚类，还提出帕累托前沿折中选择法，实验证明其聚类检测效果优于传统及现有多目标模糊聚类方法。
摘要：
模糊聚类方法用于识别数据集中自然存在的聚类，不同聚类的重叠程度可能存在差异。大多数方法都设有一个固定模糊度的参数，但合适的模糊度取决于具体应用场景。本文提出了熵c均值（Entropy $c$-Means, ECM）方法，这是一种同时优化两个相互矛盾的目标函数的模糊聚类方法，能够生成具有不同模糊度的模糊聚类，使得ECM可以识别不同重叠程度的聚类。ECM采用两种多目标优化方法来优化这两个目标函数，分别是非支配排序遗传算法II（Non-dominated Sorting Genetic Algorithm II, NSGA-II）和基于分解的多目标进化算法（Multiobjective Evolutionary Algorithm based on Decomposition, MOEA/D）。我们还提出了一种从帕累托前沿中选择合适折中聚类结果的方法。在具有挑战性的合成数据集以及真实世界数据集上的实验表明，与传统模糊聚类方法以及此前用于模糊聚类的多目标方法相比，ECM的聚类检测效果更优。
英文摘要：
Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents Entropy $c$-Means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multi-objective optimization methods, Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D). We also propose a method to select a suitable trade-off clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multi-objective methods for fuzzy clustering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
