优化模糊化因子向量提高模糊C均值算法重构性能
Augmentation of the Reconstruction Performance of Fuzzy C-Means with an Optimized Fuzzification Factor Vector
摘要：
信息粒被认为是粒计算（GrC）的基本结构。模糊C均值（FCM）作为一种有用的无监督学习技术，是构造信息粒最常用的方法之一。基于FCM的颗粒化-脱粒机制在GrC中起着关键作用。在本文中，为了提高质量的脱粒（重建）过程中，我们增加了基于FCM的脱粒机制，通过引入一个矢量的模糊化因子（模糊化因子矢量），并建立一个调整机制来修改原型和分区矩阵。设计被视为一个优化问题，这是指导下的重建准则。在该方案中，初始划分矩阵和原型生成的FCM。然后引入模糊化因子向量，为每一个类构造一个合适的模糊化因子，建立一个修改原型和划分矩阵的调整方案。利用粒度-去粒度过程的监督学习模式，构造了模糊化因子向量、原型和划分矩阵的复合目标函数。随后，粒子群优化算法（PSO）被用来优化模糊化因子向量，以细化原型和开发最佳的分区矩阵。最后，提高了FCM算法的重建性能。我们提供了一个全面的分析开发计划。特别是，我们表明，经典的FCM算法形成一个特殊的情况下，所提出的计划。合成和公开可用的数据集完成的实验表明，所提出的方法优于通用的数据重建方法。
英文摘要：
Information granules have been considered to be the fundamental constructs of Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation-degranulation mechanism plays a pivotal role in GrC. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation-degranulation process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization (PSO) is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.
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