To effectively optimize Takagi-Sugeno-Kang (TSK) fuzzy systems for regression problems, a mini-batch gradient descent with regularization, DropRule, and AdaBound (MBGD-RDA) algorithm was recently proposed. This paper further proposes FCM-RDpA, which improves MBGD-RDA by replacing the grid partition approach in rule initialization by fuzzy c-means clustering, and AdaBound by Powerball AdaBelief, which integrates recently proposed Powerball gradient and AdaBelief to further expedite and stabilize parameter optimization. Extensive experiments on 22 regression datasets with various sizes and dimensionalities validated the superiority of FCM-RDpA over MBGD-RDA, especially when the feature dimensionality is higher. We also propose an additional approach, FCM-RDpAx, that further improves FCM-RDpA by using augmented features in both the antecedents and consequents of the rules.

为了有效地优化 Takagi-Sugeno-Kang (TSK) 模糊系统的回归问题，具有正则化的小批量梯度下降、DropRule 和 AdaBound (MBGD-RDA) 算法最近被提出。本文进一步提出了 FCM-RDpA，它通过模糊 c 均值聚类替换规则初始化中的网格划分方法来改进 MBGD-RDA，以及 Powerball AdaBelief 的 AdaBound，它集成了最近提出的 Powerball 梯度和 AdaBelief 以进一步加速和稳定参数优化. 在 22 个不同大小和维度的回归数据集上进行的大量实验验证了 FCM-RDpA 优于 MBGD-RDA，尤其是在特征维度更高的情况下。我们还提出了一种额外的方法，FCM-RDpAx，它通过在规则的前件和后件中使用增强特征来进一步改进 FCM-RDpA。