  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.
