基于正则化的模糊 C - 均值聚类算法及其在T - S 模糊系统辨识问题中的应用
Fuzzy C-means Clustering Algorithm Based Regularization and
Its Application in the Problem of T-S Fuzzy System Identification
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摘要: 在模糊 C - 均值聚类问题目标函数中使用正则化泛函, 将聚类中心解的误差指标引入到模糊聚类的目标函数中, 构造出新的模糊 C - 均值聚类算法 R B F CM ( R e g u l a r i z a t i o nb a s e dF u z z yC - m e a n s ) 算法 . 算法R B F CM 不仅具有较高的聚类精度, 且计算结果具有更好的稳定性 . 进一步, 将此 R B F CM 算法应用于基于 T - S模糊模型的系统辨识问题 . 由于 R B F CM 算法优化了模糊系统的输入空间划分, 提高了隶属度函数的精度, 使得后继得到的 T - S 模糊系统辨识精度也有所提高, 且系统辨识过程的收敛速度也有所改善 . 最后, 通过对经典I R I S 数据集、 带有噪声的 I R I S 数据集的聚类算例和对 B o x - J e n k i n s 煤气炉数据集进行辨识算例, 验证了 R B F -CM 算法的有效性和优越性 .Abstract: A new fuzzy C-means clustering algorithm (RBFCM, Regularization based Fuzzy C-means) algorithm was established by adding a regularization functional, which was constructed by the errors of clustering centers, in the objective function of fuzzy C-means clustering algorithm. Algorithm RBFCM could not only achieve high clustering accuracy, but also stable the computed results. Furthermore, the obtained RBFCM algorithm was applied in T-S fuzzy model based on system identification problem. Because of the optimized partition of the input space and the improved membership functions, the accuracy of the solution and the convergence speed of the followed T-S fuzzy system identification process were improved too. Finally, the validity and advances of RBFCM algorithm were illustrated by the cluster examples of IRIS data set and the noised IRIS data set and the identification example of Box-Jenkins gas furnace data set.
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