面向高维数据的Takagi-Sugeno模糊系统建模新方法

对高维数据进行建模是Takagi-Sugeno(T-S)模糊系统建模面临的一个重大挑战。为此，该文提出一种特征选择与组稀疏编码相结合的模糊系统建模新方法WOMP-GS-FIS。首先，运用一种新型的加权正交匹配追踪算法对原始样本进行特征选择，在此基础上提取出模糊规则前件并产生模糊系统字典；然后，基于组稀疏正则化构造关于后件参数的组稀疏优化问题，在优化问题求解的同时得到重要的模糊规则。实验结果表明，在保证模型泛化性能的前提下，该方法不仅能对所获得的模糊规则结构进行精简还可以进一步减少模糊规则数，进而解决高维数据环境下模糊规则可解释性差的问题。

A Novel Takagi-Sugeno Fuzzy Systems Modeling Method for High Dimensional Data

It is a great challenge to model Takagi-Sugeno(T-S) fuzzy systems on high dimensional data due to the problem of the curse of dimensionality. To this end, a novel T-S fuzzy system modeling method called WOMP-GS-FIS is proposed. The proposed method considers feature selection and group sparse coding simultaneously. Specifically, feature selection is performed by a novel Weighted Orthogonal Matching Pursuit (WOMP) method, based on which the fuzzy rule antecedent part is extracted and the dictionary of the fuzzy system is generated. Then, a group sparse optimization problem based on the group sparse regularization is formulated to obtain the optimal consequent parameters. In this way, the major fuzzy rules are selected by utilizing the group information that existing in the T-S fuzzy systems. The experimental results show that the proposed method can not only simplify the rule,s structure, but also reduce the number of fuzzy rules under the premise of good generalization performance, so as to solve the poor interpretation problem of fuzzy rules on high dimensional data effectively.