Hierarchical Structured Sparse Representation for T–S Fuzzy Systems Identification

“The curse of dimensionality” has become a significant bottleneck for fuzzy system identification and approximation. In this paper, we cast the Takagi-Sugeno (T-S) fuzzy system identification into a hierarchical sparse representation problem, where our goal is to establish a T-S fuzzy system with a minimal number of fuzzy rules, which simultaneously have a minimal number of nonzero consequent parameters. The proposed method, which is called hierarchical sparse fuzzy inference systems ( H-sparseFIS), explicitly takes into account the block-structured information that exists in the T-S fuzzy model and works in an intuitive way: First, initial fuzzy rule antecedent part is extracted automatically by an iterative vector quantization clustering method; then, with block-structured sparse representation, the main important fuzzy rules are selected, and the redundant ones are eliminated for better model accuracy and generalization performance; moreover, we simplify the selected fuzzy rules consequent with sparse regularization such that more consequent parameters can approximate to zero. This algorithm is very efficient and shows good performance in well-known benchmark datasets and real-world problems.