Hierarchical Fuzzy Topological System for High-Dimensional Data Regression Problems

High-dimensional data regression presents significant challenges due to factors such as strong nonlinearity among features, an excessive number of intermediate variables, and rule explosion, all of which hinder the model's ability to capture complex features and achieve low regression accuracy. This paper proposes a method for high-dimensional data regression using a Hierarchical Fuzzy Topological System (HFTS). The HFTS adopts a modular design, where each layer consists of an independent fuzzy logic system, enabling flexible operation based on feature distribution and output requirements. It utilizes a Graph Neural Network (GNN)-based hierarchical feature classification approach to group high-dimensional data, mapping features into nodes and establishing edges based on similarity. This process creates a topological structure that facilitates high-density feature representation through neighborhood aggregation. HFTS introduces a cross-layer rule-sharing mechanism and an interpolation expansion algorithm to smooth fuzzy rules, thereby reducing interaction complexity. Additionally, an adaptive weight adjustment strategy dynamically optimizes feature importance, enhancing both robustness and predictive accuracy. When applied to eleven KEEL regression datasets, HFTS demonstrates superior accuracy, effectively addressing high-dimensional interactions while maintaining a balance between interpretability and performance