Rule-Based Modeling of Low-Dimensional Data with PCA and Binary Particle Swarm Optimization (BPSO) in ANFIS

Abstract: Fuzzy rule-based systems interpret data in low-dimensional domains, providing transparency and interpretability. In contrast, deep learning excels in complex tasks like image and speech recognition but is prone to overfitting in sparse, unstructured, or low-dimensional data. This interpretability is crucial in fields like healthcare and finance. Traditional rule-based systems, especially ANFIS with grid partitioning, suffer from exponential rule growth as dimensionality increases. We propose a strategic rule-reduction model that applies Principal Component Analysis (PCA) on normalized firing strengths to obtain linearly uncorrelated components. Binary Particle Swarm Optimization (BPSO) selectively refines these components, significantly reducing the number of rules while preserving precision in decision-making. A custom parameter update mechanism fine-tunes specific ANFIS layers by dynamically adjusting BPSO parameters, avoiding local minima. We validated our approach on standard UCI respiratory, keel classification, regression datasets, and a real-world ischemic stroke dataset, demonstrating adaptability and practicality. Results indicate fewer rules, shorter training, and high accuracy, underscoring the methods effectiveness for low-dimensional interpretability and complex data scenarios. This synergy of fuzzy logic and optimization fosters robust solutions. Our method contributes a powerful framework for interpretable AI in multiple domains. It addresses dimensionality, ensuring a rule base.