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

TL;DR

This paper tackles the interpretability and rule explosion of ANFIS when handling low-dimensional data by introducing a two-stage reduction that first applies PCA to normalized firing strengths and then uses Binary Particle Swarm Optimization to select the most informative components. The proposed ANFIS-PCA-BPSO framework embeds this reduction between ANFIS layers and incorporates adaptive updates to BPSO parameters to maintain performance while minimizing rule growth and training time. Extensive experiments on UCI/KEEL benchmarks for classification and regression, plus a real ischemic stroke dataset, show that the method substantially reduces the rule base and training time with competitive or improved accuracy, advancing interpretable AI for practical domains like healthcare and finance. Overall, the work demonstrates a robust, generalizable approach to balancing interpretability and accuracy in fuzzy-rule-based models through principled feature reduction and metaheuristic rule selection, including a compelling real-world application.

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.

Figures (8)

• Figure 1: Main Challenges in ANFIS.
• Figure 2: Detailed Traditional ANFIS Architecture with Five Distinct Layers, where the squared nodes refer to the adaptive nodes and the circle nodes refer to the fixed nodes.
• Figure 3: The architecture of the proposed ANFIS-PCA-BPSO, showing the addition of the two stages of PCA and BPSO between layers 3 and 4.
• Figure 4: Comparative Evaluation of ANFIS and ANFIS-PCA-BPSO Models on Various Classification Datasets.
• Figure 5: Comparative Evaluation of ANFIS and ANFIS-PCA-BPSO Models on Various Regression Datasets.