<p>Evolving (Fuzzy and Neuro-Fuzzy) Systems are known for expanding or contracting their structure and updating their parameters on the fly in a single pass, eventually in real-time, to react to process drifts while obtaining the output. The system’s structure can be adjusted by creating, merging, splitting, deleting, or updating its structural components, such as rules, clusters, neurons, granules, leaves, or clouds. On the other hand, the consequent (output weight) parameters can be updated using modeling and optimization methods. Typically, in an Evolving System, the consequent parameters are updated using the recursive least square algorithm or its variations. This paper provides a comprehensive analysis of recursive learning methods used to update the consequent parameters in Evolving Systems. Seven methods are detailed and revisited, namely Recursive Least Squares (RLS), Weighted Recursive Least Squares (WRLS), Recursive Weighted Total Least Squares (RWTLS), Multi-Innovations Recursive Weighted Least Squares (MI), Kernel Recursive Least Squares (KRLS), Recursive Maximum Correntropy (RMC), and Gradient Descent (GD). These seven approaches were implemented in three distinct Evolving Systems and compared in ten data stream regression tasks. The experimental results suggest that the WRLS achieved the average best performance, followed by RMC and RLS. The study also indicates that there is no one-size-fits-all or universally optimal method for updating consequent parameters across all Evolving Systems and datasets. Future work should prioritize developing methods focusing on accuracy and computational efficiency, especially in high-dimensional data streams. Additionally, research should explore robust approaches to handle noise and context changes, ensuring consistent performance across various conditions.</p>

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Recursive methods for updating consequent parameters in evolving fuzzy systems: a comprehensive review with computational experiments

  • Fernanda P. S. Rodrigues,
  • Alisson Marques Silva

摘要

Evolving (Fuzzy and Neuro-Fuzzy) Systems are known for expanding or contracting their structure and updating their parameters on the fly in a single pass, eventually in real-time, to react to process drifts while obtaining the output. The system’s structure can be adjusted by creating, merging, splitting, deleting, or updating its structural components, such as rules, clusters, neurons, granules, leaves, or clouds. On the other hand, the consequent (output weight) parameters can be updated using modeling and optimization methods. Typically, in an Evolving System, the consequent parameters are updated using the recursive least square algorithm or its variations. This paper provides a comprehensive analysis of recursive learning methods used to update the consequent parameters in Evolving Systems. Seven methods are detailed and revisited, namely Recursive Least Squares (RLS), Weighted Recursive Least Squares (WRLS), Recursive Weighted Total Least Squares (RWTLS), Multi-Innovations Recursive Weighted Least Squares (MI), Kernel Recursive Least Squares (KRLS), Recursive Maximum Correntropy (RMC), and Gradient Descent (GD). These seven approaches were implemented in three distinct Evolving Systems and compared in ten data stream regression tasks. The experimental results suggest that the WRLS achieved the average best performance, followed by RMC and RLS. The study also indicates that there is no one-size-fits-all or universally optimal method for updating consequent parameters across all Evolving Systems and datasets. Future work should prioritize developing methods focusing on accuracy and computational efficiency, especially in high-dimensional data streams. Additionally, research should explore robust approaches to handle noise and context changes, ensuring consistent performance across various conditions.