This study is concerned with the concept of Ensemble Fuzzy Radial Basis Function Neural Networks (EFRBFNN) endowed with clustering techniques, polynomial-based LSE/WLSE learning as well as their optimization implemented by Multi-Objective Particle Swarm Optimization (MOPSO). The network architecture of the proposed EFRBFNN classifier is considered three types of clustering techniques and four forms of regression polynomials. The proposed classifier can not only fully capture the local distribution (feature) information contained in the data, but also choose effective network architecture for improving classification performance and compactness. Three classes of clustering techniques (such as iterative self-organizing data analysis techniques algorithm (ISODATA), affinity propagation (AP), and extended K-means) are considered to effectively produce membership degrees based on feature information extraction suitable to fit data characteristics. Least Square Error Estimation (LSE) and Weighted Least Square Error Estimation (WLSE)-based learning with four types of regression polynomials are considered to estimate to coefficients of polynomials. MOPSO is exploited for choosing the effective architecture among different clustering techniques, polynomials, and polynomial-based learning with multi-objective parametric optimization. MOPSO helps achieve a sound compromise between the preferred classification performance and the compactness realized with the aid of four objective functions such as a) classification accuracy (CA), b) complexity of clustering, c) complexity of polynomial and d) sum of squared coefficients (SSC). The improvement and effectiveness of the proposed network architecture are quantified on a basis of the comprehensive experimental results and also a comparative analysis is offered to demonstrate the superiority of the proposed classifier.

本研究关注具有聚类技术的集成模糊径向基函数神经网络 (EFRBFNN) 概念、基于多项式的 LSE/WLSE 学习以及通过多目标粒子群优化 (MOPSO) 实现的优化。所提出的 EFRBFNN 分类器的网络架构被认为是三种类型的聚类技术和四种形式的回归多项式。所提出的分类器不仅可以充分捕捉数据中包含的局部分布（特征）信息，而且可以选择有效的网络架构来提高分类性能和紧凑性。三类聚类技术（如迭代自组织数据分析技术算法（ISODATA）、亲和传播（AP）、和扩展的K-means）被认为是基于适合数据特征的特征信息提取有效地产生隶属度。考虑使用四种类型的回归多项式的最小二乘误差估计（LSE）和加权最小二乘误差估计（WLSE）来估计多项式的系数。MOPSO 被用于在不同的聚类技术、多项式和基于多项式的多目标参数优化学习中选择有效的架构。MOPSO 借助四个目标函数（例如 a) 分类精度 (CA)、b) 聚类的复杂性、c) 多项式的复杂性和 d) 平方系数之和，有助于在首选分类性能和实现的紧凑性之间取得良好的折衷（SSC）。