Parsimonious Fuzzy Neural Network Research Articles

Data driven modeling based on dynamic parsimonious fuzzy neural network

In this paper, a novel fuzzy neural network termed as dynamic parsimonious fuzzy neural network (DPFNN) is proposed. DPFNN is a four layers network, which features coalescence between TSK (Takagi–Sugeno–Kang) fuzzy architecture and multivariate Gaussian kernels as membership functions. The training procedure is characterized by four aspects: (1) DPFNN may evolve fuzzy rules as new training datum arrives, which enables to cope with non-stationary processes. We propose two criteria for rule generation: system error and ε-completeness reflecting both a performance and sample coverage of an existing rule base. (2) Insignificant fuzzy rules observed over time based on their statistical contributions are pruned to truncate the rule base complexity and redundancy. (3) The extended self organizing map (ESOM) theory is employed to dynamically update the centers of the ellipsoidal basis functions in accordance with input training samples. (4) The optimal fuzzy consequent parameters are updated by time localized least square (TLLS) method that exploits a concept of sliding window in order to reduce the computational burden of the least squares (LS) method. The viability of the new method is intensively investigated based on real-world and artificial problems as it is shown that our method not only arguably delivers more compact and parsimonious network structures, but also achieves lower predictive errors than state-of-the-art approaches.

A Generalized Ellipsoidal Basis Function Based Online Self-constructing Fuzzy Neural Network

In this paper, we propose a Generalized ellipsoidal basis function based online self-constructing fuzzy neural network (GEBF-OSFNN) which extends the ellipsoidal basis function (EBF)-based fuzzy neural networks (FNNs) by permitting input variables to be modeled by dissymmetrical Gaussian functions (DGFs). Due to the flexibility and dissymmetry of left and right widths of the DGF, the partitioning made by DGFs in the input space is more flexible and more interpretable, and therefore results in a parsimonious FNN with high performance under the online learning algorithm. The geometric growing criteria and the error reduction ratio (ERR) method are used as growing and pruning strategies respectively to realize the structure learning algorithm which implements an optimal and compact network structure. The GEBF-OSFNN starts with no hidden neurons and does not need to partition the input space a priori. In addition, all free parameters in premises and consequents are adjusted online based on the ?-completeness of fuzzy rules and the linear least square (LLS) approach, respectively. The performance of the GEBF-OSFNN paradigm is compared with other well-known algorithms like RAN, RANEKF, MRAN, ANFIS, OLS, RBF-AFS, DFNN, GDFNN GGAP-RBF, OS-ELM, SOFNN and FAOS-PFNN, etc., on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification, chaotic time-series prediction and real-world benchmark problems. Simulation results demonstrate that the proposed GEBF-OSFNN approach can facilitate a more powerful and more parsimonious FNN with better performance of approximation and generalization.

AN ONLINE SELF-ORGANIZING SCHEME FOR PARSIMONIOUS AND ACCURATE FUZZY NEURAL NETWORKS

In this paper, an online self-organizing scheme for Parsimonious and Accurate Fuzzy Neural Networks (PAFNN), and a novel structure learning algorithm incorporating a pruning strategy into novel growth criteria are presented. The proposed growing procedure without pruning not only simplifies the online learning process but also facilitates the formation of a more parsimonious fuzzy neural network. By virtue of optimal parameter identification, high performance and accuracy can be obtained. The learning phase of the PAFNN involves two stages, namely structure learning and parameter learning. In structure learning, the PAFNN starts with no hidden neurons and parsimoniously generates new hidden units according to the proposed growth criteria as learning proceeds. In parameter learning, parameters in premises and consequents of fuzzy rules, regardless of whether they are newly created or already in existence, are updated by the extended Kalman filter (EKF) method and the linear least squares (LLS) algorithm, respectively. This parameter adjustment paradigm enables optimization of parameters in each learning epoch so that high performance can be achieved. The effectiveness and superiority of the PAFNN paradigm are demonstrated by comparing the proposed method with state-of-the-art methods. Simulation results on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification and chaotic time-series prediction demonstrate that the proposed PAFNN algorithm can achieve more parsimonious network structure, higher approximation accuracy and better generalization simultaneously.

A fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks

In this paper, we present a fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks (FAOS-PFNN), where a novel structure learning algorithm incorporating a pruning strategy into new growth criteria is developed. The proposed growing procedure without pruning not only speeds up the online learning process but also facilitates a more parsimonious fuzzy neural network while achieving comparable performance and accuracy by virtue of the growing and pruning strategy. The FAOS-PFNN starts with no hidden neurons and parsimoniously generates new hidden units according to the proposed growth criteria as learning proceeds. In the parameter learning phase, all the free parameters of hidden units, regardless of whether they are newly created or originally existing, are updated by the extended Kalman filter (EKF) method. The effectiveness and superiority of the FAOS-PFNN paradigm is compared with other popular approaches like resource allocation network (RAN), RAN via the extended Kalman filter (RANEKF), minimal resource allocation network (MRAN), adaptive-network-based fuzzy inference system (ANFIS), orthogonal least squares (OLS), RBF-AFS, dynamic fuzzy neural networks (DFNN), generalized DFNN (GDFNN), generalized GAP-RBF (GGAP-RBF), online sequential extreme learning machine (OS-ELM) and self-organizing fuzzy neural network (SOFNN) on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification, chaotic time-series prediction and real-world regression problems. Simulation results demonstrate that the proposed FAOS-PFNN algorithm can achieve faster learning speed and more compact network structure with comparably high accuracy of approximation and generalization.