A PSO-Based Fuzzy c-Regression Model Applied to Nonlinear Data Modeling

2015 ◽  
Vol 23 (06) ◽  
pp. 881-891 ◽  
Author(s):  
Moez Soltani ◽  
Abdelkader Chaari
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Regression Models ◽  
Clustering Algorithm ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Identification Procedure ◽  
Swarm Optimization

This paper presents a new method for fuzzy c-regression models clustering algorithm. The main motivation for this work is to develop an identification procedure for nonlinear systems using weighted recursive least squares and particle swarm optimization. The fuzzy c-regression models algorithm is sensitive to initialization which leads to the convergence to a local minimum of the objective function. In order to overcome this problem, particle swarm optimization is employed to achieve global optimization of FCRM and to finally tune parameters of obtained fuzzy model. The weighted recursive least squares is used to identify the unknown parameters of the local linear model. Finally, validation results involving simulation of two examples have demonstrated the effectiveness and practicality of the proposed algorithm.

scholarly journals A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

2012 ◽  
Vol 22 (3) ◽  
pp. 617-628 ◽  
Author(s):  
Moêz Soltani ◽  
Abdelkader Chaari ◽  
Fayçal Ben Hmida
Keyword(s):  
Particle Swarm Optimization ◽  
Regression Model ◽  
Objective Function ◽  
Clustering Algorithm ◽  
Least Squares Method ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Unknown Parameters ◽  
Swarm Optimization ◽  
Error Measure

Abstract This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.

scholarly journals Training High-Order Takagi-Sugeno Fuzzy Systems Using Batch Least Squares and Particle Swarm Optimization

2019 ◽  
Vol 22 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Krzysztof Wiktorowicz ◽  
Tomasz Krzeszowski
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Piecewise Linear ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Takagi Sugeno

AbstractThis paper proposes two methods for training Takagi–Sugeno (T-S) fuzzy systems using batch least squares (BLS) and particle swarm optimization (PSO). The T-S system is considered with triangular and Gaussian membership functions in the antecedents and higher-order polynomials in the consequents of fuzzy rules. In the first method, the BLS determines the polynomials in a system in which the fuzzy sets are known. In the second method, the PSO algorithm determines the fuzzy sets, whereas the BLS determines the polynomials. In this paper, the ridge regression is used to stabilize the solution when the problem is close to the singularity. Thanks to this, the proposed methods can be applied when the number of observations is less than the number of predictors. Moreover, the leave-one-out cross-validation is used to avoid overfitting and this way to choose the structure of a fuzzy model. A method of obtaining piecewise linear regression by means of the zero-order T-S system is also presented.

A novel weighted recursive least squares based on Euclidean particle swarm optimization

Kybernetes ◽  
2013 ◽  
Vol 42 (2) ◽  
pp. 268-281 ◽  
Author(s):  
Moêz Soltani ◽  
Abdelkader Chaari
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Learning Algorithm ◽  
Particle Swarm ◽  
New Method ◽  
Recursive Least Squares ◽  
Swarm Optimization ◽  
Content Type ◽  
Initial States ◽  
Two Phases

PurposeThe purpose of this paper is to present a new methodology for identification of the parameters of the local linear Takagi‐Sugeno fuzzy models using weighted recursive least squares. The weighted recursive least squares (WRLS) is sensitive to initialization which leads to no converge. In order to overcome this problem, Euclidean particle swarm optimization (EPSO) is employed to optimize the initial states of WRLS. Finally, validation results are given to demonstrate the effectiveness and accuracy of the proposed algorithm. A comparative study is presented. Validation results involving simulations of numerical examples and the liquid level process have demonstrated the practicality of the algorithm.Design/methodology/approachA new method for nonlinear system modelling. The proposed algorithm is employed to optimize the initial states of WRLS algorithm in two phases of learning algorithm.FindingsThe results obtained using this novel approach were comparable with other modeling approaches reported in the literature. The proposed algorithm is able to handle various types of modeling problems with high accuracy.Originality/valueIn this paper, a new method is employed to optimize the initial states of WRLS algorithm in two phases of the learning algorithm.

scholarly journals Data and Feature Reduction in Fuzzy Modeling through Particle Swarm Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
S. Sakinah S. Ahmad ◽  
Witold Pedrycz
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Fuzzy Model ◽  
Fuzzy Rule ◽  
Search Space ◽  
Fuzzy Modeling ◽  
Optimization Techniques ◽  
Feature Reduction ◽  
Data Sets ◽  
Swarm Optimization

The study is concerned with data and feature reduction in fuzzy modeling. As these reduction activities are advantageous to fuzzy models in terms of both the effectiveness of their construction and the interpretation of the resulting models, their realization deserves particular attention. The formation of a subset of meaningful features and a subset of essential instances is discussed in the context of fuzzy-rule-based models. In contrast to the existing studies, which are focused predominantly on feature selection (namely, a reduction of the input space), a position advocated here is that a reduction has to involve both data and features to become efficient to the design of fuzzy model. The reduction problem is combinatorial in its nature and, as such, calls for the use of advanced optimization techniques. In this study, we use a technique of particle swarm optimization (PSO) as an optimization vehicle of forming a subset of features and data (instances) to design a fuzzy model. Given the dimensionality of the problem (as the search space involves both features and instances), we discuss a cooperative version of the PSO along with a clustering mechanism of forming a partition of the overall search space. Finally, a series of numeric experiments using several machine learning data sets is presented.

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