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Abstract: In this study, we introduce a design methodology of polynomial function-based Neural Network (pf-NN) classifiers (predictors). The essential design components include Fuzzy C-Means (FCM) regarded as a generic clustering algorithm and polynomials providing all required nonlinear capabilities of the model. The learning method uses a weighted cost function (objective function) while to analyze the performance of the system we engage a standard receiver operating characteristics (ROC) analysis. The proposed networks are used to detect software defects. From the conceptual standpoint, the classifier of this form can be expressed as a collection of “if-then” rules. Fuzzy clustering (Fuzzy C-Means, FCM) is aimed at the development of premise layer of the rules while the corresponding consequences of the rules are formed by some local polynomials. A detailed learning algorithm for the pf-NNs is presented with particular provisions made for dealing with imbalanced classes encountered quite commonly in software quality problems. The use of simple measures such as accuracy of classification becomes questionable. In the assessment of quality of classifiers, we confine ourselves to the use of the area under curve (AUC) in the receiver operating characteristics (ROCs) analysis. AUC comes as a sound classifier metric capturing a tradeoff between the high true positive rate (TP) and the low false positive rate (FP). The performance of the proposed classifier is contrasted with the results produced by some “standard” Radial Basis Function (RBF) neural networks. [Copyright &y& Elsevier]

Abstract: We investigate a new category of fuzzy-neural networks such as Hybrid Fuzzy Set-based Polynomial Neural Networks (HFSPNN). These networks consist of a genetically optimized multi-layer with two kinds of heterogeneous neurons such as fuzzy set-based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology that helps determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (referred to as gHFSPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of gHFSPNN leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, the structural optimization is realized via GAs, whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFSPNN is demonstrated through intensive experimentation where we use a number of modeling benchmarks—synthetic and experimental datasets are already being used in fuzzy or neurofuzzy modeling. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new architecture of genetic algorithms (GA)-based self-organizing polynomial neural networks (SOPNN) and discuss a comprehensive design methodology. Let us recall that the design of the “conventional” PNNs uses an extended group method of data handling (GMDH) and exploits polynomials (such as linear, quadratic, and modified quadratic functions) as well as considers a fixed number of input nodes (as being selected in advance by a network designer) at polynomial neurons (or nodes) located in each layer. The proposed GA-based SOPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional PNNs. The design procedure applied in the construction of each layer of a PNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomial, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the network. To evaluate the performance of the GA-based SOPNN, the model is experimented with using chaotic time series data. A comparative analysis reveals that the proposed GA-based SOPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature. [Copyright &y& Elsevier]