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In this paper, we propose a polynomial kernel neural network classifier (PKNNC) based on the random sampling and information gain. Random sampling is used here to generate datasets for the construction of polynomial neurons located in the neural networks, while information gain is used to evaluate the importance of the input variables (viz. dataset features) of each neuron. Both random sampling and information gain stem from the concepts of well-known random forest models. Some traditional neural networks have certain limitations, such as slow convergence speed, easily falling to local optima and difficulty describing the polynomial relation between the input and output. In this regard, a general PKNNC is proposed, and it consists of three parts: the premise, conclusion, and aggregation. The method of designing the PKNNC is summarized as follows. In the premise section, random sampling and information gain are used to obtain multiple subdatasets that are passed to the aggregation part, and the conclusion part uses three types of polynomials. In the aggregation part, the least squares method (LSM) is used to estimate the parameters of polynomials. Furthermore, the particle swarm optimization (PSO) algorithm is exploited here to optimize the PKNNC. The overall optimization of the PKNNC combines structure optimization and parameter optimization. The PKNNC takes advantage of three types of polynomial kernel functions, random sampling techniques and information gain algorithms, which have a good ability to describe the higher-order nonlinear relationships between input and output variables and have high generalization and fast convergence capabilities. To evaluate the effectiveness of the PKNNC, numerical experiments are carried out on two types of data: machine learning data and face data. A comparative study illustrates that the proposed PKNNC leads to better performance than several conventional models. [ABSTRACT FROM AUTHOR]

Abstract: In this study, polynomial-based radial basis function neural networks are proposed as one of the functional components of the overall face recognition system. The system consists of the preprocessing and recognition module. The design methodology and resulting procedure of the proposed P-RBF NNs are presented. The structure helps construct a solution to high-dimensional pattern recognition problems. In data preprocessing part, principal component analysis (PCA) is generally used in face recognition. It is useful in reducing the dimensionality of the feature space. However, because it is concerned with the overall face image, it cannot guarantee the same classification rate when changing viewpoints. To compensate for these limitations, linear discriminant analysis (LDA) is used to enhance the separation between different classes. In this paper, we elaborate on the PCA-LDA algorithm and design an optimal P-RBF NNs for the recognition module. The proposed P-RBF NNs architecture consists of three functional modules such as the condition part, the conclusion part, and the inference part realized in terms of fuzzy “if–then” rules. In the condition part of fuzzy rules, the input space is partitioned with the use of fuzzy clustering realized by means of the Fuzzy C-Means (FCM) algorithm. In the conclusion part of rules, the connection weight is realized through three types of polynomials such as constant, linear, and quadratic. The coefficients of the P-RBF NNs model are obtained by fuzzy inference method forming the inference part of fuzzy rules. The essential design parameters (including learning rate, momentum, fuzzification coefficient, and the feature selection mechanism) of the networks are optimized by means of differential evolution (DE). The experimental results completed on benchmark face datasets – the AT&T, and Yale datasets demonstrate the effectiveness and efficiency of PCA-LDA combined algorithm compared with other algorithms such as PCA, LPP, 2D-PCA and 2D-LPP. A real time face recognition system realized in this way is also presented. [Copyright &y& Elsevier]

We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x)" where A is a fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data. [ABSTRACT FROM AUTHOR]