Polynomial neural networks architecture: analysis and design

Oh, Sung‐Kwun; Pedrycz, Witold; Park, Byoung-Jun

doi:10.1016/s0045-7906(02)00045-9

Cited by 160 publications

(71 citation statements)

References 12 publications

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“…These networks result as a synergy between two other general constructs such as FNN [13] and PNN [9].…”

Section: The Architecture and Development Of Genetically Optimized Hfmentioning

confidence: 99%

“…When we construct PNs of each layer in the conventional PNN [9], such parameters as the number of input variables (nodes), the order of polynomial, and input variables available within a PN are fixed (selected) in advance by the designer. This could have frequently contributed to the difficulties in the design of the optimal network.…”

Section: Genetically Optimized Pnn (Gpnn)mentioning

confidence: 99%

“…The role of the PNN is to carry out nonlinear transformation at the level of the fuzzy sets formed at the level of FNN. The PNN that exhibits a flexible and versatile structure [9] is constructed on a basis of Group Method of Data Handling (GMDH [10]) method and genetic algorithms (GAs). The design procedure applied in the construction of each layer of the PNN deals with its structural optimization involving the selection of optimal nodes (polynomial neurons; 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.…”

Section: Introductory Remarksmentioning

confidence: 99%

mentioning

confidence: 99%

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Information Granulation-Based Multi-layer Hybrid Fuzzy Neural Networks: Analysis and Design

Park

Pedrycz

et al. 2004

Computational Science - ICCS 2004

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Abstract. In this study, a new architecture and comprehensive design methodology of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) are introduced and a series of numeric experiments are carried out. The gHFNN architecture results from a synergistic usage of the hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). FNN contributes to the formation of the premise part of the overall network structure of the gHFNN. The consequence part of the gHFNN is designed using PNN. Introductory RemarksEfficient modeling techniques should allow for a selection of pertinent variables and a formation of highly representative datasets. The models should be able to take advantage of the existing domain knowledge and augment it by available numeric data to form a coherent data-knowledge modeling entity. The omnipresent modeling tendency is the one that exploits techniques of Computational Intelligence (CI) by embracing fuzzy modeling [1-6], neurocomputing [7], and genetic optimization [8].In this study, we develop a hybrid modeling architecture, called genetically optimized Hybrid Fuzzy Neural Networks (gHFNN). In a nutshell, gHFNN is composed of two main substructures driven to genetic optimization, namely a fuzzy set-based fuzzy neural network (FNN) and a polynomial neural network (PNN). From a standpoint of rule-based architectures, one can regard the FNN as an implementation of the antecedent part of the rules while the consequent is realized with the aid of a PNN. The role of the FNN is to interact with input data, granulate the corresponding input spaces. In the first case (Scheme I) we concentrate on the use of simplified fuzzy inference. In the second case (Scheme II), we take advantage of linear fuzzy inference. The role of the PNN is to carry out nonlinear transformation at the level of the fuzzy sets formed at the level of FNN. The PNN that exhibits a flexible and versatile structure [9] is constructed on a basis of Group Method of Data Handling (GMDH [10])

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“…These networks result as a synergy between two other general constructs such as FNN [13] and PNN [9].…”

Section: The Architecture and Development Of Genetically Optimized Hfmentioning

confidence: 99%

Section: Genetically Optimized Pnn (Gpnn)mentioning

confidence: 99%

Section: Introductory Remarksmentioning

confidence: 99%

mentioning

confidence: 99%

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Information Granulation-Based Multi-layer Hybrid Fuzzy Neural Networks: Analysis and Design

Park

Pedrycz

et al. 2004

Computational Science - ICCS 2004

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“…a linear dependence and pattern [ 10 ] identification but it could be applied also to linear function approximation [ 11 ] . There is also possible to use several extended or modified forms of the GMDH polynomial (bicubic, [ 12 ] , which might improve some applications however this study applied only the general form of the polynomial (2), which generally yields the best results. D-PNN can combine the PNN functionality with some mathematical techniques of differential equation (DE) substitutions.…”

Section: Introductionmentioning

confidence: 99%

Short-term Power Demand Forecasting using the Differential Polynomial Neural Network

Zjavka¹

2015

IJCIS

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Power demand forecasting is important for economically efficient operation and effective control of power systems and enables to plan the load of generating unit. The purpose of the short-term electricity demand forecasting is to forecast in advance the system load, represented by the sum of all consumers load at the same time. A precise load forecasting is required to avoid high generation cost and the spinning reserve capacity. Under-prediction of the demands leads to an insufficient reserve capacity preparation and can threaten the system stability, on the other hand, over-prediction leads to an unnecessarily large reserve that leads to a high cost preparations. Differential polynomial neural network is a new neural network type, which forms and resolves an unknown general partial differential equation of an approximation of a searched function, described by data observations. It generates convergent sum series of relative polynomial derivative terms which can substitute for the ordinary differential equation, describing 1-parametric function time-series. A new method of the short-term power demand forecasting, based on similarity relations of several subsequent day progress cycles at the same time points is presented and tested on 2 datasets. Comparisons were done with the artificial neural network using the same prediction method.Keywords: power demand prediction, week and day load cycle, differential polynomial neural network, sum relative derivative term, ordinary differential equation composition * Typeset names in 10 pt Times Roman, uppercase. Use the footnote to indicate the present or permanent address of the author.

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Genetically Optimized Hybrid Fuzzy Neural Networks Based on TSK Fuzzy Rules and Polynomial Neurons

Park

Kim

2005

Advances in Neural Networks — ISNN 2005

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Polynomial neural networks architecture: analysis and design

Cited by 160 publications

References 12 publications

Information Granulation-Based Multi-layer Hybrid Fuzzy Neural Networks: Analysis and Design

Information Granulation-Based Multi-layer Hybrid Fuzzy Neural Networks: Analysis and Design

Short-term Power Demand Forecasting using the Differential Polynomial Neural Network

Genetically Optimized Hybrid Fuzzy Neural Networks Based on TSK Fuzzy Rules and Polynomial Neurons

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