• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.312-320
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• 2012

In this study, we introduce a new design methodology of a granular-oriented self-organizing polynomial neural networks (GoSOPNNs) that is based on multi-layer perceptron with Context-based Polynomial Neurons (CPNs) or Polynomial Neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a methodological design strategy of GoSOPNNs as follows : (a) The 1st layer of the proposed network consists of Context-based Polynomial Neuron (CPN). In here, CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Context-based Fuzzy C-Means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data while the build of the clusters is guided by a collection of some predefined fuzzy sets (so-called contexts) defined in the output space. (b) The proposed design procedure being applied at each layer of GoSOPNN leads to the selection of preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of performance of the proposed GoSOPNN network, we describe a detailed characteristic of the proposed model using a well-known learning machine data(Automobile Miles Per Gallon Data, Boston Housing Data, Medical Image System Data).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.2
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• pp.45-51
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• 2006

In this paper, we propose a new architecture of Information Granulation based genetically optimized Self-Organizing Fuzzy Polynomial Neural Networks (IG_gSOFPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially information granulation and genetic algorithms. The proposed IG_gSOFPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional SOFPNNs. The design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial of the consequent part of fuzzy rules, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. In addition, the fuzzy rules used in the networks exploit the notion of information granules defined over system's variables and formed through the process of information granulation. That is, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. This granulation is realized with the aid of the hard c-menas clustering method (HCM). To evaluate the performance of the IG_gSOFPNN, the model is experimented with using two time series data(gas furnace process and NOx process data).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.6
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• pp.264-273
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• 2006

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) by means of consecutive optimization and also discuss its comprehensive design methodology involving mechanisms of genetic optimization. The network is based on a structurally as well as parametrically optimized fuzzy polynomial neurons (FPNs) conducted with the aid of information granulation and genetic algorithms. In structurally identification of FPN, the design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics and addresses specific aspects of parametric optimization. In addition, the fuzzy rules used in the networks exploit the notion of information granules defined over system's variables and formed through the process of information granulation. That is, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. This granulation is realized with the aid of the hard c-menas clustering method (HCM). For the parametric identification, we obtained the effective model that the axes of MFs are identified by GA to reflect characteristic of given data. Especially, the genetically dynamic search method is introduced in the identification of parameter. It helps lead to rapidly optimal convergence over a limited region or a boundary condition. To evaluate the performance of the proposed model, the model is experimented with using two time series data(gas furnace process, nonlinear system data, and NOx process data).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.3
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• pp.135-144
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• 2004

In this paper, we propose competitive fuzzy polynomial neurons-based advanced Self-Organizing Neural Networks(SONN) architecture for optimal model identification and discuss a comprehensive design methodology supporting its development. The proposed SONN dwells on the ideas of fuzzy rule-based computing and neural networks. And it consists of layers with activation nodes based on fuzzy inference rules and regression polynomial. Each activation node is presented as Fuzzy Polynomial Neuron(FPN) which includes either the simplified or regression polynomial fuzzy inference rules. As the form of the conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership (unction are studied and the number of the premise input variables used in the rules depends on that of the inputs of its node in each layer. We introduce two kinds of SONN architectures, that is, the basic and modified one with both the generic and the advanced type. Here the basic and modified architecture depend on the number of input variables and the order of polynomial in each layer. The number of the layers and the nodes in each layer of the SONN are not predetermined, unlike in the case of the popular multi-layer perceptron structure, but these are generated in a dynamic way. The superiority and effectiveness of the Proposed SONN architecture is demonstrated through two representative numerical examples.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.459-469
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• 2012

This article proposes a couple of parallel implementations of the self-organizing network for normal mixtures. In principle, self-organizing networks should be able to be implemented in a parallel computing environment without issue. However, the network for normal mixtures has inherent problem in being operated parallel in pure sense due to estimating conditional expectations of the mixing proportion in each iteration. This article shows the result of the parallel implementations of the network using Java. According to the results, both of the implementations achieved a faster execution without any performance degradation.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2762-2764
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• 2001

In this study, we introduce and investigate a class of dynamic perceptron architectures, discuss a comprehensive design methodology and carry out a series of numeric experiments. The proposed dynamic perceptron architectures are called as Polynomial Neural Networks(PNN). PNN is a flexible neural architecture whose topology is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. PNN has two kinds of networks, Polynomial Neuron(FPN)-based and Fuzzy Polynomial Neuron(FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based Self-organizing Polynomial Neural Networks(SOPNN) dwells on the Group Method of Data Handling (GMDH) [1]. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A detailed comparative analysis is included as well.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.123-132
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• 1998

The group formation problem of the machine and part is a very important issue in the planning stage of cellular manufacturing systems. This paper investigates Self-Organizing Map(SOM) neural networks approach to machine-part grouping problem. We present a two-phase algorithm based on SOM for grouping parts and machines. SOM can learn from complex, multi-dimensional data and transform them into visually decipherable clusters. Output layer in SOM network is one-dimensional structure and the number of output node has been increased sufficiently to spread out the input vectors in the order of similarity. The proposed algorithm performs remarkably well in comparison with many other algorithms for the well-known problems shown in previous papers.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.288-291
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• 2004

기존의 SOFPNN은 데이터 수가 적고 비선형 요소가 많은 시스템에 대한 체계적이고 효율적인 최적 모델 을 구축할 수 있었으며 각 층 노드의 선택 입력을 변화시킴으로써 네트워크 구조 전체의 적응능력을 향상 시켰다. SOFPNN의 구조는 퍼지 다항식 뉴론(FPN)들로 구성되어 있으며, 층이 진행하는 동안 모델 스스로 노드의 선택과 제거를 통해 최적의 네트워크 구조를 생성할 수 있는 유연성을 가지고 있다. 그러나, 노드의 입력변수의 수와 규칙 후반부 다항식 차수 그리고 입력변수는 설계자의 경험 또는 반복적인 학습을 통해 선호된 네트워크 구조를 선택하였으나, 최적의 네트워크 구조를 구축하는데는 어려옴이 내재되어 있었다. 본 논문에서는 자기구성 퍼지 다항식 뉴럴네트워크(Self-Organizing Fuzzy Polynomial Neural Networks： SOFPNN)을 최적화시키기 위해 유전자 알고리즘을 이용하여 자기구성 퍼지 다항식 뉴럴 네트워크의 입력변수의 수와 이에 해당되는 입력변수 그리고 규칙 후반부 다항식의 차수를 탐색하여 최적 의 자기구성 퍼지 다항식 뉴럴 네트워크를 구축한다. 따라서 모델 구축에 있어서 유연성과 정확성을 가지며 객관적이고 좀 더 정확한 예측 능력을 가진 SOFPNN 모델 구조를 구축할 수가 있다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.434-437
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• 2004

본 논문에서는 유전자 알고리즘에 기반을 둔 자기구성 다항식 뉴럴네트워크(Self-Organizing Polynomial Neural Networks： SOPNN)의 새로운 구조를 제안하고, 포괄적인 설계 방법론을 토의한다. 기존의 자기구성 다항식 뉴럴 네트워크는 확장된 GMDH 방법에 기반을 두며, 네트워크의 성장과정을 통하여 각 충의 다항식 뉴런에서 고정된 노드 입력들의 수 뿐만 아니라 다항식 차수(1차, 2차, 그리고 수정된 2차식)를 이용하였다. 더구나, 그 방법은 학습을 통해 생성된 SOPNN이 최적 네트워크 구조를 가진다는 것을 보증하지 못한다. 그러나, 제안된 GA 기반 SOPNN은 그 구조를 구조적으로 더 최적화된 네트워크가 되도록 하고, 기존의 SOPNN보다 훨씬 더 유연하고, 선호된 뉴럴 네트워크가 되도록 한다. 구조적으로 더 최적화된 SOPNN을 생성하기 위해, SOPNN의 각 단계에서의 GA기반 설계 절차는 SOPNN내에서 이용할 수 있는 다음의 최적 파라미터들- 즉 입력변수의 수, 입력변수, 및 다항식 차수-을 가진 선호된 노드들의 선택으로 이끈다. 하중계수를 가진 합성성능지수가 그 모델의 근사화 및 일반화(예측) 능력 사이의 상호 균형을 얻기 위해 제안된다. 상세 설계 절차가 상세히 토의된다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.127-135
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• 2000

This paper provides a new method of initializing neurons used in self-organizing neural networks and sequencing input nodes for applying to Euclidean traveling salesman problem. We use a general property that in any optimal solution for Euclidean traveling salesman problem, vertices located on the convex hull are visited in the order in which they appear on the convex hull boundary. We composite input nodes as number of convex hulls and initialize neurons as shape of the external convex hull. And then adapt input nodes as the convex hull unit and all convex hulls are adapted as same pattern, clockwise or counterclockwise. As a result of our experiments, we obtain l∼3 % improved solutions and these solutions can be used for initial solutions of any global search algorithms.