• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1223-1229
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• 2009

The performance of Radial Basis Function Neural Networks depends on setting up the Radial Basis Functions over the input space which are the important design procedure of Radial Basis Function Neural Networks. The existing method to initialize the location of the radial basis functions over the input space is to use the conditional fuzzy C-means clustering. However, the researchers which are interested in the conditional fuzzy C-means clustering cannot get as good modeling performance as they expect because the conditional fuzzy C-means clustering cannot project the information which is extracted over the output space into the input space. To compensate the above mentioned drawback of the conditional fuzzy C-means clustering, we apply a fuzzy K-nearest neighbors approach to project the auxiliary information defined over the output space into the input space without lose of the information.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.1
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• pp.184-192
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• 2011

In this study, we introduce a identification methodology for FCM-based fuzzy model. The two underlying design mechanisms of such networks involve Fuzzy C-Means (FCM) clustering method and Particle Swarm Optimization(PSO). The proposed algorithm is based on FCM clustering method for efficient processing of data and the optimization of model was carried out using PSO. The premise part of fuzzy rules does not construct as any fixed membership functions such as triangular, gaussian, ellipsoidal because we build up the premise part of fuzzy rules using FCM. As a result, the proposed model can lead to the compact architecture of network. In this study, as the consequence part of fuzzy rules, we are able to use four types of polynomials such as simplified, linear, quadratic, modified quadratic. In addition, a Weighted Least Square Estimation to estimate the coefficients of polynomials, which are the consequent parts of fuzzy model, can decouple each fuzzy rule from the other fuzzy rules. Therefore, a local learning capability and an interpretability of the proposed fuzzy model are improved. Also, the parameters of the proposed fuzzy model such as a fuzzification coefficient of FCM clustering, the number of clusters of FCM clustering, and the polynomial type of the consequent part of fuzzy rules are adjusted using PSO. The proposed model is illustrated with the use of Automobile Miles per Gallon(MPG) and Boston housing called Machine Learning dataset. A comparative analysis reveals that the proposed FCM-based fuzzy model exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.619-624
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• 1998

This paper presents a new clustering algorithm called FCM algorithm for the design of fuzzy controller. FCM is an extended version of FCM(Fuzzy c-Means) algorithm and can estimate the number of clusters automatically and give membership grades $u_{ik}$ suitable for making fuzzy control rules. This paper also shows an example of its application to the line pursuit control of a car.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.491-499
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• 2001

In this paper, the scheme of an efficient fuzzy rule generation and fuzzy system construction using GA(genetic algorithm) and FCM(fuzzy c-means) clustering algorithm is proposed for TSK(Takagi-Sugeno-Kang) type fuzzy system. In the structure identification, input data is transformed by PCA(Principal Component Analysis) to reduce the correlation among input data components. And then, a set fuzzy rules are generated for a given criterion by FCM clustering algorithm . In the parameter identification premise parameters are optimally searched by GA. On the other hand, the consequent parameters are estimated by RLSE(Recursive Least Square Estimate) to reduce the search space. From this one can systematically obtain the valid number of fuzzy rules which shows satisfying performance for the given problem. Finally, we applied the proposed method to the Box-Jenkins data and rice taste data modeling problems and obtained a better performance than previous works.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.16-19
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• 2001

This paper presents a type-2 fuzzy C-means (FCM) algorithm that is an extension of the conventional fuzzy C-means algorithm. In our proposed method, the membership values for each pattern are extended as type-2 fuzzy memberships by assigning membership grades to the type-1 memberships. In doing so, cluster centers that are estimated by type-2 memberships may converge to a more desirable location than cluster centers obtained by a type-1 FCM method in the presence of noise.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.5 no.4
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• pp.224-231
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• 2012

In this paper, we introduce a fuzzy inference systems based on fuzzy c-means clustering algorithm for fuzzy modeling of nonlinear process. Typically, the generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, the fuzzy rules of fuzzy model are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process.

• Journal of the Korea Society of Computer and Information
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• v.17 no.12
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• pp.83-93
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• 2012

This paper proposes an image segmentation framework that modifies the objective function of Fuzzy C-Means (FCM) to improve the performance and computational efficiency of the conventional FCM-based image segmentation. The proposed image segmentation framework includes a locally weighted fuzzy c-means (LWFCM) algorithm that takes into account the influence of neighboring pixels on the center pixel by assigning weights to the neighbors. Distance between a center pixel and a neighboring pixels are calculated within a window and these are basis for determining weights to indicate the importance of the memberships as well as to improve the clustering performance. We analyzed the segmentation performance of the proposed method by utilizing four eminent cluster validity functions such as partition coefficient ($V_{pc}$), partition entropy ($V_{pe}$), Xie-Bdni function ($V_{xb}$) and Fukuyama-Sugeno function ($V_{fs}$). Experimental results show that the proposed LWFCM outperforms other FCM algorithms (FCM, modified FCM, and spatial FCM, FCM with locally weighted information, fast generation FCM) in the cluster validity functions as well as both compactness and separation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.1
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• pp.1-7
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• 2020

Fuzzy clustering, represented by FCM(Fuzzy C-Means), is a simple and efficient clustering method. However, the object function in FCM makes clusters affect clustering results proportional to the density of clusters, which can distort clustering results due to density difference between clusters. One method to alleviate this density problem is EDI-FCM(Extended Density-Independent FCM), which adds additional terms to the objective function of FCM to compensate for the density difference. In this paper, proposed is an enhanced EDI-FCM using regularization, Regularized EDI-FCM. Regularization is commonly used to make a solution space smooth and an algorithm noise insensitive. In clustering, regularization can reduce the effect of a high-density cluster on clustering results. The proposed method converges quickly and accurately to real centers when compared with FCM and EDI-FCM, which can be verified with experimental results.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.43 no.4 s.310
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• pp.1-8
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• 2006

This paper proposes an improved FCM(Fuzzy C-means) algorithm using intercluster and entropy-based weight in gray image. The fuzzy clustering methods have been extensively used in the image segmentation since it extracts feature information of the region. Most of fuzzy clustering methods have used the FCM algorithm. But, FCM algorithm is still sensitive to noise, as it does not include spatial information. In addition, it can't correctly classify pixels according to the feature-based distributions of clusters. To solve these problems, we applied a weight and intercluster to the traditional FCM algorithm. A weight is obtained from the entropy information based on the cluster's number of neighboring pixels. And a membership for one pixel is given based on the information considering the feature-based intercluster. Experiments has confirmed that the proposed method was more tolerant to noise and superior to existing methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.