• Journal of the Korea Society of Computer and Information
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• v.15 no.4
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• pp.11-18
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• 2010

Fuzzy c-means (FCM) is a simple but efficient clustering algorithm using the concept of a fuzzy set that has been proved to be useful in many areas. There are, however, several well known problems with FCM, such as sensitivity to initialization, sensitivity to outliers, and limitation to convex clusters. In this paper, global fuzzy c-means (G-FCM) and kernel fuzzy c-means (K-FCM) are combined to form a non-linear variant of G-FCM, called kernel global fuzzy c-means (KG-FCM). G-FCM is a variant of FCM that uses an incremental seed selection method and is effective in alleviating sensitivity to initialization. There are several approaches to reduce the influence of noise and accommodate non-convex clusters, and K-FCM is one of them. K-FCM is used in this paper because it can easily be extended with different kernels. By combining G-FCM and K-FCM, KG-FCM can resolve the shortcomings mentioned above. The usefulness of the proposed method is demonstrated by experiments using artificial and real world data sets.

• 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 IKEEE
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• v.23 no.2
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• pp.419-424
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• 2019

The FCM algorithm finds the optimal solution through iterative optimization technique. In particular, there is a difference in execution time depending on the initial center of clustering, the location of noise, the location and number of crowded densities. However, this method gradually updates the center point, and the center of the initial cluster is shifted to one side. In this paper, we propose a TI-FCM(Triangular Inequality-Fuzzy C-Means) clustering algorithm that determines the cluster center density by maximizing the distance between clusters using triangular inequality. The proposed method is an effective method to converge to real clusters compared to FCM even in large data sets. Experiments show that execution time is reduced compared to existing FCM.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.05a
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• pp.144-146
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• 2022

본 논문에서는 Kernel based Fuzzy C-Means(K-FCM) 기반 양자화 기법을 적용하여 의료 초음파 영상에서 특징을 분할하는 기법을 제안한다. 결절종의 경우에는 초음파 영상 내에서 무에코, 저에코의 특징을 가진 낭포성 종양 객체를 특징 영역으로 영상을 분할한다. K-FCM 클러스터링은 기존의 FCM 클러스터링에서 Kernel Function을 적용한 형태의 클러스터링 기법이다. 본 논문에서는 Gaussian Kernel 기반 K-FCM을 적용하여 의료 초음파 영상에서 특징들을 분할하였다. 결절종 초음파 영상에서는 FCM 클러스터링이 F1 Score가 85.574%로 나타났고, K-FCM이 86.442%로 나타났다.

• Journal of Korea Multimedia Society
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• v.16 no.7
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• pp.810-819
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• 2013

FCM (Fuzzy C-Means) clustering algorithm, a typical split-based clustering algorithm, has been successfully applied to the various fields. Nonetheless, the FCM clustering algorithm has some problems, such as high sensitivity to noise and local data, the different clustering result from the intuitive grasp, and the setting of initial round and the number of clusters. To address these problems, in this paper, we determine fuzzy numbers which project the FCM clustering result on the axis with the specific attribute. And we propose a model that the fuzzy numbers apply to FDT (Fuzzy Decision Tree). This model improves the two problems of FCM clustering algorithm such as elevated sensitivity to data, and the difference of the clustering result from the intuitional decision. And also, this paper compares the effect of the proposed model and the result of FCM clustering algorithm through the experiment using real traffic and rainfall data. The experimental results indicate that the proposed model provides more reliable results by the sensitivity relief for data. And we can see that it has improved on the concordance of FCM clustering result with the intuitive expectation.

• 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 Society of Computer and Information
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• v.16 no.1
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• pp.39-46
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• 2011

Clustering is one of the well-known unsupervised learning methods, in which a data set is grouped into some number of homogeneous clusters. There are numerous clustering algorithms available and they have been used in various applications. Fuzzy c-means (FCM), the most well-known partitional clustering algorithm, was established in 1970's and still in use. However, there are some unsolved problems in FCM and variants of FCM are still under development. In this paper, the problems in FCM are first explained and the available solutions are investigated, which is aimed to give researchers some possible ways of future research. Most of the FCM variants try to solve the problems using domain knowledge specific to a given problem. However, in this paper, we try to give general solutions without using any domain knowledge. Although there are more things left than discovered, this paper may be a good starting point for researchers newly entered into a clustering area.

• Journal of the Korea Society of Computer and Information
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• v.17 no.2
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• pp.49-57
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• 2012

Conventional fuzzy c-means (FCM) algorithms have achieved a good clustering performance. However, they do not fully utilize the spatial information in the image and this results in lower clustering performance for images that have low contrast, vague boundaries, and noises. To overcome this issue, we propose an enhanced spatial fuzzy c-means (ESFCM) algorithm that takes into account the influence of neighboring pixels on the center pixel by assigning weights to the neighbors in a $3{\times}3$ square window. To evaluate between the proposed ESFCM and various FCM based segmentation algorithms, we utilized clustering validity functions such as partition coefficient ($V_{pc}$), partition entropy ($V_{pe}$), and Xie-Bdni function ($V_{xb}$). Experimental results show that the proposed ESFCM outperforms other FCM based algorithms in terms of clustering validity functions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.211-214
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• 2006

Fuzzy C-Means(FCM) 알고리즘은 probabilitic 멤버쉽을 사용하는 클러스터링 방법으로서 널리 쓰이고 있다. 하지만 이 방법은 노이즈에 대하여 민감한 성질을 가진다는 단점이 있다. 따라서 본 논문에서는 이러한 노이즈에 민감한 성질을 보완하기 위해서 데이터의 밀도추정을 이용하여 새로운 FCM 알고리즘을 제안한다. 본 논문에서 제안된 알고리즘은 FCM과 비슷한 성능의 클러스터링 수행이 가능하며, 노이즈가 포함된 데이터에서는 FCM보다 더 나은 성능을 보여준다.

• The KIPS Transactions:PartB
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• v.9B no.2
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• pp.202-214
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• 2002

In this paper, we propose a modified FCM (MFCM) algorithm to solve the problems of the FCM algorithm and the fuzzy clustering algorithm using an average intracluster distance (FCAID). The MFCM algorithm grants the regular grade of membership in the small size of cluster. And it clears up the convergence problem of objective function because its objective function is designed according to the grade of membership of it, verified, and used for clustering data. So, it can solve the problem of the FCM algorithm in different size of cluster and the FCAID algorithm in the convergence problem of objective function. To verify the MFCM algorithm, we compared with the result of the FCM and the FCAID algorithm in data clustering. From the experimental results, the MFCM algorithm has a good performance compared with others by classification entropy.