• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.94-97
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• 2000

We introduce an approximate fuzzy clustering method, which is simple but computationally efficient, based on density functions in this paper. The density functions are defined by the number of data within the predetermined interval. Numerical examples are presented to show the validity of the proposed clustering method.

• 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.

• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.589-602
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• 2020

The development of smart grids has enabled the easy collection of a large amount of power data. There are some common patterns that make it useful to cluster power consumption patterns when analyzing s power big data. In this paper, clustering analysis is based on distance functions for time series and clustering algorithms to discover patterns for power consumption data. In clustering, we use 10 distance measures to find the clusters that consider the characteristics of time series data. A simulation study is done to compare the distance measures for clustering. Cluster validity measures are also calculated and compared such as error rate, similarity index, Dunn index and silhouette values. Real power consumption data are used for clustering, with five distance measures whose performances are better than others in the simulation.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.7
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• pp.199-210
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• 1994

Most of clustering methods usually employ a center or predefined shape of a cluster to assign the input data into the cluster. When there is no information about data set, it is impossible to predict how many clusters are to be or what shape clusters take. (the shape of clusters could not be easily represented by the center or predefined shape of clusters) Therefore, it is difficult to assign input data into a proper cluster using previous methods. In this paper, to overcome such a difficulty a cluster is to be represented as a collection of several subclusters representing boundary of the cluster. And membership functions are used to represent how much input data bllongs to subclusters. Then the position of the nearest subcluster is adaptively corrected for expansion of cluster, which the subcluster belongs to by use of a competitive learning neural network. To show the validity of the proposed method a numerical example is illustrated where FMMC(Fuzzy Min-Max Clustering) algorithm is compared with the proposed method.

• 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 Electrical Engineering and information Science
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• v.1 no.1
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• pp.164-172
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• 1996

The partitioning of related objects should be performed before clustering for an efficient access in object-oriented databases. In this paper, a horizontal partition of related objects in object-oriented databases is presented. All subclass nodes in a class inheritance hierarchy of a schema graph are shrunk to a class node in the graph that is called condensed schema graph because the aggregation hierarchy has more influence on the partition than the class inheritance hierarchy. A set function and an accessibility function are defined to find a maximal subset of related objects among the set of objects in a class. A set function maps a subset of the domain class objects to a subset of the range class objects. An accessibility function maps a subset of the objects of a class into a subset of the objects of the same class through a composition of set functions. The algorithm derived in this paper is to find the related objects of a condensed schema graph using accessibility functions and set functions. The existence of a maximal subset of the related objects in a class is proved to show the validity of the partition algorithm using the accessibility function.

• Journal of KIISE:Software and Applications
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• v.31 no.12
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• pp.1591-1601
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• 2004

Clustering, a technique for the analysis of the genes, organizes the patterns into groups by the similarity of the dataset and has been used for identifying the functions of the genes in the cluster or analyzing the functions of unknown gones. Since the genes usually belong to multiple functional families, fuzzy clustering methods are more appropriate than the conventional hard clustering methods which assign a sample to a group. In this paper, a Bayesian validation method is proposed to evaluate the fuzzy partitions effectively. Bayesian validation method is a probability-based approach, selecting a fuzzy partition with the largest posterior probability given the dataset. At first, the proposed Bayesian validation method is compared to the 4 representative conventional fuzzy cluster validity measures in 4 well-known datasets where foray c-means algorithm is used. Then, we have analyzed the results of Saccharomyces cell cycle expression data evaluated by the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.4
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• pp.285-292
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• 2000

In general, exploratory data analysis consists of three processes: i) assessment of clustering tendency, ii) cluster analysis, and iii) cluster validation. This analysis method requiring a number of iterations of step ii) and iii) to converge is computationally inefficient. In this paper, we propose a density function-based approximate fuzzy clustering method with a hierachical structure which consosts of two phases: Phase I is a features(i.e., number of clusters and cluster centers) extraction process based on the tendency assessment of a given data and Phase II is a standard FCM with the cluster centers intialized by the results of the Phase I. Numerical examples are presented to show the validity of the proposed clustering method.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.724-730
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• 1993

Most of clustering methods usually employ the center of a cluster to assign the input data into a cluster. When the shape of a cluster could not be easily represented by the center of cluster, however, it is difficult to assign input data into a proper cluster using previous methods. In this paper, to overcome such a difficulty, a cluster is to be represented as a collection of several subclusters. And membership functions are used to represent how much input data belong to subclusters. Then the position of each subcluster is adoptively corrected by use of a competitive learning neural network. To show the validity of the proposed method, a numerical example is illustrated, where FMMC(Fuzzy Min-Max Clustering) algorithm is compared with the proposed method.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.7
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• pp.51-60
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• 1997

Prototype based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a fuzzy clustering method that involves adaptively expanding convex polytopes. Thus, the dependency on the use of prototypes can be eliminated. The proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. Specifically, nonlinear membership functions are utilized to determine whether a new cluster is created or which vertex of the cluster should be expanded. For this, the membership function of a new vertex is assigned according to not only a distance measure between an incoming pattern vector and a current vertex, but also the amount how much the current vertex has been modified. Therefore, cluster expansion can be only allowed for one cluster per incoming pattern. Several experimental results are given to show the validity of our mehtod.