An Improved Type-2 Possibilistic Fuzzy C-Means Clustering Algorithm with Application for MR Image Segmentation

Xiangjian Chen,Di Li,Hongmei Li 보안공학연구지원센터 2016 International Journal of Signal Processing, Image Vol.9 No.11

This paper presents a new clustering algorithm named improved type-2 possibilistic fuzzy c-means (IT2PFCM) for fuzzy segmentation of magnetic resonance imaging, which combines the advantages of type 2 fuzzy set, the fuzzy c-means (FCM) and Possibilistic fuzzy c-means clustering (PFCM). First of all, the type 2 fuzzy is used to fuse the membership function of the two segmentation algorithms (FCM and PCM), the membership function is an interval distribution, the determined fuzzy values which are the outputs of the FCM and PCM. Secondly, the initialization of cluster center and the process of type-reduction are optimized in this algorithm, which can greatly reduce the calculation of IT2PFCM and accelerate the convergence of the algorithm. Finally, experimental results are given to show the effectives of proposed method in contrast to conventional FCM, PFCM and type 2 fuzzy c-means.

Clustering using K-Means and Fuzzy C-Means on Food Productivity

Adriyendi 보안공학연구지원센터 2016 International Journal of u- and e- Service, Scienc Vol.9 No.12

This paper provided an overview of analysis and implementation clustering for food productivity. Food productivity is determined by food production. Rice is one of staple food in Indonesia. Rice production is influencing adequacy level of national food production. Rice productivity is very important to accomplishment food affordability. Rice productivity per province in Indonesia must be increased, because large population and high consumption. Rice productivity that fluctuates and tends to decrease, need to clustering to determinant category cluster of productivity. Clustering is using K-Means and Fuzzy C-Means. Method improvement of K-Means is modification Intra Cluster Distance and Inter Cluster Distance. Calculate distance (Inter Cluster Distance and Intra Cluster Distance) to evaluate the clustering results and to compare the efficiency of the clustering algorithms. Method improvement of Fuzzy C-Means is modification algorithm, alternative process and iteration. Data processing is using Excel software. Clustering produce three cluster (C1, C2, C3) is convergence. Measurement cluster based on comparison of membership cluster, consistency, and productivity. Membership cluster, there is point data anomaly (x22, x23, x29, x33). Consistency data on K-Means (C1 = 72.73%, C2 = 93.75%, C3 = 100%). Consistency data on Fuzzy C-Means (C1 = 100%, C2 = 88.33%, C3 = 87.50%). Rice Productivity is Cluster 1 (decrease), Cluster 2 (decrease, except 3 provinces), and Cluster 3 (increase, except 1 province). Majority in rice productivity is 70.59%. Result of clustering showed that majority rice productivity on category cluster is low productivity.

Regularization을 이용한 Possibilistic Fuzzy C-means의 확장

허경용(Gyeong-Yong Heo),남궁영환(Young-Hwan NamKoong),김성훈(Seong-Hoon Kim) 한국컴퓨터정보학회 2010 韓國컴퓨터情報學會論文誌 Vol.15 No.1

Fuzzy c-means(FCM)와 possibilistic c-means(PCM)는 퍼지 클러스터링 영역에서 대표적인 두 가지 방법으로 많은 패턴 인식 문제들에 성공적으로 활용되어져 왔다. 하지만 이들 방법 역시 잡음 민감성과 중첩 클러스터 문제를 가지고 있다. 이들 문제점을 극복하기 위해, 최근 두 방법을 결합하려는 시도가 있어왔고, possibilistic fuzzy c-means(PFCM)는 FCM과 PCM을 목적 함수 단계에서 통합함으로써 두 방법이 가지는 문제점을 완화시키는 성공적인 결과를 보여주었다. 이 논문에서는 PFCM에 regularization을 도입함으로써 PFCM의 잡음 민감성을 한층 더 줄여줄 수 있는 향상된 PFCM을 소개한다. Regularization은 해공간을 평탄화 함으로써 잡음의 영향을 줄이는 대표적인 방법 중 하나이다. 제안한 방법은 PFCM의 장점과 더불어 regularization에 의해 잡음의 영향을 더욱 줄일 수 있으며, 이는 실험을 통해 확인할 수 있다. Fuzzy c-means (FCM) and possibilistic c-means (PCM) are the two most well-known clustering algorithms in fuzzy clustering area, and have been applied in many applications in their original or modified forms. However, FCM's noise sensitivity problem and PCM's overlapping cluster problem are also well known. Recently there have been several attempts to combine both of them to mitigate the problems and possibilistic fuzzy c-means (PFCM) showed promising results. In this paper, we proposed a modified PFCM using regularization to reduce noise sensitivity in PFCM further. Regularization is a well-known technique to make a solution space smooth and an algorithm noise insensitive. The proposed algorithm, PFCM with regularization (PFCM-R), can take advantage of regularization and further reduce the effect of noise. Experimental results are given and show that the proposed method is better than the existing methods in noisy conditions.

차감 및 중력 fuzzy C-means 클러스터링을 이용한 칼라 영상 분할에 관한 연구

진영근,김태균,Jin, Young-Goun,Kim, Tae-Gyun 한국전기전자학회 1997 전기전자학회논문지 Vol.1 No.1

칼라 영상 분할의 한 방법으로 fuzzy C-means를 이용한 방법이 많이 연구되었으나, 이 방법은 클러스터의 개수가 정해져야 사용할 수 있는 방법이다. 분할해야 할 데이터가 많은 경우 예비 분할을 수행하여 예비 분할 되지 않는 데이터들에 대해서 상세 분할을 fuzzy C-means를 사용하여 분할 하나 예비 분할된 데이터의 클러스터 중심과 상세 분할로 만들어진 클러스터의 중심과는 연계성이 없어진다. 본 연구에서는 이것을 보완하기 위하여 차감 클러스터링을 사용하여 칼라 영상의 클러스터의 개수와 중심을 구한 후, 이것을 이용하여 영상을 예비 분할하고 중력을 가진 fuzzy C-means를 사용하여 분할되지 않은 나머지 부분과 클러스터의 중심을 최적화 시켜 분할하는 알고리듬을 제안한다. 제안된 방법의 정성적인 평가를 수행하여 본 논문에서 제시된 방법이 우수함을 보인다. In general, fuzzy C-means clustering method was used on the segmentation of true color image. However, this method requires number of clusters as an input. In this study, we suggest new method that uses subtractive and gravity fuzzy C-means clustering. We get number of clusters and initial cluster centers by applying subtractive clustering on color image. After coarse segmentation of the image, we apply gravity fuzzy C-means for optimizing segmentation of the image. We show efficiency of the proposed algorithm by qualitative evaluation.

FCM기반 퍼지추론 시스템의 구조 설계

김욱동(Wook-Dong Park),오성권(Sung-Kwun Oh),김현기(Hyun-Ki Kim) 대한전기학회 2010 전기학회논문지 Vol.59 No.5

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.

입자 군집 최적화를 이용한 FCM 기반 퍼지 모델의 동정 방법론

오성권(Sung-Kwun Oh),김욱동(Wook-Dong Kim),박호성(Ho-Sung Park),손명희(Myung-Hee Son) 대한전기학회 2011 전기학회논문지 Vol.60 No.1

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.

Fuzzy Clustering 기반의 화재 상황 인식 모델

송재원,안태기,김문현,홍유식 한국인터넷방송통신학회 2011 한국인터넷방송통신학회 논문지 Vol.11 No.1

기존의 화재 감시 시스템은 보통 연기, CO 혹은 온도나 온도의 변화량을 가지고 화재여부를 판단하였다. 대부분 각각의 센서에서 측정된 값을 미리 설정한 값과 비교하여 기준을 넘었을 경우에 화재라고 결정한다. 그러나 화재 가능성이 있는 상황도 정확히 예측하는 것이 화재를 예방하기 위해 요구된다. 본 연구에서는 여러 인자들 간의 조합에 의한 규칙을 생성하고, 불명확한 데이터 처리가 가능한 퍼지추론을 사용하여 화재상황을 인식하는 방식을 제안한다. 또한 퍼지추론 방식에서 지식의 일반화, 형식화의 문제점을 해결하기 위해, 화재의 특정 패턴들의 특징을 찾아서 분석하고 규칙베이스를 구축함으로써 시스템의 성능을 더욱 향상 시킨다. 화재의 레벨을 3단계(정상, 주의, 위험)로 나누고, 각 단계별로 훈련데이터를 FCM(fuzzy C-means clustering)에 의해 규칙화 하여 추론하는 시스템을 제안한다. 제안된 방식을 UCI의 삼림화재 데이터를 이용하여 성능을 평가한다. Fire monitoring system detects a fire based on the values of various sensors, such as smoke, CO, temperature, or change of temperature. It detects a fire by comparing sensed values with predefined threshold values for each sensor. However, to prevent a fire it is required to predict a situation which has a possibility of fire occurrence. In this work, we propose a fire recognition system using a fuzzy inference method. The rule base is constructed as a combination of fuzzy variables derived from various sensed values. In addition, in order to solve generalization and formalization problems of rule base construction from expert knowledge, we analyze features of fire patterns. The constructed rule base results in an improvement of the recognition accuracy. A fire possibility is predicted as one of 3 levels(normal, caution, danger). The training data of each level is converted to fuzzy rules by FCM(fuzzy C-means clustering) and those rules are used in the inference engine. The performance of the proposed approach is evaluated by using forest fire data from the UCI repository.

Reinforced rule-based fuzzy models: Design and analysis

Kim, Eun-Hu,Oh, Sung-Kwun,Pedrycz, Witold Elsevier 2017 Knowledge-based systems Vol.119 No.-

<P><B>Abstract</B></P> <P>This paper is concerned with a reinforced rule-based fuzzy model and its design realized with the aid of fuzzy clustering. The objective of this study is to develop a new design methodology of constructing incremental fuzzy rules formed through fuzzy clustering. The proposed model consists of four functional modules. The premise part of the fuzzy rules involves membership functions designed with the aid of the Fuzzy C-Means (FCM) clustering algorithm. The consequent part comprises local models (linear functions). The parameters of the local models are estimated by Weighted Least Squares (WLS). In the inference part, after determining the error associated with each fuzzy rule, the rule with the highest error is identified and refined. The selected rule is split into two or more specialized more detailed rules providing a better insight and detailed view into the system. These new rules are formed with the aid of the context-based Fuzzy C-Means (C-FCM) clustering. Along with the refinement of the rule, the linear conclusion part can be also refined by admitting quadratic functions. The effectiveness of the proposed rule-based model is discussed and illustrated with the aid of some numeric studies including both synthetic and machine learning data.</P>

영상 분할을 위한 Context Fuzzy c-Means 알고리즘을 이용한 공간 분할

노석범(Seok-Beom Roh),안태천(Tae-Chon Ahn),백용선(Yong-Sun Baek),김용수(Yong-Soo Kim) 한국지능시스템학회 2010 한국지능시스템학회논문지 Vol.20 No.3

영상 분할 (Image Segmentation)은 패턴 인식, 환경 인식, 문서 분석을 위한 영상 처리 과정에서 가장 기본적인 단계이다. 영상 분할 방법들 중 Otsu의 영상의 정규화된 히스토그램의 분포 정보를 이용하여 클래스 간의 분산을 최대화 시키는 임계치값을 결정하는 자동 임계치값 선정방법이 가장 잘 알려진 방법이다. Otsu의 방법은 영상의 전 영역에 대한 히스토그램을 분석함으로써 영상의 부분적인 특성을 반영하여 임계치값을 결정하기는 어렵다. 본 논문에서는 이 어려움 해소하기 위하여 Context Fuzzy c-Means 알고리즘을 이용하여 영상을 여러 개의 부분 영역으로 나누고, 정의된 부 영역에 영상 분할 기법을 적용함으로써 부 영역들에 적합한 여러 개의 임계치값을 계산함으로써 영상 분할 성능을 개선하고자 하였다. Image segmentation is the basic step in the field of the image processing for pattern recognition, environment recognition, and context analysis. The Otsu's automatic threshold selection, which determines the optimal threshold value to maximize the between class scatter using the distribution information of the normalized histogram of a image, is the famous method among the various image segmentation methods. For the automatic threshold selection proposed by Otsu, it is difficult to determine the optimal threshold value by considering the sub-region characteristic of the image because the Otsu's algorithm analyzes the global histogram of a image. In this paper, to alleviate this difficulty of Otsu's image segmentation algorithm and to improve image segmentation capability, the original image is divided into several sub-images by using context fuzzy c-means algorithm. The proposed fuzzy Otsu threshold algorithm is applied to the divided sub-images and the several threshold values are obtained.

Fast Global Kernel Fuzzy C-Means Clustering Algorithm for Consonant/Vowel Segmentation of Speech Signal

Xian Zang,Kil To Chong(정길도) 제어로봇시스템학회 2012 제어로봇시스템학회 각 지부별 자료집 Vol.2012 No.12

A clustering method using fast global kernel fuzzy c-means is developed to segment the speech signal into small non-overlapping blocks for consonant/vowel segmentation. This method proceeds in an incremental way attempting to optimally add new cluster center at each stage through kernel fuzzy c-means. It overcomes the well-known shortcomings of the most popular clustering method, fuzzy c-means, and improves the clustering accuracy. Due to the speeding up scheme, the complexity is lowered and the convergence speed is improved. Simulation results demonstrate the effectiveness of the proposed method in consonant/vowel segmentation.