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.

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.

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.

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.

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>

퍼지 K-평균 군집화의 재현성 평가

허명회,손은진 高麗大學校統計硏究所 2003 應用統計 Vol.18 No.-

Rand index는 군집화의 재현성을 평가하기 위한 자료 분할법에서 두 군집화 결과간의 일치도를 재는 지표이지만 (Rand, 1971) 개체가 1개 군집에 명확히 할당되는 군집화에만 적용될 수 있다. 따라서, 본 연구의 대상인 퍼지 K-평균 군집화(fuzzy K-means clustering)에서는 개체가 각 군집에 속할 소속도(membership)로 제시되므로 Rand index를 원형 그대로 사용할 수 없다. 본 연구의 목적은 퍼지 K-평균 군집화 결과 간 일치성 평가에 활용 가능하도록 Rand index를 확장하는 것이다. 제안 방법을 요약하면 다음과 같다. 1) 훈련 데이터로부터 얻은 퍼지 K-평균 군집화 규칙을 테스트 자료의 각 개체에 적용하여 K개 (=군집 수) 퍼지 소속도를 구한다. 독립적인 다른 훈련 데이터로부터 얻게 되는 퍼지 K-평균 군집화 규칙을 테스트 자료의 동일 개체에 적용하여 또 다른 K개 퍼지 소속도를 구한다. 2) 각 퍼지 군집화 규칙에 따른 군집 소속도에 비례하게 테스트 자료의 개체를 독립적으로 K개 군집 중 하나에 임의 할당하는 역 퍼지화 작업을 시행하여 명확한 분할(hard partition) 자료를 만든다. 3) 대응하는 두 개의 분할 군집화 결과로부터 통상적인 Rand index (또는 Hubert and Arabie (1985)의 C.(corrected) Rand index)를 산출한다. 4) 앞의 두 단계를 일정 수 반복하여 Rand index의 몬테칼로(Monte Carlo) 분포를 산출한다. 그 분포의 평균을 확장(extended) Rand index로 정의한다. 퍼지 K-평균 군집화에서 군집 수 K를 결정하는 문제에 확장 Rand index를 활용할 수 있다. 몇 개의 적용 사례를 제시하고 토의할 것이다. Rand index is an evaluation measure of consistency between two clustering rules (Rand. 1971). Hence it can be used to predict whether the clustering patterns are reproducible in the future. The index, however, cannot be applied to the fuzzy K-means clustering which has clear merits in dealing with overlapping clusters. The aim of this study is to extend Rand index or corrected Rand index of Hubert and Arabie (1985) for the use in fuzzy K-means clustering. The proposed method can be summarized as follows : Step 1: Partition the data into three parts - two training samples and one. test sample. Then, derive a K-means clustering rule from the first training sample and another rule from the second training sample. Then, apply both rules separately to the test sample units to obtain the list of cluster membership pairs. Step 2: Perform the inverse procedure opposite to make things fuzzy. In other words, generate a pair of hard partitions according to respective memberships of fuzzy partitions. Step 3: Compute Rand index or corrected Rand index of Hubert and Arabie (1985) from a pair of hard partitions. Step 4: Repeat Steps 3 and 4 for sufficient number of times. Then, one obtains a batch of Rand indices. Define Extended Rand Index by the average of Rand indices. We may use Extended Rand Index in determination of the number of clusters Kin fuzzy K-means clustering. Several examples are illustrated.

A Novel Image Segmentation Method Based on Improved Intuitionistic Fuzzy C-Means Clustering Algorithm

( Jun Kong ),( Jian Hou ),( Min Jiang ),( Jinhua Sun ) 한국인터넷정보학회 2019 KSII Transactions on Internet and Information Syst Vol.13 No.6

Segmentation plays an important role in the field of image processing and computer vision. Intuitionistic fuzzy C-means (IFCM) clustering algorithm emerged as an effective technique for image segmentation in recent years. However, standard fuzzy C-means (FCM) and IFCM algorithms are sensitive to noise and initial cluster centers, and they ignore the spatial relationship of pixels. In view of these shortcomings, an improved algorithm based on IFCM is proposed in this paper. Firstly, we propose a modified non-membership function to generate intuitionistic fuzzy set and a method of determining initial clustering centers based on grayscale features, they highlight the effect of uncertainty in intuitionistic fuzzy set and improve the robustness to noise. Secondly, an improved nonlinear kernel function is proposed to map data into kernel space to measure the distance between data and the cluster centers more accurately. Thirdly, the local spatial-gray information measure is introduced, which considers membership degree, gray features and spatial position information at the same time. Finally, we propose a new measure of intuitionistic fuzzy entropy, it takes into account fuzziness and intuition of intuitionistic fuzzy set. The experimental results show that compared with other IFCM based algorithms, the proposed algorithm has better segmentation and clustering performance.