Interval Type-2 Fuzzy C-means Algorithm Research Articles

Typical Characteristic-Based Type-2 Fuzzy C-Means Algorithm

Type-2 fuzzy sets provide an efficient vehicle for handling uncertainties of real-world problems, including noisy observations. Bringing type-2 fuzzy sets to clustering algorithms offers more flexibility to handle uncertainties associated with membership concepts caused by a noisy environment. However, the existing type-2 fuzzy clustering algorithms suffer from a time-consuming type-reduction process, which not only hampers the clustering performance but also increases the burden of understanding the clustering results. In order to alleviate the problem, this article introduces a set of typical characteristics of type-2 fuzzy sets and establishes a characteristic-based type-2 fuzzy clustering algorithm. Being different from the objective function used in the fuzzy C-means (FCM) algorithm that produces cluster centers and type-1 memberships, the objective function in the proposed algorithm contains additional characteristics of type-2 membership grades, namely, centers of gravity and cardinalities of the secondary fuzzy sets. The derived iterative formulas used for these parameters are much more efficient than the interval type-2 FCM algorithm. The experiments carried out in this study show that the proposed typical characteristic-based type-2 FCM algorithm has an ability of detecting noise as well as assigning suitable membership degrees to the individual data.

Remote sensing image classification based on semi-supervised adaptive interval type-2 fuzzy c-means algorithm

Because of the uncertainty in remote sensing images and the ill-posedness of the problem, it is difficult for traditional unsupervised classification algorithms to create an accurate classification model. In contrast, pattern recognition methods based on fuzzy set theory, such as fuzzy c-means clustering, can manage the fuzziness of data effectively. Of these methods, the type-2 fuzzy c-means algorithm is better able to control uncertainty. Furthermore, semi-supervised training can use prior knowledge to deal with ill-posedness, and hence is more suitable. Therefore, we propose a novel classification method based the semi-supervised adaptive interval type-2 fuzzy c-means algorithm (SS-AIT2FCM). First, by integrating the semi-supervised approach, an evolutional fuzzy weight index m is proposed that improves the robustness and well-posedness of the model used in the clustering algorithm. This makes the algorithm suitable for remote sensing images with severe spectral aliasing, large coverage areas, and abundant features. In addition, soft constraint supervision is performed using a small number of labeled samples, which optimizes the iterative process of the algorithm and determines the optimal set of features for the data. This further reduces the ill-posedness of the model itself. The experimental data consist of three study areas: SPOT5 imagery from Big Hengqin Island, Guangdong, China, and the Summer Palace, Beijing, China, as well as TM imagery from Hengqin Island. Compared with several state-of-the-art fuzzy classification algorithms, our algorithm improves classification accuracy by more than 5% overall and obtains clearer boundaries in remote sensing images with serious mixed pixels. Moreover, it is able to suppress the phenomenon of isomorphic spectra.

Multi-channeled MR brain image segmentation: A new automated approach combining BAT and clustering technique for better identification of heterogeneous tumors

Segregation of tumor region in brain MR image is a prominent task that instantly provides easier tumor diagnosis, which leads to effective radiotherapy planning. For decades together, several segmentation methods for a brain tumor have been presented and until now, enhanced tumor segmentation procedure tends to be a challenging task because, MR images are mostly inbred with varied tumor dimensions of disproportioned boundaries. To address this issue, we develop an improved brain image segmentation technique called BAT based Interval Type-2 Fuzzy C-Means (BAT-IT2FCM) clustering. The BAT algorithm is utilized to find out the optimal cluster location from which the clustering operation by Interval Type-2 Fuzzy C-Means (IT2FCM) is performed. The optimal cluster location pointed/identified by the BAT algorithm helps in easing the clustering operation performed by IT2FCM algorithm, and thereby reducing computational complexity. The efficient outcome from BAT-IT2FCM methodology was affirmed using the performance metrics such as computational time, Peak Signal to Noise Ratio, Mean Squared Error, Jaccard Tanimoto Co-efficient Index and Dice Overlap Index. Also, segmentation results of clinical brain MR images produced by the proposed methodology were evaluated with the support from radiologists (Gold Standard). The suggested BAT based fuzzy related clustering produces sensitivity and specificity values of 98.56±1.2 and 97.67±1.3, respectively, which are better than the existing techniques used for brain image segmentation. Heterogeneous tumor types of different grade levels and tissue structures present in the brain MR slices of three different axes are precisely segmented by the proposed methodology for better visualization of oncologists.

An interval number distance- and ranking-based method for remotely sensed image fuzzy clustering

ABSTRACTFuzzy c-means clustering is an important non-supervised classification method for remote-sensing images and is based on type-1 fuzzy set theory. Type-1 fuzzy sets use singleton values to express the membership grade; therefore, such sets cannot describe the uncertainty of the membership grade. Interval type-2 fuzzy c-means (IT2FCM) clustering and relevant methods are based on interval type-2 fuzzy sets. Real vectors are used to describe the clustering centres, and the average values of the upper and lower membership grades are used to determine the classification of each pixel. Thus, the width information for interval clustering centres and interval membership grades are ignored. The main contribution of this article is to propose an improved IT2FCM* algorithm by adopting interval number distance (IND) and ranking methods, which use the width information of interval clustering centres and interval membership grades, thus distinguishing this method from existing fuzzy clustering methods. Three different IND definitions are tested, and the distance definition proposed by Li shows the best performance. The second contribution of this work is that two fuzzy cluster validity indices, FS- and XB-, are improved using the IND. Three types of multi/hyperspectral remote-sensing data sets are used to test this algorithm, and the experimental results show that the IT2FCM* algorithm based on the IND proposed by Li performs better than the IT2FCM algorithm using four cluster validity indices, the confusion matrix, and the kappa coefficient (κ). Additionally, the improved FS- index has more indicative ability than the original FS- index.

Enhanced IT2FCM algorithm using object-based triangular fuzzy set modeling for remote-sensing clustering

Object-based fuzzy clustering method has been widely used to remote-sensing clustering analysis. Mean and interval spectral signatures are typically used to describe an object's features. However, accurately distinguishing two objects with the same mean or interval values and different internal distributions is difficult. Focus on this problem, we developed triangular fuzzy set modeling to describe objects and designed an interval distance metric to measure the dissimilarities between triangular fuzzy sets. Furthermore, using the variation of fuzzifier (two fuzzifiers) to construct interval type-2 fuzzy c-means (IT2FCM) clustering methods, which are sensitive to the choice of fuzzifier, has uncertainty and subjectivity. Thus, an enhanced IT2FCM clustering algorithm that directly adopts the interval distance metric rather than the variation of fuzzifier is proposed for high-resolution remote-sensing clustering. We performed land-cover classification experiments for three study areas by utilizing remote-sensing images from the SPOT-5 and Gaofen-2 satellite sensor, which spatial resolution are approximately 10 m and 1 m, respectively. Visual and numerical results, including Kappa coefficients and the confusion matrix, were utilized to verify the classification results. The experimental results indicated that triangular fuzzy set modeling is appropriate for extracting features from ground objects; moreover, it limits the classification errors caused by same objects with different spectral features. Compared with the object-based interval-valued fuzzy c-means (IV-FCM) method reported in the literature, the proposed algorithm results in improved classification quality and accuracy.

An Extension of the Fuzzy Possibilistic Clustering Algorithm Using Type-2 Fuzzy Logic Techniques

In this work an extension of the Fuzzy Possibilistic C-Means (FPCM) algorithm using Type-2 Fuzzy Logic Techniques is presented, and this is done in order to improve the efficiency of FPCM algorithm. With the purpose of observing the performance of the proposal against the Interval Type-2 Fuzzy C-Means algorithm, several experiments were made using both algorithms with well-known datasets, such as Wine, WDBC, Iris Flower, Ionosphere, Abalone, and Cover type. In addition some experiments were performed using another set of test images to observe the behavior of both of the above-mentioned algorithms in image preprocessing. Some comparisons are performed between the proposed algorithm and the Interval Type-2 Fuzzy C-Means (IT2FCM) algorithm to observe if the proposed approach has better performance than this algorithm.

Semi-supervising Interval Type-2 Fuzzy C-Means clustering with spatial information for multi-spectral satellite image classification and change detection

Data clustering has been widely applied to numerous real-world problems such as natural resource management, urban planning, and satellite image analysis. Especially, fuzzy clustering with its ability of handling uncertainty has been developed for image segmentation or image analysis e.g. in health image analysis, satellite image classification. Normally, image segmentation algorithms like fuzzy clustering use spatial information along with the color information to improve the cluster quality. This paper introduces an approach, which exploits local spatial information between the pixel and its neighbors to compute the membership degree by using an interval type-2 fuzzy clustering algorithm, called IIT2-FCM. Besides, a Semi-supervising Interval Type-2 Fuzzy C-Means algorithm using spatial information, called SIIT2-FCM, is proposed to move the prototype of clusters to the expected centroids which are pre-defined on a basis of available samples. The proposed algorithms are applied to the problems of satellite image analysis consisting of land cover classification and change detection. Experimental results are reported for various datasets of the LandSat7 imagery at multi-temporal points and compared with the results produced by some existing algorithms and obtained from some survey data. The clustering results assessed with regard to some validity indexes demonstrate that the proposed algorithms form clusters of better quality and higher accuracy in problems of land cover classification and change detection.

Enhanced interval type-2 fuzzy c-means algorithm with improved initial center

Uncertainties are common in the applications like pattern recognition, image processing, etc., while FCM algorithm is widely employed in such applications. However, FCM is not quite efficient to handle the uncertainties well. Interval type-2 fuzzy theory has been incorporated into FCM to improve the ability for handling uncertainties of these algorithms, but the complexity of algorithm will increase accordingly. In this paper an enhanced interval type-2 FCM algorithm is proposed in order to reduce these shortfalls. The initialization of cluster center and the process of type-reduction are optimized in this algorithm, which greatly reduce the calculation time of interval type-2 FCM and accelerate the convergence of the algorithm. Many simulations have been performed on random data clustering and image segmentation to show the validity of our proposed algorithm.

A modified interval type-2 fuzzy C-means algorithm with application in MR image segmentation

The fuzzy C-means (FCM) algorithm has significant importance compared to other methods in Medical image segmentation. Conventional FCM algorithm is sensitive to noise especially in the presence of intensity inhomogeneity in MRI. Main reason is that a single fuzzifier in FCM cannot properly represent pattern memberships for all clusters. In this paper, we present a novel algorithm for fuzzy segmentation of MRI data. The algorithm utilizes two fuzzifiers used in interval type-2 FCM and a spatial constraint on the membership functions. Also, in our investigation, validity functions are extended to generalized form for interval type-2 fuzzy clustering. The experimental results on both synthetic and MR images show that the proposed algorithm has better performance on image segmentation than conventional FCM based algorithms.