Paper proposes the Fuzzy C-means++ method for improving the effectiveness and speed of the Fuzzy C-means algorithm.This method works by spreading the initial cluster representatives in the data space at initialization.The proposed algorithm achieves superior results on both artificially generated and real world data sets. Fuzzy C-means has been utilized successfully in a wide range of applications, extending the clustering capability of the K-means to datasets that are uncertain, vague and otherwise hard to cluster. This paper introduces the Fuzzy C-means++ algorithm which, by utilizing the seeding mechanism of the K-means++ algorithm, improves the effectiveness and speed of Fuzzy C-means. By careful seeding that disperses the initial cluster centers through the data space, the resulting Fuzzy C-means++ approach samples starting cluster representatives during the initialization phase. The cluster representatives are well spread in the input space, resulting in both faster convergence times and higher quality solutions. Implementations in R of standard Fuzzy C-means and Fuzzy C-means++ are evaluated on various data sets. We investigate the cluster quality and iteration count as we vary the spreading factor on a series of synthetic data sets. We run the algorithm on real world data sets and to account for the non-determinism inherent in these algorithms we record multiple runs while choosing different k parameter values. The results show that the proposed method gives significant improvement in convergence times (the number of iterations) of up to 40 (2.1 on average) times the standard on synthetic datasets and, in general, an associated lower cost function value and Xie-Beni value. A proof sketch of the logarithmically bounded expected cost function value is given.

Fuzzy C-means++

Brain image segmentation is one of the most important parts of clinical diagnostic tools. Fuzzy C-mean (FCM) is one of the most popular clustering based segmentation methods. In this paper, a review of the FCM based segmentation algorithms for brain MRI images is presented. The review covers algorithms for FCM based segmentation algorithms, their comparative evaluations based on reported results and the result of experiments for neighborhood based extensions for FCM.

Fuzzy C-mean based brain MRI segmentation algorithms

Fuzzy clustering is a widely applied method for extracting the underlying models within data. It has been applied successfully in many real-world applications. Fuzzy c-means is one of the most popular fuzzy clustering methods because it produces reasonable results and its implementation is straightforward. One problem with all fuzzy clustering algorithms such as fuzzy c-means is that some data points which are assigned to some clusters have low membership values. It is possible that many samples may be assigned to a cluster with low-confidence. In this paper, an efficient and noise-aware implementation of support vector machines, namely relaxed constraints support vector machines, is used to solve the mentioned problem and improve the performance of fuzzy c-means algorithm. First, fuzzy c-means partitions data into appropriate clusters. Then, the samples with high membership values in each cluster are selected for training a multi-class relaxed constraints support vector machine classifier. Finally, the class labels of the remaining data points are predicted by the latter classifier. The performance of the proposed clustering method is evaluated by quantitative measures such as cluster entropy and Minkowski scores. Experimental results on real-life data sets show the superiority of the proposed method.

Fuzzy c-means improvement using relaxed constraints support vector machines

Clustering is a useful approach in data mining, image segmentation, and other problems of pattern recognition. Fuzzy clustering process can be quite slow when there are many objects or pattern to be clustered. This article discusses about an algorithm, ckMeans, which is able to reduce the number of distinct patterns which must be clustered without adversely affecting partition quality. The reduction is done by calculating a new mathematical equation to obtaining center cluster. To validate the proposed methodology we compared the original fuzzy c-means algorithm with that proposed in this paper.

A comparative study between fuzzy c-means and ckMeans algorithms

Image segmentation is a preliminary stage in diagnosis tools and the accurate segmentation of medical images is crucial for a correct diagnosis by these tools. Sometimes, due to inhomogeneity, low contrast, noise and inequality of content with semantic, automatic methods fail to segment image correctly. Therefore, for these images, it is necessary to use user help to correct method's error. We proposed to upgrade FAST FCM method to use training data to have more accurate results. In this paper, instead of using pixels as training data which is usual, we used different gray levels as training data and that is why we have used FAST FCM, because the input of FAST FCM is gray levels exist in image (histogram of the image). We named the new clustering method improved fast fuzzy C-mean (FCM). We use two facts to improve fast FCM. First, training data for each class are the member of the class. Second, the relevance distance of each input data from the training data of a class show the distance of the input data from the class. To cluster an image, first, the color image is converted to gray level image; then, from histogram of image, user selects training data for each target class, afterwards, the image is clustered using postulated clustering method. Experimental result is demonstrated to show effectiveness of the new method.

/pdf/improved-fast-fuzzy-c-mean-and-its-application-in-medical-oyf0cgsmjw.pdf

Improved fast fuzzy c-mean and its application in medical image segmentation

In this paper an initialization method for fuzzy c-means (FCM) algorithm is proposed in order to solve the two problems of clustering performance affected by initial cluster centers and lower computation speed for FCM. Grid and density are needed to extract approximate clustering center from sample space. Then, an initialization method for fuzzy c-means algorithm is proposed by using amount of approximate clustering centers to initialize classification number, and using approximate clustering centers to initialize initial clustering centers. Experiment shows that this method can improve clustering result and shorten clustering time validly.

An new initialization method for fuzzy c-means algorithm

In this paper an initialization method for fuzzy c-means (FCM) algorithm is proposed in order to solve the two problems of clustering performance affected by initial cluster centers and lower computation speed for FCM. Grid and density are needed to determine the number of clusters and the initial cluster centers automatically. Experiment shows that this method can improve clustering result and shorten clustering time validly.

An New Initialization Method for Fuzzy c-Means Algorithm Based on Density

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An new initialization method for fuzzy c-means algorithm

An New Initialization Method for Fuzzy c-Means Algorithm Based on Density