MODIFIED POSSIBILISTIC FUZZY C-MEANS ALGORITHM FOR CLUSTERING INCOMPLETE DATA SETS

A possibilistic fuzzy c-means (PFCM) algorithm is a reliable algorithm proposed to deal with the weaknesses associated with handling noise sensitivity and coincidence clusters in fuzzy c-means (FCM) and possibilistic c-means (PCM). However, the PFCM algorithm is only applicable to complete data sets. Therefore, this research modified the PFCM for clustering incomplete data sets to OCSPFCM and NPSPFCM with the performance evaluated based on three aspects, 1) accuracy percentage, 2) the number of iterations, and 3) centroid errors. The results showed that the NPSPFCM outperforms the OCSPFCM with missing values ranging from 5% − 30% for all experimental data sets. Furthermore, both algorithms provide average accuracies between 97.75%−78.98% and 98.86%−92.49%, respectively

A Parameter Based Modified Fuzzy Possibilistic C-Means Clustering Algorithm for Lung Image Segmentation

Image processing is a technique necessary for modifying an image. The important part of image processing is Image segmentation. The identical medical images can be segmented manually. However the accurateness of image segmentation using the segmentation algorithms is more when compared with the manual segmentation. Medical image segmentation is an indispensable pace for the majority of subsequent image analysis tasks. In this paper, FCM and different extension of FCM Algorithm is discussed. The unique FCM algorithm yields better results for segmenting noise free images, but it fails to segment images degraded by noise, outliers and other imaging artifact. This paper presents an image segmentation approach using Modified Fuzzy Possibilistic C-Means algorithm (MFPCM). This approach is a generalized adaptation of standard Fuzzy C-Means Clustering (FCM) algorithm and Fuzzy Possibilistic C-Means algorithm. The drawback of the conventional FCM technique is eliminated in modifying the standard technique. The Modified FCM algorithm is formulated by modifying the distance measurement of the standard FCM algorithm to permit the labeling of a pixel to be influenced by other pixels and to restrain the noise effect during segmentation. Instead of having one term in the objective function, a second term is included, forcing the membership to be as high as possible without a maximum frontier restraint of one. Experiments are carried out on real images to examine the performance of the proposed modified Fuzzy Possibilistic FCM technique in segmenting the medical images. Standard FCM, Modified FCM, Possibilistic C-Means algorithm (PCM), Fuzzy Possibilistic C-Means algorithm (FPCM) and Modified FPCM are compared to explore the accuracy of our proposed approach

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved

A fuzzy clustering algorithm to detect planar and quadric shapes

In this paper, we introduce a new fuzzy clustering algorithm to detect an unknown number of planar and quadric shapes in noisy data. The proposed algorithm is computationally and implementationally simple, and it overcomes many of the drawbacks of the existing algorithms that have been proposed for similar tasks. Since the clustering is performed in the original image space, and since no features need to be computed, this approach is particularly suited for sparse data. The algorithm may also be used in pattern recognition applications

Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise

A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Analysis of fuzzy clustering and a generic fuzzy rule-based image segmentation technique

Many fuzzy clustering based techniques when applied to image segmentation do not incorporate spatial relationships of the pixels, while fuzzy rule-based image segmentation techniques are generally application dependent. Also for most of these techniques, the structure of the membership functions is predefined and parameters have to either automatically or manually derived. This paper addresses some of these issues by introducing a new generic fuzzy rule based image segmentation (GFRIS) technique, which is both application independent and can incorporate the spatial relationships of the pixels as well. A qualitative comparison is presented between the segmentation results obtained using this method and the popular fuzzy c-means (FCM) and possibilistic c-means (PCM) algorithms using an empirical discrepancy method. The results demonstrate this approach exhibits significant improvements over these popular fuzzy clustering algorithms for a wide range of differing image types