Possibilistic Clustering Methods Research Articles

Interval type-2 possibilistic picture C-means clustering incorporating local information for noisy image segmentation

Picture fuzzy C-means clustering is a novel computational intelligence method that has some advantages over fuzzy clustering in pattern analysis and machine intelligence. However, picture fuzzy clustering is easily affected by noise and weighting exponent, which seriously limits its widespread application. To address this issue, this paper proposes a new robust possibilistic clustering method called “interval type-2 possibilistic picture C-means clustering with local information”. This method combines interval type-2 fuzzy sets with possibilistic C-means clustering based on picture fuzzy sets, strengthening the noise resistance of picture fuzzy clustering. Firstly, this paper creatively extends an improved possibilistic clustering with double weighing exponents to picture fuzzy sets, solving the problem of consistency clustering in existing possibilistic picture clustering. Second, this paper originally introduces a new picture local information factor in possibilistic picture clustering and further enhances the anti-noise robustness of the method by using spatial possibilistic picture partition information. Finally, this paper skillfully extends this clustering method to interval type-2 fuzzy sets, which can handle more flexibly high-order uncertainties than type-1 clustering method. Experimental results indicate that this proposed method has better segmentation performance and stronger noise suppression ability compared with existing picture fuzzy clustering and interval type-2 fuzzy clustering. In summary, this work has made significant contributions to the development of picture fuzzy clustering theory and its applications.

An Instinctive Application of Spatially Weighted Possibilistic Clustering Methods for the Detection of Lesions in Diabetic Retinopathy Images in Multi-dimensional Kernel Space

Diabetic Retinopathy is a result of microvascular changes linked with hyperglycemia. The pathology is characterized by swollen and weak blood capillaries resulted due to excess glucose absorption by endothelial walls of them. The swollen and thick capillaries may burst and exude protein and fat based particles into the retinal fundus, which get clotted and obstruct the vision flow into the eye. The clotted particles are called Exudates, whose volume and number will decide the severity of the condition. As a result new blood capillaries are triggered to nourish the retina. But they are weak and fragile and may eventually burst making the complication more critical. Eye diagnosis requires dilation of the pupa using mydriatic drops which tends to many temporary and prolonged side effects. Also the reliability of the diagnosis is dependent on the Ophthalmologists experience and require hectic labor and time. This paper presents an instinctive multi-dimensional kernel possibilistic c means clustering method with induced spatial constraint for the detection of retinal abnormalities. The proposed method helps the clinician by automating the lesion detection process and has proven its statistical significance compared to the existing state of art methods.

An Instinctive Method for Lesion Detection in Diabetic Retinopathy Images using a Novel Spatial Possibilistic C means Clustering in Kernel Space

Diabetic Retinopathy (DR) is the prime cause of vision impediment which originates due micro vascular changes and hyperglycemia stimulated by Diabetes Mellitus (DM). Endothelial lining of the blood capillaries absorbs excess amount of glucose (glycoproteins), hence become thick but are fragile. The swollen capillaries may burst and leak water, proteins, and lipids and tends to fovea expansion. Further it triggers the revascularization to nourish retinal fundus. These new blood capillaries are weak and fragile and can further progress the state to chronic. Pupil dilation for fundus observation leads to many ill effects like head ache, brow pain, blurred vision and light sensitivity. Ophthalmologists cannot administer the pathos well if the symptoms are indolently addressed by the patient and therefore reliability during subjective diagnosis lags. This paper address a qualitative evaluation of novel possibilistic clustering methods with induced spatial constraint in kernel domain to detect the presence of exudates in non-dilated DR images. This methods are compiled in an N dimensional Kernel space which helps to easily segregate the non-linear data regions present in the lower dimensional input space. Also the inclusion of spatial information of a pixel neighborhood will improves the noise handling capability of the proposed methods by easily extricating the noisy pixels from the target lesions and hence improves the system’s accuracy in attaining reliable data. Statistical evaluation reveals that the proposed algorithms has attained better sensitivity and specificity compared to existing state-of-art works.

Bounded Fuzzy Possibilistic Method

This paper introduces the Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, the data object's membership values should sum to 1. Hence, any data object may obtain full membership in at most one cluster. Possibilistic clustering methods remove this restriction. However, BFPM differs from previous fuzzy and possibilistic clustering approaches by allowing the membership function to take larger values with respect to all clusters. Furthermore, in BFPM, a data object can have full membership in multiple clusters or even in all clusters. BFPM relaxes the boundary conditions (restrictions) in membership assignment. The assigned boundaries satisfy the necessity of obtaining full memberships and overcome the issues with conventional methods (overlapping). The functionality of the proposed method has been proved in geometry, set theory, and other disciplines, when learning methods should provide the important arithmetic operations on different domains. Weighted Feature Distance function (WFD) is also used to cover diversity. Validity and comparison indexes have been applied to evaluate the accuracy of BFPM. Conventional fuzzy and possibilistic methods are compared with BFPM and BFPM-WFD, in terms of accuracy, fuzzification constant, different norms, and covering diversity and overlapping. The results show that the proposed algorithms perform better than other fuzzy and possibilistic methods.

Rough possibilistic C-means clustering based on multigranulation approximation regions and shadowed sets

The management of uncertain information in a data set is crucial for clustering models. In this study, we present a rough possibilistic C-means clustering approach based on multigranulation approximation regions and shadowed sets, which can handle the uncertainties implicated in data and generated by the model parameters simultaneously. In particular, all patterns are first partitioned into three approximation regions with respect to a fixed cluster according to their possibilistic membership degrees based on shadowed set theory, which can help capture the natural topology of the data, especially when dealing with outliers and noisy data. The multigranulation approximation regions of each cluster can then be formed under a series of fuzzifier values, where the uncertainty caused by a specific fuzzifier value can be detected based on variations in the approximation regions with different levels of granularity. We also introduce a framework for updating prototypes based on ensemble strategies to attenuate the distortions due to iteration during clustering procedures. Finally, an adaptive mechanism is developed for dynamically adjusting scale parameters based on the notion of the maximal compatible regions of clusters. By integrating various granular computing techniques, i.e., rough sets, fuzzy sets, shadowed sets, and the notion of multigranulation, the uncertainties implicated in data and produced by model parameters can be adequately addressed, and the possibilistic membership values involved make the method sufficiently robust to deal with noisy environments. The improved performance of the proposed approach was demonstrated in experiments based on the comparisons with other available fuzzy and possibilistic clustering methods.

A generalized possibilistic approach to shell clustering of template-based shapes

ABSTRACTEfficiently and effectively detecting shell-like structures of particular shapes is an important task in computer vision and image processing. This paper presents a generalized possibilistic c-means algorithm (PCM) for shell clustering based on the diversity index of degree-λ proposed by Patil and Taillie [Diversity as a concept and its measurement. J Amer Statist Assoc. 1982;77:548–561]. Experiments on various data sets in Wang [Possibilistic shell clustering of template-based shapes. IEEE Trans Fuzzy Syst. 2009;17:777–793] show that the the proposed generalized PCM performs better than Wang's [Possibilistic shell clustering of template-based shapes. IEEE Trans Fuzzy Syst. 2009;17:777–793] possibilistic shell clustering method according two two criteria: (i) the ‘grade of detection’ for each target cluster; (ii) the amount of computation, denoted as , required to attain a given .

A Robust Automatic Merging Possibilistic Clustering Method

Krishnapuram and Keller [IEEE Trans. Fuzzy Syst., vol. 1, no. 2, pp. 98-110, May 1993] proposed a possibilistic c-means (PCM) clustering by relaxing the constraint in fuzzy c-means (FCMs) that the memberships of a data point across classes sum to 1. The PCM algorithm has a tendency to produce coincident clusters. This can be a merit of PCM as a good mode-seeking algorithm if initials and parameters are suitably chosen. However, the performance of PCM heavily depends on initializations and parameter selection. In this paper, we propose a mechanism of robust automatic merging. We then create an automatic merging possibilistic clustering method (AM-PCM), where the proposed algorithm does not only solve these parameter-selection and initialization problems but also obtains an optimal cluster number. The proposed AM-PCM algorithm first uses all data points as initial cluster centers and then automatically merges these surrounding points around each cluster mode such that it can self-organize data groups according to the original data structure. The AM-PCM can exhibit the robustness to parameter, noise, cluster number, different volumes, and initializations. The computational complexity of AM-PCM is also analyzed. Comparisons between AM-PCM and other clustering methods are made. Some numerical data and real datasets are used to show these good aspects of AM-PCM. Experimental results and comparisons actually demonstrate that the proposed AM-PCM is an effective and parameter-free robust clustering algorithm.

Fuzzy Clustering Based on Total Uncertainty Degree

Traditional Fuzzy c-Means (FCM) methods have probabilistic and additive restrictions that ∑ μ (x) = 1; the sum of membership values on the identified membership function is one. Possibilistic clustering methods identify membership functions without such constraints, but some parameters used in objective functions are difficult to understand and membership function shapes are independent of clusters estimated through possibilistic methods. We propose novel fuzzy clustering using a total uncertainty degree based on evidential theory with which we obtain nonadditive membership functions whose their shapes depend on data distribution, i.e., they mutually differ. Cluster meanings thus become easier to understand than in possibilistic methods and our proposal requires only one parameter “fuzzifier.” Numerical experiments demonstrated the feasibility of our proposal conducted.