Possibilistic Fuzzy C-means Clustering Algorithm Research Articles

Suppressed possibilistic fuzzy c-means clustering based on shadow sets for noisy data with imbalanced sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images which are characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

A feature-weighted suppressed possibilistic fuzzy c-means clustering algorithm and its application on color image segmentation

The possibilistic fuzzy c-means clustering (PFCM) algorithm is a hybridization of possibilistic c-means clustering (PCM) and fuzzy c-means clustering (FCM) algorithms. However, there are two main problems in PFCM. One is that the Euclidean distance employed in PFCM always disregards the imbalance among sample features because it treats all features of data equally, which easily causes misclassification for feature-imbalanced multidimensional data. The other is that PFCM always produces significant center deviations and overlapping centers for multiclass datasets with strong noise injection, due to the difficulty of PFCM in the membership-weight parameter setting and the lack of between-class relationships in possibilistic memberships. Therefore, a feature-weighted suppressed possibilistic fuzzy c-means clustering (FW-S-PFCM) algorithm is presented by introducing a feature-weighted method and “suppressed competitive learning” strategy into the PFCM algorithm in this paper. First, the FW-S-PFCM algorithm introduces a feature-weight matrix into the objective function that can automatically assign feature-weight values to different features and different clusters according to the distribution of samples, thus overcoming the influence of feature imbalance and improving clustering effects for noisy multidimensional datasets. Second, combined with the feature-weight matrix, a “suppressed competitive learning” strategy is designed to resolve the center-overlapping problem in noisy multiclass dataset clustering. Specifically, partial crucial points of each class near the center are selected according to a cluster core generated by a cross-section of a threshold on the possibilistic membership surface. Third, their possibilistic memberships participate in the suppressed learning process to overcome the lack of between-class relationships. Last, a segmentation algorithm for noisy color images based on FW-S-PFCM is proposed combined with the feature-weight method and noise-identification ability of possibilistic memberships. Experiments on synthetic data, UCI data and color image segmentation demonstrate that the proposed FW-S-PFCM algorithm can overcome the partial center-overlapping problem and improve clustering performance on complex datasets with feature imbalance and strong noise injection. The proposed algorithm can also reduce the iteration number, sensitivity to membership weights, and initializations of PFCM.

An Improved Type-2 Possibilistic Fuzzy C-Means Clustering Algorithm with Application for MR Image Segmentation

An Improved Type-2 Possibilistic Fuzzy C-Means Clustering Algorithm with Application for MR Image Segmentation

Improved kernel possibilistic fuzzy clustering algorithm based on invasive weed optimization

Fuzzy c-means (FCM) clustering algorithm is sensitive to noise points and outlier data, and the possibilistic fuzzy c-means (PFCM) clustering algorithm overcomes the problem well, but PFCM clustering algorithm has some problems: it is still sensitive to initial clustering centers and the clustering results are not good when the tested datasets with noise are very unequal. An improved kernel possibilistic fuzzy c-means algorithm based on invasive weed optimization (IWO-KPFCM) is proposed in this paper. This algorithm first uses invasive weed optimization (IWO) algorithm to seek the optimal solution as the initial clustering centers, and introduces kernel method to make the input data from the sample space map into the high-dimensional feature space. Then, the sample variance is introduced in the objection function to measure the compact degree of data. Finally, the improved algorithm is used to cluster data. The simulation results of the University of California-Irvine (UCI) data sets and artificial data sets show that the proposed algorithm has stronger ability to resist noise, higher cluster accuracy and faster convergence speed than the PFCM algorithm.

Identification of pore spaces in 3D CT soil images using PFCM partitional clustering

Recent advances in non-destructive imaging techniques, such as X-ray computed tomography (CT), make it possible to analyse pore space features from the direct visualisation from soil structures. A quantitative characterisation of the three-dimensional solid-pore architecture is important to understand soil mechanics, as they relate to the control of biological, chemical, and physical processes across scales. This analysis technique therefore offers an opportunity to better interpret soil strata, as new and relevant information can be obtained. In this work, we propose an approach to automatically identify the pore structure of a set of 200-2D images that represent slices of an original 3D CT image of a soil sample, which can be accomplished through non-linear enhancement of the pixel grey levels and an image segmentation based on a PFCM (Possibilistic Fuzzy C-Means) algorithm. Once the solids and pore spaces have been identified, the set of 200-2D images is then used to reconstruct an approximation of the soil sample by projecting only the pore spaces. This reconstruction shows the structure of the soil and its pores, which become more bounded, less bounded, or unbounded with changes in depth. If the soil sample image quality is sufficiently favourable in terms of contrast, noise and sharpness, the pore identification is less complicated, and the PFCM clustering algorithm can be used without additional processing; otherwise, images require pre-processing before using this algorithm. Promising results were obtained with four soil samples, the first of which was used to show the algorithm validity and the additional three were used to demonstrate the robustness of our proposal. The methodology we present here can better detect the solid soil and pore spaces on CT images, enabling the generation of better 2D–3D representations of pore structures from segmented 2D images.