In some complicated datasets, due to the presence of noisy data points and outliers, cluster validity indices can give conflicting results in determining the optimal number of clusters. This paper presents a new validity index for fuzzy-possibilistic c-means clustering called Fuzzy-Possibilistic (FP) index, which works well in the presence of clusters that vary in shape and density. Moreover, FPCM like most of the clustering algorithms is susceptible to some initial parameters. In this regard, in addition to the number of clusters, FPCM requires a priori selection of the degree of fuzziness and the degree of typicality. Therefore, we presented an efficient procedure for determining their optimal values. The proposed approach has been evaluated using several synthetic and real-world datasets. Final computational results demonstrate the capabilities and reliability of the proposed approach compared with several well-known fuzzy validity indices in the literature. Furthermore, to clarify the ability of the proposed method in real applications, the proposed method is implemented in microarray gene expression data clustering and medical image segmentation.
University of Florida（佛罗里达大学）；University of Missouri（密苏里大学）
The Possibilistic Fuzzy Local Information C-Means (PFLICM) method is presented as a technique to segment side-look synthetic aperture sonar (SAS) imagery into distinct regions of the sea-floor. In this work, we investigate and present the results of an automated feature selection approach for SAS image segmentation. The chosen features and resulting segmentation from the image will be assessed based on a select quantitative clustering validity criterion and the subset of the features that reach a desired threshold will be used for the segmentation process.
University of Florida（佛罗里达大学）；University of Missouri（密苏里大学）
Side-look synthetic aperture sonar (SAS) can produce very high quality images of the sea-floor. When viewing this imagery, a human observer can often easily identify various sea-floor textures such as sand ripple, hard-packed sand, sea grass and rock. In this paper, we present the Possibilistic Fuzzy Local Information C-Means (PFLICM) approach to segment SAS imagery into sea-floor regions that exhibit these various natural textures. The proposed PFLICM method incorporates fuzzy and possibilistic clustering methods and leverages (local) spatial information to perform soft segmentation. Results …
Velalar College Of Engineering and Technology（维拉拉尔工程技术学院）；Kongu Engineering College（孔古工程学院）
Image segmentation is a vital part of image processing. Segmentation has its application widespread in the field of medical images in order to diagnose curious diseases. The same medical images can be segmented manually. But the accuracy of image segmentation using the segmentation algorithms is more when compared with the manual segmentation. In the field of medical diagnosis an extensive diversity of imaging techniques is presently available, such as radiography, computed tomography (CT) and magnetic resonance imaging (MRI). Medical image segmentation is an essential step for most consequent…
Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学）；Climax Data Pattern（Climax数据模式公司）
This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any 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 clu…
University of Florida（佛罗里达大学）；University of Missouri（密苏里大学）
Synthetic aperture sonar (SAS) imagery can generate high resolution images of the seafloor. Thus, segmentation algorithms can be used to partition the images into different seafloor environments. In this paper, we compare two possibilistic segmentation approaches. Possibilistic approaches allow for the ability to detect novel or outlier environments as well as well known classes. The Possibilistic Fuzzy Local Information C-Means (PFLICM) algorithm has been previously applied to segment SAS imagery. Additionally, the Possibilistic K-Nearest Neighbors (PKNN) algorithm has been used in other doma…
Boston University（波士顿大学）；University of Toronto（多伦多大学）；Amirkabir University of Technology（阿米尔卡比尔理工大学）
Both FCM and PCM clustering methods have been widely applied to pattern recognition and data clustering. Nevertheless, FCM is sensitive to noise and PCM occasionally generates coincident clusters. PFCM is an extension of the PCM model by combining FCM and PCM, but this method still suffers from the weaknesses of PCM and FCM. In the current paper, the weaknesses of the PFCM algorithm are corrected and the enhanced possibilistic fuzzy c-means (EPFCM) clustering algorithm is presented. EPFCM can still be sensitive to noise. Therefore, we propose an interval type-2 enhanced possibilistic fuzzy c-m…
Unsatisfying accuracy of learning methods is mostly caused by omitting the influence of important parameters such as membership assignments, type of data objects, and distance or similarity functions. The proposed method, called Bounded Fuzzy Possibilistic Method (BFPM) addresses different issues that previous clustering or classification methods have not sufficiently considered in their membership assignments. In fuzzy methods, the object's memberships should sum to 1. Hence, any data object may obtain full membership in at most one cluster or class. Possibilistic methods relax this condition…
International University of Business Agriculture and Technology（国际商业农业与技术大学）；Mississippi State University（密西西比州立大学）；Rajshahi College（拉杰沙希学院）
In this paper, several two-dimensional clustering scenarios are given. In those scenarios, soft partitioning clustering algorithms (Fuzzy C-means (FCM) and Possibilistic c-means (PCM)) are applied. Afterward, VAT is used to investigate the clustering tendency visually, and then in order of checking cluster validation, three types of indices (e.g., PC, DI, and DBI) were used. After observing the clustering algorithms, it was evident that each of them has its limitations; however, PCM is more robust to noise than FCM as in case of FCM a noise point has to be considered as a member of any of the …
This paper proposes a Genetic Algorithm based segmentation method that can automatically segment gray-scale images. The proposed method mainly consists of spatial unsupervised grayscale image segmentation that divides an image into regions. The aim of this algorithm is to produce precise segmentation of images using intensity information along with neighborhood relationships. In this paper, Fuzzy Hopfield Neural Network (FHNN) clustering helps in generating the population of Genetic algorithm which there by automatically segments the image. This technique is a powerful method for image segment…
A correlation-based fuzzy cluster validity index with secondary options detector
Mathematics and Statistics with Applications Research Group (MaSA) Department of Mathematics, King Mongkut’s University of Technology Thonburi（数学与应用统计学应用研究组（MaSA）数学系，皇室技术大学唐奔寺分校）
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Like k-means and Gaussian Mixture Model (GMM), fuzzy c-means (FCM) with soft partition has also become a popular clustering algorithm and still is extensively studied. However, these algorithms and their variants still suffer from some difficulties such as determination of the optimal number of clusters which is a key factor for clustering quality. A common approach for overcoming this difficulty is to use the trial-and-validation strategy, i.e., traversing every integer from large number like $\sqrt{n}$ to 2 until finding the optimal number corresponding to the peak value of some cluster vali…
Université de Lyon（里昂大学）；ERIC EA 3083；ArAr UMR 5138
Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters, as is the case in text categorization. Thus, we need more flexible clustering. Fuzzy clustering methods, where each data point can belong to several clusters, are an interesting alternative. Yet, seeding iterative fuzzy algorithms to achieve high quality clustering is an issue.…
Imperial College London（伦敦帝国学院）；Sciemus Ltd（Sciemus有限公司）；University of Oxford（牛津大学）
In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by calculating the model evidence or marginal likelihood. We explain why this is an attractive alternative over simply minimizing a mean squared error metric of prediction and show the validity of the propos…
Guise AI, Inc.（Guise AI 公司）；Applied Computational Intelligence Laboratory, Missouri University of Science and Technology（密苏里科技大学应用计算智能实验室）
This paper presents an adaptive resonance theory predictive mapping (ARTMAP) model which uses incremental cluster validity indices (iCVIs) to perform unsupervised learning, namely iCVI-ARTMAP. Incorporating iCVIs to the decision-making and many-to-one mapping capabilities of ARTMAP can improve the choices of clusters to which samples are incrementally assigned. These improvements are accomplished by intelligently performing the operations of swapping sample assignments between clusters, splitting and merging clusters, and caching the values of variables when iCVI values need to be recomputed. …
The existence of large volumes of time series data in many applications has motivated data miners to investigate specialized methods for mining time series data. Clustering is a popular data mining method due to its powerful exploratory nature and its usefulness as a preprocessing step for other data mining techniques. This article develops two novel clustering algorithms for time series data that are extensions of a crisp c-shapes algorithm. The two new algorithms are heuristic derivatives of fuzzy c-means (FCM). Fuzzy c-Shapes plus (FCS+) replaces the inner product norm in the FCM model with…
Missouri University of Science and Technology（密苏里科技大学）；CAPES Foundation（巴西高等教育人员素质提升协调局）
Validation is one of the most important aspects of clustering, but most approaches have been batch methods. Recently, interest has grown in providing incremental alternatives. This paper extends the incremental cluster validity index (iCVI) family to include incremental versions of Calinski-Harabasz (iCH), I index and Pakhira-Bandyopadhyay-Maulik (iI and iPBM), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP) and Representative Cross Entropy (irH), and Conn_Index (iConn_Index). Additionally, the effect of under- and over-partitioning on the beha…
Clustering is one of the widely used data mining techniques for medical diagnosis. Clustering can be considered as the most important unsupervised learning technique. Most of the clustering methods group data based on distance and few methods cluster data based on similarity. The clustering algorithms classify gene expression data into clusters and the functionally related genes are grouped together in an efficient manner. The groupings are constructed such that the degree of relationship is strong among members of the same cluster and weak among members of different clusters. In this work, we…
As a representative evidential clustering algorithm, evidential c-means (ECM) provides a deeper insight into the data by allowing an object to belong not only to a single class, but also to any subset of a collection of classes, which generalizes the hard, fuzzy, possibilistic, and rough partitions. However, compared with other partition-based algorithms, ECM must estimate numerous additional parameters, and thus insufficient or contaminated data will have a greater influence on its clustering performance. To solve this problem, in this study, a transfer learning-based ECM (TECM) algorithm is …
