A Possibilistic Fuzzy c-Means Clustering Algorithm

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.     

Suppressed possibilistic c-means clustering algorithm

The possibilistic c-means (PCM) clustering algorithm always suffers from a coincident clustering problem since it relaxes the probabilistic constraint in the fuzzy c-means (FCM) clustering algorithm. In this paper, to overcome the shortcoming of the PCM, a novel suppressed possibilistic c-means (S-PCM) clustering algorithm by introducing a suppressed competitive learning strategy into the PCM so as to improve the between-cluster relationships is proposed. Specifically, in the updating process the new algorithm searches for the biggest typicality which is regarded as winner by a competitive mechanism. Then it suppresses the non-winner typicalities with a suppressed rate which is used to control the learning strength. Moreover, the parameter setting problems of the suppressed rate and the penalty parameter in the S-PCM are also discussed in detail. In addition, the suppressed competitive learning strategy is still introduced into the possibilistic Gustafson–Kessel (PGK) clustering algorithm and a novel suppressed possibilistic Gustafson–Kessel (S-PGK) clustering model is proposed, which is more applicable to the ellipsoidal data clustering. Finally, experiments on several synthetic and real datasets with noise injection demonstrate the effectiveness of the proposed algorithms.     

An invisible hybrid color image system using spread vector quantization neural networks with penalized FCM

In this paper, an invisible hybrid color image hiding scheme based on spread vector quantization (VQ) neural network with penalized fuzzy c-means (PFCM) clustering technology (named SPFNN) is proposed. The goal is to offer safe exchange of a color stego-image in the internet. In the proposed scheme, the secret color image is first compressed by a spread-unsupervised neural network with PFCM based on interpolative VQ (IVQ), then the block cipher Data Encryption Standard (DES) and the Rivest, Shamir and Adleman (RSA) algorithms are hired to provide the mechanism of a hybrid cryptosystem for secure communication and convenient environment in the internet. In the SPFNN, the penalized fuzzy clustering technology is embedded in a two-dimensional Hopfield neural network in order to generate optimal solutions for IVQ. Then we encrypted color IVQ indices and sorted the codebooks of secret color image information and embedded them into the frequency domain of the cover color image by the Hadamard transform (HT). Our proposed method has two benefits comparing with other data hiding techniques. One is the high security and convenience offered by the hybrid DES and RSA cryptosystems to exchange color image data in the internet. The other benefit is that excellent results can be obtained using our proposed color image compression scheme SPFNN method.     

Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem

In this study a fuzzy c-means clustering algorithm based method is proposed for solving a capacitated multi-facility location problem of known demand points which are served from capacitated supply centres. It involves the integrated use of fuzzy c-means and convex programming. In fuzzy c-means, data points are allowed to belong to several clusters with different degrees of membership. This feature is used here to split demands between supply centers. The cluster number is determined by an incremental method that starts with two and designated when capacity of each cluster is sufficient for its demand. Finally, each group of cluster and each model are solved as a single facility location problem. Then each single facility location problem given by fuzzy c-means is solved by convex programming which optimizes transportation cost is used to fine-tune the facility location. Proposed method is applied to several facility location problems from OR library (Osman & Christofides, 1994) and compared with centre of gravity and particle swarm optimization based algorithms. Numerical results of an asphalt producer’s real-world data in Turkey are reported. Numerical results show that the proposed approach performs better than using original fuzzy c-means, integrated use of fuzzy c-means and center of gravity methods in terms of transportation costs.     

Soft fuzzy rough set-based MR brain image segmentation

Fuzzy sets, rough sets are efficient tools to handle uncertainty and vagueness in the medical images and are widely used for medical image segmentation. Soft sets are a new mathematical approach to uncertainty and vagueness. In this paper, a hybrid segmentation algorithm based on soft sets namely soft fuzzy rough c-means is proposed to extract the white matter, gray matter and the cerebro spinal fluid from MR brain image with bias field correction. In this algorithm, soft fuzzy rough approximations are applied to obtain the rough regions of image. These approximations are free from defining thresholds, weight parameters and are less complex compared to the existing rough set based algorithms. Soft sets use similarity coefficients to find the similarity of the clusters formed in present and previous step. The proposed algorithm does not involve any negative region, hence all the pixels participate in clustering avoiding clustering mistakes. Also, the histogram based centroids choose the centroids close to the ground truth that in turn effect the definition of approximations, standardizing the clusters. The proposed algorithm evaluated through simulation, compared it with existing k-means, rough k-means, fuzzy c-means and other hybrid algorithms. The soft fuzzy rough c-means algorithm outperforms the considered algorithms in all analyzed scenarios even in extracting the tumor from the brain tissue.     

基于网格和密度的模糊c均值聚类初始化方法

模糊c均值聚类算法是目前聚类分析中最受欢迎的算法之一,但其聚类效果往往受初始参数的影响.针对这一问题,提出一种基于网格和密度的模糊c均值聚类初始化方法.以网格和密度为工具提取聚类样本的类聚类中心,以此来初始化模糊c均值聚类算法的初始参数,从而弥补原算法的不足.实验证明方法是可行的、有效的.     

一种基于Mahalanobis距离的增量聚类算法

经典的模糊c均值聚类算法对非球型或椭球型分布的数据集进行聚类效果较差。将经典的模糊c均值聚类中的欧氏距离用Mahalanobis距离替代,利用Mahalanobis距离的优点,将其用于增量学习中,提出一种基于马氏距离的模糊增量聚类学习算法。实验结果表明该算法能较有效地解决模糊聚类方法中的缺陷,提高了训练精度。     

Hadoop based uncertain possibilistic kernelized c-means algorithms for image segmentation and a comparative analysis

Over the years data clustering algorithms have been used for image segmentation. Due to the presence of uncertainty in real life datasets, several uncertainty based data clustering algorithms have been developed. The c-means clustering algorithms form one such family of algorithms. Starting with the fuzzy c-means (FCM) a subfamily of this family comprises of rough c-means (RCM), intuitionistic fuzzy c-means (IFCM) and their hybrids like rough fuzzy c-means (RFCM) and rough intuitionistic fuzzy c-means (RIFCM). In the basic subfamily of this family of algorithms, the Euclidean distance was being used to measure the similarity of data. However, the sub family of algorithms obtained replacing the Euclidean distance by kernel based similarities produced better results. Especially, these algorithms were useful in handling viably cluster data points which are linearly inseparable in original input space. During this period it was inferred by Krishnapuram and Keller that the membership constraints in some rudimentary uncertainty based clustering techniques like fuzzy c-means imparts them a probabilistic nature, hence they suggested its possibilistic version. In fact all the other member algorithms from basic subfamily have been extended to incorporate this new notion. Currently, the use of image data is growing vigorously and constantly, accounting to huge figures leading to big data. Moreover, since image segmentation happens to be one of the most time consuming processes, industries are in the need of algorithms which can solve this problem at a rapid pace and with high accuracy. In this paper, we propose to combine the notions of kernel and possibilistic approach together in a distributed environment provided by Apache™ Hadoop. We integrate this combined notion with map-reduce paradigm of Hadoop and put forth three novel algorithms; Hadoop based possibilistic kernelized rough c-means (HPKRCM), Hadoop based possibilistic kernelized rough fuzzy c-means (HPKRFCM) and Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means (HPKRIFCM) and study their efficiency in image segmentation. We compare their running times and analyze their efficiencies with the corresponding algorithms from the other three sub families on four different types of images, three different kernels and six different efficiency measures; the Davis Bouldin index (DB), Dunn index (D), alpha index (α), rho index (ρ), alpha star index (α*) and gamma index (γ). Our analysis shows that the hyper-tangent kernel with Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means is the best one for image segmentation among all these clustering algorithms. Also, the times taken to render segmented images by the proposed algorithms are drastically low in comparison to the other algorithms. The implementations of the algorithms have been carried out in Java and for the proposed algorithms we have used Hadoop framework installed on CentOS. For statistical plotting we have used matplotlib (python library).     

基于FCM和RVGA的FNN在非线性辨识中的应用

提出一种新的基于模糊C-均值聚类(FCM)和实值遗传算法(RVGA)的模糊神经网络(FNN)。在对模糊规则进行训练之前,利用模糊C-均值聚类从训练数据中提取出典型数据,以删除野值和协调数据内部冲突。然后利用一种新的实值遗传算法对此典型数据进行训练。此遗传算法的交叉和变异运算均直接对实值进行操作,而不是传统的位操作,因此,可以极大地减少训练时间并实现全局寻优。对非线性函数辨识的仿真实验证明了该方法的优越性。     

A new ECG beat clustering method based on kernelized fuzzy c-means and hybrid ant colony optimization for continuous domains

The kernelized fuzzy c-means algorithm uses kernel methods to improve the clustering performance of the well known fuzzy c-means algorithm by mapping a given dataset into a higher dimensional space non-linearly. Thus, the newly obtained dataset is more likely to be linearly seprable. However, to further improve the clustering performance, an optimization method is required to overcome the drawbacks of the traditional algorithms such as, sensitivity to initialization, trapping into local minima and lack of prior knowledge for optimum paramaters of the kernel functions. In this paper, to overcome these drawbacks, a new clustering method based on kernelized fuzzy c-means algorithm and a recently proposed ant based optimization algorithm, hybrid ant colony optimization for continuous domains, is proposed. The proposed method is applied to a dataset which is obtained from MIT–BIH arrhythmia database. The dataset consists of six types of ECG beats including, Normal Beat (N), Premature Ventricular Contraction (PVC), Fusion of Ventricular and Normal Beat (F), Artrial Premature Beat (A), Right Bundle Branch Block Beat (R) and Fusion of Paced and Normal Beat (f). Four time domain features are extracted for each beat type and training and test sets are formed. After several experiments it is observed that the proposed method outperforms the traditional fuzzy c-means and kernelized fuzzy c-means algorithms.     

A possibilistic clustering approach to novel fault detection and isolation

In this paper, a new approach for fault detection and isolation that is based on the possibilistic clustering algorithm is proposed. Fault detection and isolation (FDI) is shown here to be a pattern classification problem, which can be solved using clustering and classification techniques. A possibilistic clustering based approach is proposed here to address some of the shortcomings of the fuzzy c-means (FCM) algorithm. The probabilistic constraint imposed on the membership value in the FCM algorithm is relaxed in the possibilistic clustering algorithm. Because of this relaxation, the possibilistic approach is shown in this paper to give more consistent results in the context of the FDI tasks. The possibilistic clustering approach has also been used to detect novel fault scenarios, for which the data was not available while training. Fault signatures that change as a function of the fault intensities are represented as fault lines, which have been shown to be useful to classify faults that can manifest with different intensities. The proposed approach has been validated here through simulations involving a benchmark quadruple tank process and also through experimental case studies on the same setup. For large scale systems, it is proposed to use the possibilistic clustering based approach in the lower dimensional approximations generated by algorithms such as PCA. Towards this end, finally, we also demonstrate the key merits of the algorithm for plant wide monitoring study using a simulation of the benchmark Tennessee Eastman problem.     

DCT子空间的邻域加权模糊C均值聚类算法

模糊C均值聚类是一种有效的图像分割方法, 但存在因忽略空间上下文信息和结构信息而易为噪声所干扰的现象. 为此提出了DCT子空间的邻域加权模糊C均值聚类方法. 该方法首先结合分块的思想, 对图像块进行离散余弦变换(discrete cosine transform,DCT), 建立了一个基于图像块局部信息的相似性度量模型; 然后定义目标函数中的欧式距离为邻域加权距离; 最后将该方法应用于加噪的人工合成图像、自然图像和MR图像. 实验结果表明, 该方法能够获得较好的分割效果, 同时具有较强的抗噪性.     

Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.     

Alternative c-means clustering algorithms

In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence function, we claim that the proposed new metric is more robust than the Euclidean norm. We then create two new clustering methods called the alternative hard c-means (AHCM) and alternative fuzzy c-means (AFCM) clustering algorithms. These alternative types of c-means clustering have more robustness than c-means clustering. Numerical results show that AHCM has better performance than HCM and AFCM is better than FCM. We recommend AFCM for use in cluster analysis. Recently, this AFCM algorithm has successfully been used in segmenting the magnetic resonance image of Ophthalmology to differentiate the abnormal tissues from the normal tissues.     

一种改进的模糊C均值算法在入侵检测中的应用

为解决模糊C均值(FCM)聚类算法在入侵检测中存在的检测效率低的问题,提出一种改进方法,将改进的模糊C均值聚类算法应用于入侵检测。测试表明,该算法有效提高了聚类检测的检测率,降低了误检测率,具有可行性和有效性。     

A fuzzy c-means based hybrid evolutionary approach to the clustering of supply chain

This paper describes the work that adapts group technology and integrates it with fuzzy c-means, genetic algorithms and the tabu search to realize a fuzzy c-means based hybrid evolutionary approach to the clustering of supply chains. The proposed hybrid approach is able to organise supply chain units, transportation modes and work orders into different unit-transportation-work order families. It can determine the optimal clustering parameter, namely the number of clusters, c, and weighting exponent, m, dynamically, and is able to eliminate the necessity of pre-defining suitable values for these clustering parameters. A new fuzzy c-means validity index that takes into account inter-cluster transportation and group efficiency is formulated. It is employed to determine the promise level that estimates how good a set of clustering parameters is. The capability of the proposed hybrid approach is illustrated using three experiments and the comparative studies. The results show that the proposed hybrid approach is able to suggest suitable clustering parameters and near optimal supply chain clusters can be obtained readily.     

基于二维直方图的图像模糊聚类分割新方法

基于二维直方图的模糊聚类分割算法可以有效地抑制噪声的干扰。但是,FCM算法用于图像数据聚类时的最大缺陷是运算的开销太大,这就限制了这种方法在图像分割中的应用。该文根据FCM算法和灰度图像的特点,提出了一种适用于灰度图像分割的抑制式模糊C-均值聚类算法(S-FCM)。通过调节抑制因子α来提高分割速度和分类的正确率。实验结果表明,新算法对小目标灰度图像的分割效果优于FCM算法。     

Novel segmentation algorithm in segmenting medical images

The aim of this paper is to develop an effective fuzzy c-means (FCM) technique for segmentation of Magnetic Resonance Images (MRI) which is seriously affected by intensity inhomogeneities that are created by radio-frequency coils. The weighted bias field information is employed in this work to deal the intensity inhomogeneities during the segmentation of MRI. In order to segment the general shaped MRI dataset which is corrupted by intensity inhomogeneities and other artifacts, the effective objective function of fuzzy c-means is constructed by replacing the Euclidean distance with kernel-induced distance. In this paper, the initial cluster centers are assigned using the proposed center initialization algorithm for executing the effective FCM iteratively. To assess the performance of proposed method in comparison with other existed methods, experiments are performed on synthetic image, real breast and brain MRIs. The clustering results are validated using Silhouette accuracy index. The experimental results demonstrate that our proposed method is a promising technique for effective segmentation of medical images.     

基于模糊C-均值聚类的支持向量机

支持向量机针对大规模数据集学习问题的处理需要耗费很长的时间,提出一种数据预处理的方法对学习样本进行聚 类,以此为基础得到一种模糊支持向量机.计算机仿真结果表明提出的SVM算法与传统的SVM训练算法相比,在不降低分 类精度的情况下,大大缩短了支持向量机的学习训练时间.     

彩色地图分色算法的改进及实现

在加权模糊c-均值（FCM）聚类算法的基础上，对分色算法进行了改进．首先进行色彩空间模型转换，然后对基于样本加权的FCM算法进行改进，对隶属度进行调整，把二维彩色直方图引入加权系数中．对于模糊c-均值算法，当隶属度接近时，分类会变得模糊，而且对于不同的样本矢量，聚类效果有所不同，本算法兼顾到了这两点．该方法已用Visual C＋＋6．0编程实现，效果比较理想．