Weighted and constrained possibilistic C-means clustering for online fault detection and isolation

In this paper, a new weighted and constrained possibilistic C-means clustering algorithm is proposed for process fault detection and diagnosis (FDI) in offline and online modes for both already known and novel faults. A possibilistic clustering based approach is utilized here to address some of the deficiencies of the fuzzy C-means (FCM) algorithm leading to more consistent results in the context of the FDI tasks by relaxing the probabilistic condition in FCM cost function. The proposed algorithm clusters the historical data set into C different dense regions without having precise knowledge about the number of the faults in the data set. The algorithm incorporates simultaneously possibilistic algorithm and local attribute weighting for time-series segmentation. This allows different weights to be allocated to different features responsible for the distinguished process faults which is an essential characteristic of proper FDI operations. A set of comparative studies have been carried out on the large-scale Tennessee Eastman industrial challenge problem and the DAMADICS actuator benchmark to demonstrate the superiority of the proposed algorithm in process FDI applications with respect to some available alternative approaches.     

Unsupervised possibilistic clustering

In fuzzy clustering, the fuzzy c-means (FCM) clustering algorithm is the best known and used method. Since the FCM memberships do not always explain the degrees of belonging for the data well, Krishnapuram and Keller proposed a possibilistic approach to clustering to correct this weakness of FCM. However, the performance of Krishnapuram and Keller's approach depends heavily on the parameters. In this paper, we propose another possibilistic clustering algorithm (PCA) which is based on the FCM objective function, the partition coefficient (PC) and partition entropy (PE) validity indexes. The resulting membership becomes the exponential function, so that it is robust to noise and outliers. The parameters in PCA can be easily handled. Also, the PCA objective function can be considered as a potential function, or a mountain function, so that the prototypes of PCA can be correspondent to the peaks of the estimated function. To validate the clustering results obtained through a PCA, we generalized the validity indexes of FCM. This generalization makes each validity index workable in both fuzzy and possibilistic clustering models. By combining these generalized validity indexes, an unsupervised possibilistic clustering is proposed. Some numerical examples and real data implementation on the basis of the proposed PCA and generalized validity indexes show their effectiveness and accuracy.     

一种基于核的快速可能性聚类算法

传统的快速聚类算法大多基于模糊C均值算法（Fuzzy C-means,FCM）,而FCM对初始聚类中心敏感,对噪音数据敏感并且容易收敛到局部极小值,因而聚类准确率不高。可能性C-均值聚类较好地解决了FCM对噪声敏感的问题,但容易产生一致性聚类。将FCM和可能性C-均值聚类结合的聚类算法较好地解决了一致性聚类问题。为进一步提高算法收敛速度和鲁棒性,提出一种基于核的快速可能性聚类算法。该方法引入核聚类的思想,同时使用样本方差对目标函数中参数η进行优化。标准数据集和人造数据集的实验结果表明这种基于核的快速可能性聚类算法提高了算法的聚类准确率,加快了收敛速度。     

模糊C均值聚类与K近邻算法的故障检测研究

基于K近邻的故障检测(FD-KNN)算法可以有效处理非线性、多模态的故障检测问题,但在过程故障检测中存在故障类型多、测量变量复杂等缺陷。将模糊C均值聚类(FCM)和K近邻(KNN)相结合,提出一种新的故障检测方法FCM-KNN。该方法与传统算法相比较,故障检测率有明显的提升。首先,应用FCM聚类将多模态训练集按模态聚类,同时根据样本与各聚类中心的距离比例来得到样本对于每个聚类中心的隶属度;再根据隶属度来判断样本所属模态,进而在各个模态下完成基于KNN的故障检测。通过多模态仿真实例进一步验证该方法的有效性。该方法具有检测率高、漏报和误报率低等优点,可有效提高检测效果。     

基于分裂式K均值聚类的图像分割方法

模糊C均值聚类(FCM)算法是一种有效的无监督图像分割方法,适用于任意分类数,不需要预知图像特征,但其聚类效果直接受待分类样本噪声和分类初始条件的影响。因此,提出了一种适用于彩色图像分割的分裂式K均值聚类(FKM)算法,该算法首先使用中值滤波对分类样本去噪,然后使用一种分裂聚类法对图像样本进行预分类,得到一组样本集初始划分,最后以这组划分为起点,使用基于概率距离的K均值聚类对图像分割进行迭代优化。实验结果表明,该算法可以避免FCM的误分类,诸如陷于中心死区、中心重叠和局部极小值,而且提高了分割速度。     

一种Web用户访问路径的可能性模糊聚类算法

结合Web用户访问特点,针对Web用户访问路径聚类分析中普遍存在的对象类别不确定性现象进行了研究.结合模糊聚类和可能性聚类的特点,提出来一种新的用户访问路径的可能性模糊聚类算法.新方法通过定义相关的截集,自动地将对象分配到若干簇中,避免了人工干预,实现了交叉聚类的目的.新方法建立在leader聚类算法的框架上,只需要扫描数据集一遍使得算法效率大大提高.在标准数据集上的对比试验表明新算法不仅是有效的,而且效率较高.     

一种协同的可能性模糊聚类算法

模糊C-均值聚类（FCM）对噪声数据敏感和可能性C-均值聚类（PCM）对初始中心非常敏感易导致一致性聚类。协同聚类算法利用不同特征子集之间的协同关系并与其他算法相结合,可提高原有的聚类性能。对此,在可能性C-均值聚类算法（PCM）基础上将其与协同聚类算法相结合,提出一种协同的可能性C-均值模糊聚类算法（C-FCM）。该算法在改进的PCM的基础上,提高了对数据集的聚类效果。在对数据集Wine和Iris进行测试的结果表明,该方法优于PCM算法,说明该算法的有效性。     

Robust fuzzy relational classifier incorporating the soft class labels

Fuzzy relational classifier (FRC) is a recently proposed two-step nonlinear classifier. At first, the unsupervised fuzzy c-means (FCM) clustering is performed to explore the underlying groups of the given dataset. Then, a fuzzy relation matrix indicating the relationship between the formed groups and the given classes is constructed for subsequent classification. It has been shown that FRC has two advantages: interpretable classification results and avoidance of overtraining. However, FRC not only lacks the robustness which is very important for a classifier, but also fails on the dataset with non-spherical distributions. Moreover, the classification mechanism of FRC is sensitive to the improper class labels of the training samples, thus leading to considerable decline in classification performance. The purpose of this paper is to develop a Robust FRC (RFRC) algorithm aiming at overcoming or mitigating all of the above disadvantages of FRC and maintaining its original advantages. In the proposed RFRC algorithm, we employ our previously proposed robust kernelized FCM (KFCM) to replace FCM to enhance its robustness against outliers and its suitability for the non-spherical data structures. In addition, we incorporate the soft class labels into the classification mechanism to improve its performance, especially for the datasets containing the improper class labels. The experimental results on 2 artificial and 11 real-life benchmark datasets demonstrate that RFRC algorithm can consistently outperform FRC in classification performance.     

基于遗传算法的模糊聚类分析

模糊C-均值聚类(FCM)应用广泛，但是它容易陷入局部最优，且对初始值很敏感。该文提出了一种基于遗传算法的模糊聚类方法，首先用遗传算法对模糊聚类中聚类中心的个数和聚类中心的选取进行指导，然后利用FCM进行聚类。实验结果表明：该方法可以在一定程度上避免FCM算法对初始值敏感和容易陷入局部最优解的缺陷，使聚类更合理，效果很好。     

基于遗传FCM算法的文本聚类

本文提出基于遗传FCM算法的文本聚类方法,首先采用LSI方法对文本特征进行降维,然后通过聚类有效性分析得到文本的类别数,最后再采用遗传FCM算法对文本进行聚类,这种方法较好的克服了FCM算法收敛于局部最优的缺陷,很好的解决了FCM算法对初值敏感的问题。实验表明提出的方法具有较好的聚类性能。     

Fuzzy clustering with nonlinearly transformed data

The Fuzzy C-Means (FCM) algorithm is a widely used objective function-based clustering method exploited in numerous applications. In order to improve the quality of clustering algorithms, this study develops a novel approach, in which a transformed data-based FCM is developed. Two data transformation methods are proposed, using which the original data are projected in a nonlinear fashion onto a new space of the same dimensionality as the original one. Next, clustering is carried out on the transformed data. Two optimization criteria, namely a classification error and a reconstruction error, are introduced and utilized to guide the optimization of the performance of the new clustering algorithm and a transformation of the original data space. Unlike other data transformation methods that require some prior knowledge, in this study, Particle Swarm Optimization (PSO) is used to determine the optimal transformation realized on a basis of a certain performance index. Experimental studies completed for a synthetic data set and a number of data sets coming from the Machine Learning Repository demonstrate the performance of the FCM with transformed data. The experiments show that the proposed fuzzy clustering method achieves better performance (in terms of the clustering accuracy and the reconstruction error) in comparison with the outcomes produced by the generic version of the FCM algorithm.     

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.     

一种扩展的条件模糊C-均值聚类算法

在综合分析标准的模糊C-均值聚类算法和条件模糊C-均值聚类算法基础上,对模糊划分空间进行修改,进一步弱化模糊划分矩阵的约束,给出一种扩展的条件模糊C-均值聚类算法。算法的划分矩阵和原型不依赖于背景约束及模糊划分矩阵的隶属度总和。实验结果表明：该算法可以得到不同的聚类原型,并具有很好的聚类效果。     

基于密度敏感距离的改进模糊C均值聚类算法

模糊C均值（FCM）聚类算法无法识别非凸数据,算法中基于欧式距离的相似性度量只考虑数据点之间的局部一致性特征而忽略了全局一致性特征。提出一种利用密度敏感距离度量创建相似度矩阵的FCM算法。通过近邻传播算法获取粗类数作为最佳聚类数的搜索范围上限,以解决FCM算法聚类数目需要人为预先设定和随机选定初始聚类中心造成聚类结果不稳定的问题。在此基础上,改进最大最小距离算法,得到具有代表性的样本点作为初始聚类中心,并结合轮廓系数自动确定最佳聚类数。基于UCI数据集和人工数据集的实验结果表明,相比经典FCM、K-means和CFSFDP算法,该算法不仅具有识别复杂非凸数据的能力,而且能够在保证聚类性能和稳定性的前提下加快收敛速度。     

笛卡尔乘积下的FCM聚类研究

针对于模糊c-均值（FCM）算法在初始聚类中心选取不佳的情况下容易产生聚类错误划分的情况,从FCM算法出发提出了一种基于笛卡尔乘积的FCM聚类算法（C-FCM）,并分析了加权指数m对聚类分析的影响。C-FCM将聚类提高到更高维的空间,有效地避免了FCM 对初值敏感及容易陷入局部极小的缺陷。客运专线列控（TCC）评估测试项目对C-FCM的检验结果表明,与传统FCM算法相比,C-FCM算法更准确,效果更佳,对解决邻站数据包的划分问题是可行、有效的。     

密度和有效性指标的自适应模糊C-均值算法

FCM算法作为基于目标函数的模糊聚类算法中最经典的算法之一,在实际应用中得到了深入的研究,但FCM算法需要人为给定分类数C,因此破坏了聚类的无监督性。针对FCM算法的不足,提出了利用密度指标确定初始聚类数目上限Cmax,并且对有效性指标进行了改进,计算对于(1,Cmax]中的每一个c对应的有效性函数值,根据有效性评判,确定最佳聚类数,实现了自动得到最佳分类数的算法。     

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 new Kernelized hybrid c-mean clustering model with optimized parameters

A possibilistic approach was initially proposed for c-means clustering. Although the possibilistic approach is sound, this algorithm tends to find identical clusters. To overcome this shortcoming, a possibilistic Fuzzy c-means algorithm (PFCM) was proposed which produced memberships and possibilities simultaneously, along with the cluster centers. PFCM addresses the noise sensitivity defect of Fuzzy c-means (FCM) and overcomes the coincident cluster problem of possibilistic c-means (PCM). Here we propose a new model called Kernel-based hybrid c-means clustering (KPFCM) where PFCM is extended by adopting a Kernel induced metric in the data space to replace the original Euclidean norm metric. Use of Kernel function makes it possible to cluster data that is linearly non-separable in the original space into homogeneous groups in the transformed high dimensional space. From our experiments, we found that different Kernels with different Kernel widths lead to different clustering results. Thus a key point is to choose an appropriate Kernel width. We have also proposed a simple approach to determine the appropriate values for the Kernel width. The performance of the proposed method has been extensively compared with a few state of the art clustering techniques over a test suit of several artificial and real life data sets. Based on computer simulations, we have shown that our model gives better results than the previous models.     

距离修正的模糊C均值聚类算法

经典的模糊C均值算法基于欧氏距离,存在等划分趋势的缺陷,分错率较高,只适用于球形结构的聚类。针对这一问题,利用数据的点密度信息,在数据点与聚类中心的距离度量中引入了调节因子,提出了一种基于密度的距离修正矩阵,并用其代替经典模糊C均值算法中的距离度量矩阵。通过人造数据集和UCI数据集的两组聚类实验,证实了改进算法对非球形结构的数据同样适用,且相比经典的模糊C均值算法具有更高的聚类准确率。