一种基于决策粗糙集的模糊C均值聚类数的确定方法

Fuzzy C-Means(FCM)是模糊聚类中聚类效果较好且应用较为广泛的聚类算法,但是其对初始聚类数的敏感性导致如何选择一个较好的C值 变得十分重要。因此,确定FCM的聚类数是使用FCM进行聚类分析时的一个至关重要的步骤。通过扩展决策粗糙集模型进行聚类的有效性分析,并进一步确定FCM的聚类数,从而避免了使用FCM时不好的初始化所带来的影响。文中提出了一种基于扩展粗糙集模型的模糊C均值聚类数的确定方法,并通过图像分割实验来验证聚类的效果。实验通过比对不同聚类数下分类结果的代价获得了一个较好的分割结果,并将结果与Z.Yu等人于2015年提出的蚁群模糊C均值混合算法(AFHA)以及提高的AFHA算法(IAFHA)进行对比,结果表明所提方法的聚类结果较好,图像分割效果较明显,Bezdek分割系数比AFHA和IAFHA算法的更高,且在Xie-Beni系数上也有较大优势。     

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。     

Fuzziness parameter selection in fuzzy c-means: The perspective of cluster validation

Fuzzy c-means （FCM） algorithm is an important clustering method in pattern recognition, while the fuzziness parameter, m, in FCM algorithm is a key parameter that can significantly affect the result of clustering. Cluster validity index （CVI） is a kind of criterion function to validate the clustering results, thereby determining the optimal cluster number of a data set. From the perspective of cluster validation, we propose a novel method to select the optimal value of m in FCM, and four well-known CVIs, namely XB, VK, VT, and SC, for fuzzy clustering are used. In this method, the optimal value of m is determined when CVIs reach their minimum values. Experimental results on four synthetic data sets and four real data sets have demonstrated that the range of m is [2, 3.5] and the optimal interval is [2.5, 3].     

一种新的聚类分析算法

给出了一种新的无监督聚类算法,但这种算法并非是基于目标函数的聚类算法,而是对数据直接设计一种迭代运算,以使数据在保持类特征的情况下进行重新组合最终达到分类的目的。通过对一类数据的实验表明,该算法在无监督给出类数方面具有较好的鲁棒性;另外,该算法在数据的准确归类、无监督聚类、确定性,以及对特殊类分布的适用性等方面均优于ＨＣＭ和ＦＣＭ算法,     

Fuzzy c-means clustering algorithm for directional data (FCM4DD)

Cluster analysis is a useful tool used commonly in data analysis. The purpose of cluster analysis is to separate data sets into subsets according to their similarities and dissimilarities. In this paper, the fuzzy c-means algorithm was adapted for directional data. In the literature, several methods have been used for the clustering of directional data. Due to the use of trigonometric functions in these methods, clustering is performed by approximate distances. As opposed to other methods, the FCM4DD uses angular difference as the similarity measure. Therefore, the proposed algorithm is a more consistent clustering algorithm than others. The main benefit of FCM4DD is that the proposed method is effectively a distribution-free approach to clustering for directional data. It can be used for N-dimensional data as well as circular data. In addition to this, the importance of the proposed method is that it would be applicable for decision making process, rule-based expert systems and prediction problems. In this study, some existing clustering algorithms and the FCM4DD algorithm were applied to various artificial and real data, and their results were compared. As a result, these comparisons show the superiority of the FCM4DD algorithm in terms of consistency, accuracy and computational time. Fuzzy clustering algorithms for directional data (FCM4DD and FCD) were compared according to membership values and the FCM4DD algorithm obtained more acceptable results than the FCD algorithm.     

Sample-weighted clustering methods

Although there have been many researches on cluster analysis considering feature (or variable) weights, little effort has been made regarding sample weights in clustering. In practice, not every sample in a data set has the same importance in cluster analysis. Therefore, it is interesting to obtain the proper sample weights for clustering a data set. In this paper, we consider a probability distribution over a data set to represent its sample weights. We then apply the maximum entropy principle to automatically compute these sample weights for clustering. Such method can generate the sample-weighted versions of most clustering algorithms, such as k-means, fuzzy c-means (FCM) and expectation & maximization (EM), etc. The proposed sample-weighted clustering algorithms will be robust for data sets with noise and outliers. Furthermore, we also analyze the convergence properties of the proposed algorithms. This study also uses some numerical data and real data sets for demonstration and comparison. Experimental results and comparisons actually demonstrate that the proposed sample-weighted clustering algorithms are effective and robust clustering methods.     

融合KNN优化的密度峰值和FCM聚类算法

针对模糊C均值（Fuzzy C-Means,FCM）聚类算法对初始聚类中心和噪声敏感、对边界样本聚类不够准确且易收敛于局部极小值等问题,提出了一种K邻近（KNN）优化的密度峰值（DPC）算法和FCM相结合的融合聚类算法（KDPC-FCM）。算法利用样本的K近邻信息定义样本局部密度,快速准确搜索样本的密度峰值点样本作为初始类簇中心,改善FCM聚类算法存在的不足,从而达到优化FCM聚类算法效果的目的。在多个UCI数据集、单个人造数据集、多种基准数据集和Geolife项目中的6个较大规模数据集上的实验结果表明,改进后的新算法与传统FCM算法、DSFCM算法对比,有着更好的抗噪性、聚类效果和更快的全局收敛速度,证明了新算法的可行性和有效性。     

An interval number distance- and ranking-based method for remotely sensed image fuzzy clustering

ABSTRACT

Fuzzy c-means clustering is an important non-supervised classification method for remote-sensing images and is based on type-1 fuzzy set theory. Type-1 fuzzy sets use singleton values to express the membership grade; therefore, such sets cannot describe the uncertainty of the membership grade. Interval type-2 fuzzy c-means (IT2FCM) clustering and relevant methods are based on interval type-2 fuzzy sets. Real vectors are used to describe the clustering centres, and the average values of the upper and lower membership grades are used to determine the classification of each pixel. Thus, the width information for interval clustering centres and interval membership grades are ignored. The main contribution of this article is to propose an improved IT2FCM* algorithm by adopting interval number distance (IND) and ranking methods, which use the width information of interval clustering centres and interval membership grades, thus distinguishing this method from existing fuzzy clustering methods. Three different IND definitions are tested, and the distance definition proposed by Li shows the best performance. The second contribution of this work is that two fuzzy cluster validity indices, FS- and XB-, are improved using the IND. Three types of multi/hyperspectral remote-sensing data sets are used to test this algorithm, and the experimental results show that the IT2FCM* algorithm based on the IND proposed by Li performs better than the IT2FCM algorithm using four cluster validity indices, the confusion matrix, and the kappa coefficient (κ). Additionally, the improved FS- index has more indicative ability than the original FS- index.     

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。     

融合密度峰值和模糊C-均值聚类算法

针对模糊C—均值(FCM)聚类算法聚类结果依赖于初始中心的选取,易收敛于局部极值等问题,提出了一种密度峰值聚类(DPC)算法和FCM相结合的混合聚类方法(DPC-FCM),利用密度峰值快速搜索算法可以比较准确地刻画聚类初始中心的特点,改善FCM聚类算法存在的不足,从而实现优化聚类.在UCI数据集和人工模拟数据集上的实验结果显示:融合后的新算法和传统的FCM算法相比有着更高的正确率和更快的收敛速度,证明了新算法的可行性.     

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。     

Color image segmentation using feedforward neural networks with FCM

This paper proposes a hybrid technique for color image segmentation. First an input image is converted to the image of CIE L*a*b* color space. The color features “a” and “b” of CIE L*a*b* are then fed into fuzzy C-means (FCM) clustering which is an unsupervised method. The labels obtained from the clustering method FCM are used as a target of the supervised feed forward neural network. The network is trained by the Levenberg-Marquardt back-propagation algorithm, and evaluates its performance using mean square error and regression analysis. The main issues of clustering methods are determining the number of clusters and cluster validity measures. This paper presents a method namely co-occurrence matrix based algorithm for finding the number of clusters and silhouette index values that are used for cluster validation. The proposed method is tested on various color images obtained from the Berkeley database. The segmentation results from the proposed method are validated and the classification accuracy is evaluated by the parameters sensitivity, specificity, and accuracy.     

An initialization method to simultaneously find initial cluster centers and the number of clusters for clustering categorical data

The leading partitional clustering technique, k-modes, is one of the most computationally efficient clustering methods for categorical data. However, in the k-modes-type algorithms, the performance of their clustering depends on initial cluster centers and the number of clusters needs be known or given in advance. This paper proposes a novel initialization method for categorical data which is implemented to the k-modes-type algorithms. The proposed method can not only obtain the good initial cluster centers but also provide a criterion to find candidates for the number of clusters. The performance and scalability of the proposed method has been studied on real data sets. The experimental results illustrate that the proposed method is effective and can be applied to large data sets for its linear time complexity with respect to the number of data points.     

An automatic fuzzy c-means algorithm for image segmentation

Fuzzy c-means (FCM) algorithm is one of the most popular methods for image segmentation. However, the standard FCM algorithm must be estimated by expertise users to determine the cluster number. So, we propose an automatic fuzzy clustering algorithm (AFCM) for automatically grouping the pixels of an image into different homogeneous regions when the number of clusters is not known beforehand. In order to get better segmentation quality, this paper presents an algorithm based on AFCM algorithm, called automatic modified fuzzy c-means cluster segmentation algorithm (AMFCM). AMFCM algorithm incorporates spatial information into the membership function for clustering. The spatial function is the weighted summation of the membership function in the neighborhood of each pixel under consideration. Experimental results show that AMFCM algorithm not only can spontaneously estimate the appropriate number of clusters but also can get better segmentation quality.     

基于可靠性的鲁棒模糊聚类

相比于k-means算法,模糊C均值(FCM)通过引入模糊隶属度,考虑不同数据簇之间的相互作用,进而避免了聚类中心趋同性问题.然而模糊隶属度具有拖尾和翘尾的结构特征,因此使得FCM算法对噪声点和孤立点很敏感;此外,由于FCM算法倾向于将各数据簇均等分,因此算法对数据簇大小也很敏感,对非平衡数据簇聚类效果不佳.针对这些问...     

Mountain c-regressions method

Since Quandt [The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association 53 (1958) 873-880] initiated the research on 2-regressions analysis, switching regression had been widely studied and applied in psychology, economics, social science and music perception. In fuzzy clustering, the fuzzy c-means (FCM) is the most commonly used algorithm. Hathaway and Bezdek [Switching regression models and fuzzy clustering, IEEE Transactions on Fuzzy Systems 1 (1993) 195-204] embedded FCM into switching regression where it was called fuzzy c-regressions (FCR). However, the FCR always depends heavily on initial values. In this paper, we propose a mountain c-regressions (MCR) method for solving the initial-value problem. First, we perform data transformation for the switching regression data set, and then implement the modified mountain clustering on the transformed data to extract c cluster centers. These extracted c cluster centers in the transformed space will correspond to c regression models in the original data set. The proposed MCR method can form well-estimated c regression models for switching regression data sets. According to the properties of transformation, the proposed MCR is also robust to noise and outliers. Several examples show the effectiveness and superiority of our proposed method.     

On cluster tree for nested and multi-density data clustering

Clustering is one of the important data mining tasks. Nested clusters or clusters of multi-density are very prevalent in data sets. In this paper, we develop a hierarchical clustering approach—a cluster tree to determine such cluster structure and understand hidden information present in data sets of nested clusters or clusters of multi-density. We embed the agglomerative k-means algorithm in the generation of cluster tree to detect such clusters. Experimental results on both synthetic data sets and real data sets are presented to illustrate the effectiveness of the proposed method. Compared with some existing clustering algorithms (DBSCAN, X-means, BIRCH, CURE, NBC, OPTICS, Neural Gas, Tree-SOM, EnDBSAN and LDBSCAN), our proposed cluster tree approach performs better than these methods.     

A cluster centers initialization method for clustering categorical data

The leading partitional clustering technique, k-modes, is one of the most computationally efficient clustering methods for categorical data. However, the performance of the k-modes clustering algorithm which converges to numerous local minima strongly depends on initial cluster centers. Currently, most methods of initialization cluster centers are mainly for numerical data. Due to lack of geometry for the categorical data, these methods used in cluster centers initialization for numerical data are not applicable to categorical data. This paper proposes a novel initialization method for categorical data which is implemented to the k-modes algorithm. The method integrates the distance and the density together to select initial cluster centers and overcomes shortcomings of the existing initialization methods for categorical data. Experimental results illustrate the proposed initialization method is effective and can be applied to large data sets for its linear time complexity with respect to the number of data objects.     

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。     

A symmetry based multiobjective clustering technique for automatic evolution of clusters

In this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization (MOO) problem, optimizing a set of cluster validity indices simultaneously. The proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy. Here variable number of cluster centers is encoded in the string. The number of clusters present in different strings varies over a range. The points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing Euclidean distance. Two cluster validity indices, one based on the Euclidean distance, XB-index, and another recently developed point symmetry distance based cluster validity index, Sym-index, are optimized simultaneously in order to determine the appropriate number of clusters present in a data set. Thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters. A new semi-supervised method is also proposed in the present paper to select a single solution from the final Pareto optimal front of the proposed multiobjective clustering technique. The efficacy of the proposed algorithm is shown for seven artificial data sets and six real-life data sets of varying complexities. Results are also compared with those obtained by another multiobjective clustering technique, MOCK, two single objective genetic algorithm based automatic clustering techniques, VGAPS clustering and GCUK clustering.