一种改进的模糊聚类算法

传统模糊聚类算法如模糊C-均值(FCM)算法中,用户必须预先指定聚类类别数C,且目标函数收敛速度过慢。为此,将粒度分析原理应用在FCM算法中,提出了基于粒度原理确定聚类类别数的方法,并采用密度函数法初始化聚类中心。实验结果表明,改进后的聚类算法能够得到合理有效的聚类数目,并且与随机初始化相比,迭代次数明显减少,收敛速度明显加快。     

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.针对这些问题,本文提出了基于可靠性的鲁棒模糊聚类算法(RRFCM).该算法基于当前的聚类结果,对样本点进行可靠性分析,利用样本点的可靠性和局部近邻信息,突出不同数据簇之间的可分性,从而提高了算法对噪声的鲁棒性,并且降低了对非平衡数据簇大小的敏感性,得到了泛化性能更好的聚类结果.与相关算法进行对比,RRFCM算法在人造数据集,UCI真实数据集以及图像分割实验中均取得最优的结果.     

基于自适应蚁群的FCM聚类优化算法研究

模糊C均值聚类算法在算法初始化时需要人为设定聚类类别数、随机初始化聚类中心,致使该算法容易陷入局部最优值.为解决此类问题,在蚁群算法中引入信息素更新机制,使其输出的聚类中心更具全局优化的特征和较强鲁棒性的特点;用蚁群算法得到的聚类中心来初始化FCM算法的聚类中心,解决了FCM算法对初始聚类中心敏感的问题;使用结合熵信息与数据几何结构的聚类有效性评价方法对FCM算法和优化FCM算法进行评价,评价结果表明优化的FCM算法性能更优.在仿真实验中,利用提出的优化算法和FCM算法对自然图像、纹理图像和SAR图像进行分割实验,从图像分割的准确性和算法的实时性做对比实验,验证了优化算法的有效性.     

基于模糊C均值算法的类合并聚类算法研究

针对FCM（Fuzzy C-Means）算法对于初始聚类中心敏感,并只适合于发现球状类型簇的缺陷,提出采用冗余聚类中心初始化的方法降低算法对初始聚类中心的依赖,并先暂时将大簇或者延伸形状的簇分割成用多个小类表示,再利用隶属度矩阵提供的信息合并相邻的小类为大类,对FCM算法进行改进。实验结果显示改进的FCM算法能够在一定程度上识别不规则的簇,并减小FCM算法对初始聚类中心的依赖。     

基于模糊K-harmonic means的谱聚类算法

谱聚类作为一种有效的方法广泛应用于机器学习。通过分析谱聚类初始化敏感的实质,引入对初值不敏感的模糊K-harmonic means算法来克服这一缺点,提出一种基于模糊K-harmonic means的谱聚类算法（FKHM-SC）。与传统谱聚类算法以及对初值敏感的K-means、FCM算法相比,改进算法不仅可以识别有挑战性的人工数据,并且可以得到稳定的聚类中心和聚类结果,同时提高了聚类的精确度。实验结果表明了该算法的有效性和可行性。     

改进的模糊C-均值聚类算法研究

为解决模糊C-均值（FCM）聚类算法对噪声和孤立点数据敏感、样本分布不均衡的问题,提出了具体的改进和提高的方法：改进隶属度函数,以消除孤立点对聚类结果的影响;为每个样本点赋予一个定量的权值,以区分不同的样本点对于知识发现的不同作用,改善噪音和分布不均衡的样本集的聚类结果。实验结果表明该算法具有更好的健壮性和聚类效果。     

模糊C-均值聚类算法的优化

针对传统模糊C-均值聚类算法（FCM算法）初始聚类中心选择的随机性和距离向量公式应用的局限性,提出一种基于密度和马氏距离优化的模糊C-均值聚类算法（Fuzzy C-Means Based on Mahalanobis and Density,FCMBMD算法）。该算法通过计算样本点的密度来确定初始聚类中心,避免了初始聚类中心随机选取而产生的聚类结果的不稳定;采用马氏距离计算样本集的相似度,以满足不同度量单位数据的要求。实验结果表明,FCMBMD算法在聚类中心、收敛速度、迭代次数以及准确率等方面具有良好的效果。     

结合蚁群聚类算法的模糊 C 均值聚类

模糊 C 均值(FCM)聚类算法采取随机选取聚类中心的方法,这种方法使得 FCM 算法在局部范围内容易获得最优解,但在全局范围内效果较差,且 FCM 算法中聚类簇的个数一般需要人为设定.面对上述种种问题,文中将蚁群聚类算法和 FCM 聚类算法进行结合,获得了一种改进的 FCM 聚类算法.该算法在初步聚类中利用蚁群聚类产生聚类中心和簇的个数,将产生的聚类中心提供给 FCM 算法进行再次聚类.利用蚁群聚类的全局搜索和并行运算的优点避免了聚类易陷入局部最优解的缺陷.经过实验验证,该算法较一般 FCM 算法具有更好的性能.     

一种基于隶属度优化的演化聚类算法

针对FCM中数据点隶属度的计算是影响算法执行效率的主要因素,提出一种新的加速FCM算法(accelerated fuzzy C-means,AFCM),用于加速FCM及基于FCM的演化聚类算法.AFCM算法采用抽样初始化操作,产生较好的初始聚类中心,对于拥有较大隶属度的数据点,通过一步k-means操作更新模糊聚类中心,同时仅更新小隶属度来达到加速FCM算法的目的.为了验证所提出方法的有效性并提高聚类算法的效率,将AFCM应用于基于演化算法的模糊聚类算法.实验表明,此方法在保持良好的聚类结果前提下,能够减少大规模数据集上聚类算法的计算时间.     

模糊C均值聚类与硬聚类的性能比较及改进

本文以灰度值的图像分割为基础,对模糊C均值聚类算法(Fuzzy C-means,FCM)[1]和硬聚类进行了详尽的讨论,在此基础上对两者进行了比较,包括两者的迭代速度比较和两者的分割效果比较,聚类中心的初始化对迭代速度和分割效果的影响,并以此为基础对FCM聚类算法进行了改进。实验表明,改进的FCM聚类算法在迭代速度和分割效果方面都明显优于原始的FCM聚类算法。     

Collaborative fuzzy clustering

In this study, we introduce a new clustering architecture in which several subsets of patterns can be processed together with an objective of finding a structure that is common to all of them. To reveal this structure, the clustering algorithms operating on the separate subsets of data collaborate by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns that are directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. A detailed clustering algorithm is developed on a basis of the standard FCM method and illustrated by means of numeric examples.     

Accelerating fuzzy clustering

This paper extends earlier work [C. Borgelt, R. Kruse, Speeding up fuzzy clustering with neural network techniques, in: Proceedings of the 12th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’03, St. Louis, MO, USA), IEEE Press, Piscataway, NJ, USA, 2003] on an approach to accelerate fuzzy clustering by transferring methods that were originally developed to speed up the training process of (artificial) neural networks. The core idea is to consider the difference between two consecutive steps of the alternating optimization scheme of fuzzy clustering as providing a gradient. This “gradient” may then be modified in the same way as a gradient is modified in error backpropagation in order to enhance the training. Even though these modifications are, in principle, directly applicable, carefully checking and bounding the update steps can improve the performance and can make the procedure more robust. In addition, this paper provides a new and much more detailed experimental evaluation that is based on fuzzy cluster comparison measures [C. Borgelt, Resampling for fuzzy clustering, Int. J. Uncertainty, Fuzziness Knowledge-based Syst. 15 (5) (2007), 595-614], which can be used nicely to study the convergence speed.     

Convex-set-based fuzzy clustering

Prototype-based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. We propose a two-level fuzzy clustering method that involves adaptively expanding and merging convex polytopes, where the convex polytopes are considered as a “flexible” prototype. Therefore, the dependency on the use of a specified prototype can be eliminated. Also, the proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. In the first level of our proposed method, each cluster is represented by a convex polytope which is described by its set of vertices. Specifically, nonlinear membership functions are utilized to determine whether an input pattern creates a new cluster or whether an existing cluster should be modified. In the second level, the expandable clusters that are selected by an intercluster distance measure are merged to improve clustering efficiency and to reduce the order dependency of the incoming input patterns. Several experimental results are given to show the validity of our method     

基于Canopy聚类的噪声自适应模糊C-均值算法

针对局部空间信息的模糊C-均值算法（WFLICM）中空间影响因子容易受到噪声影响出现错误标识的问题,提出一种融合局部和非局部空间信息的模糊C-均值聚类图像分割算法(NLWFLICM),在WFLICM算法的模糊影响因子中引入非局部空间信息,根据噪声程度自适应地设置局部和非局部信息权重,并重新标记中心点的模糊影响因子。实验结果表明,NLWFLICM算法具有比WFLICM算法更强的鲁棒性和自适应性,并在一定程度上提高了WFLICM算法对含有大量噪声图像进行分割的鲁棒性,同时保留了图像的纹理。为了提高算法的聚类性能和收敛速度,结合Canopy算法能够快速对数据进行粗聚类的优点,提出基于Canopy聚类与非局部空间信息的FCM图像分割改进算法（Canopy-NLWFLICM）,可以在NLWFLICM算法聚类前,对聚类中心进行预处理,从而提高收敛速度和图像分割精度。     

一种新的基于模糊聚类的组合分类器算法

提出一种新的基于模糊聚类的组合分类器算法,该算法利用模糊聚类技术产生训练样本的分布特征,据此为每一个样本赋予一个权值,来确定它们被采样的概率,利用采样样本训练的分类器调整训练集的采样概率,依次生成新的分类器直至达到一定的精度。该组合分类器算法在UCI的多个标准数据集上进行了测试,并与Bagging和AdaBoost算法进行了比较,实验结果表明新的算法具有更好的健壮性和更高的分类精度。     

Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques

In this paper, we present a new method for multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. First, the proposed method constructs training samples based on the variation rates of the training data set and then uses the training samples to construct fuzzy rules by making use of the fuzzy C-means clustering algorithm, where each fuzzy rule corresponds to a given cluster. Then, we determine the weight of each fuzzy rule with respect to the input observations and use such weights to determine the predicted output, based on the multiple fuzzy rules interpolation scheme. We apply the proposed method to the temperature prediction problem and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) data. The experimental results show that the proposed method produces better forecasting results than several existing methods.     

基于模糊聚类的模糊神经网络控制

对于复杂的非线性离散系统,提出将模糊聚类算法同神经网络相结合,使用衡量聚类有效性的S函数确定模糊规则数目,进而确定模糊神经网络的结构;控制器的设计应用LMI方法。以典型的非线性系统二级倒立摆为例,在Matlab中进行仿真实验,结果表明,基于聚类算法的神经网络控制能够在较大范围的初始状态下使系统获得稳定。     

Evolutionary semi-supervised fuzzy clustering

For learning classifier from labeled and unlabeled data, this paper proposes an evolutionary semi-supervised fuzzy clustering algorithm. Class labels information provided by labeled data is used to guide the evolution process of each fuzzy partition on unlabeled data, which plays the role of chromosome. The fitness of each chromosome is evaluated with a combination of fuzzy within cluster variance of unlabeled data and misclassification error of labeled data. The structure of the clusters obtained can be used to classify a future new pattern. The performance of the proposed approach is evaluated using two benchmark data sets. Experimental results indicate that the proposed approach can improve classification accuracy significantly, compared to classifier trained with a small number of labeled data only. Also, it outperforms a similar approach SSFCM.     

Hierarchical unsupervised fuzzy clustering

A recursive algorithm for hierarchical fuzzy partitioning is presented. The algorithm has the advantages of hierarchical clustering, while maintaining fuzzy clustering rules. Each pattern can have a nonzero membership in more than one subset of the data in the hierarchy. Optimal feature extraction and reduction is optionally reapplied for each subset. Combining hierarchical and fuzzy concepts is suggested as a natural feasible solution to the cluster validity problem of real data. The convergence and membership conservation of the algorithm are proven. The algorithm is shown to be effective for a variety of data sets with a wide dynamic range of both covariance matrices and number of members in each class     

Active semi-supervised fuzzy clustering

Clustering algorithms are increasingly employed for the categorization of image databases, in order to provide users with database overviews and make their access more effective. By including information provided by the user, the categorization process can produce results that come closer to user's expectations. To make such a semi-supervised categorization approach acceptable for the user, this information must be of a very simple nature and the amount of information the user is required to provide must be minimized. We propose here an effective semi-supervised clustering algorithm, active fuzzy constrained clustering (AFCC), that minimizes a competitive agglomeration cost function with fuzzy terms corresponding to pairwise constraints provided by the user. In order to minimize the amount of constraints required, we define an active mechanism for the selection of candidate constraints. The comparisons performed on a simple benchmark and on a ground truth image database show that with AFCC the results of clustering can be significantly improved with few constraints, making this semi-supervised approach an attractive alternative in the categorization of image databases.