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。     

局部搜索自适应核模糊聚类方法

核模糊C-均值聚类KFCM是利用核函数将数据映射到高维空间,通过计算数据点与聚类中心的隶属度对数据进行聚类的算法,拥有高效、快捷的特点而被广泛应用于各领域,然而KFCM算法存在对聚类中心的初始值敏感和不能自适应确定聚类数两个局限性。针对这两个问题,提出一种局部搜索自适应核模糊聚类方法,该方法引入核方法提高数据的可分性,并构造基于核函数的评价函数来确定最优的聚类数目和利用部分样本数据进行局部搜索以寻找初始聚类中心。人工数据和UCI数据集上的实验结果验证了该算法的有效性。     

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。     

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。     

A tabu search-based algorithm for the fuzzy clustering problem

The Fuzzy Clustering Problem (FCP) is a mathematical program which is difficult to solve since it is nonconvex, which implies possession of many local minima. The fuzzy C-means heuristic is the widely known approach to this problem, but it is guaranteed only to yield local minima. In this paper, we propose a new approach to this problem which is based on tabu search technique, and aims at finding a global solution of FCP. We compare the performance of the algorithm with the fuzzy C-means algorithm.     

基于密度的模糊代表点聚类算法

结合密度聚类和模糊聚类的特点,提出一种基于密度的模糊代表点聚类算法.首先利用密度对数据点成为候选聚类中心点的可能性进行处理,密度越高的点成为聚类中心点的可能性越大;然后利用模糊方法对聚类中心点进行确定;最后通过合并聚类中心点确定最终的聚类中心.所提出算法具有很好的自适应性,能够处理不同形状的聚类问题,无需提前规定聚类个数,能够自动确定真实存在的聚类中心点,可解释性好.通过结合不同聚类方法的优点,最终实现对数据的有效划分.此外,所提出的算法对于聚类数和初始化、处理不同形状的聚类问题以及应对异常值等方面具有较好的鲁棒性.通过在人工数据集和UCI真实数据集上进行实验,表明所提出算法具有较好的聚类性能和广泛的适用性.     

基于遗传算法和遗传模糊聚类的混合聚类算法

为了动态确定聚类数目C和该数目下的最优分类,构造出遗传算法和模糊遗传C均值聚类的混合聚类算法(HGA-FGCM),该方法构造了一个既考虑类与类之间的分散程度,又考虑同一类紧凑程度的目标评价函数;运用遗传算法的全局寻优能力,求得最佳聚类数下的最优聚类。     

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。     

基于改进型模糊聚类的模糊系统建模方法

结合减法聚类和模糊C均值聚类,提出了一种改进型聚类算法,加快了收敛速度．利用改进后的算法对模糊系统输入或输出的样本集聚类,对聚类结果采用Trust-Region法拟合高斯型和S型函数,以实现模糊系统输入、输出空间的划分和隶属度函数参数的确定．结合MATLAB的模糊和曲线拟合工具箱,详述了如何在标准算法上进行改进和模糊系统建模．通过对IRIS标准数据聚类实验以及在解决机械加工误差复映问题上的应用,验证了改进后算法和建模方法的有效性．     

改进的模糊C-均值聚类算法

为了克服模糊C-均值（FCM）聚类算法易陷入局部极小值和对初始值敏感的缺点,提出了一种基于改进量子蚁群的模糊聚类算法。将量子计算原理和蚁群算法相结合来改进FCM算法。初期采用量子遗传算法生成信息素分布,后期利用蚁群算法的全局搜索性、并行计算性等特点避免聚类陷入局部最优解。实验证明该算法保证了种群的多样性,有较好的全局收敛性,克服了模糊C-均值聚类算法的不足,能有效解决未成熟收敛的问题,使聚类问题最终快速、有效地收敛到全局最优解。     

自适应半监督模糊谱聚类算法

半监督聚类利用少部分标签的数据辅助大量未标签的数据进行非监督的学习,从而提高聚类的性能。大部分的谱聚类算法都需事先确定聚类数目,利用半监督机器学习技术和自适应聚类算法,解决算法中存在的聚类数目需要事先确定、易陷入局部最优、收敛速度缓慢、对孤立点敏感等缺陷。实验证明该算法有很好的聚类效果。     

A multi-objective genetic algorithm with fuzzy c-means for automatic data clustering

This article presents a multi-objective genetic algorithm which considers the problem of data clustering. A given dataset is automatically assigned into a number of groups in appropriate fuzzy partitions through the fuzzy c-means method. This work has tried to exploit the advantage of fuzzy properties which provide capability to handle overlapping clusters. However, most fuzzy methods are based on compactness and/or separation measures which use only centroid information. The calculation from centroid information only may not be sufficient to differentiate the geometric structures of clusters. The overlap-separation measure using an aggregation operation of fuzzy membership degrees is better equipped to handle this drawback. For another key consideration, we need a mechanism to identify appropriate fuzzy clusters without prior knowledge on the number of clusters. From this requirement, an optimization with single criterion may not be feasible for different cluster shapes. A multi-objective genetic algorithm is therefore appropriate to search for fuzzy partitions in this situation. Apart from the overlap-separation measure, the well-known fuzzy J_m index is also optimized through genetic operations. The algorithm simultaneously optimizes the two criteria to search for optimal clustering solutions. A string of real-coded values is encoded to represent cluster centers. A number of strings with different lengths varied over a range correspond to variable numbers of clusters. These real-coded values are optimized and the Pareto solutions corresponding to a tradeoff between the two objectives are finally produced. As shown in the experiments, the approach provides promising solutions in well-separated, hyperspherical and overlapping clusters from synthetic and real-life data sets. This is demonstrated by the comparison with existing single-objective and multi-objective clustering techniques.     

Fuzzy J-Means: a new heuristic for fuzzy clustering

A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called Fuzzy J-Means, where the neighbourhood is defined by all possible centroid-to-pattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the well-known Fuzzy C-Means heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.     

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。     

基于遗传算法和模糊C均值聚类的WSN分簇路由算法

针对无线传感器网络（WSN）的节点能量有限、生命周期短、吞吐量低等问题，提出一种基于遗传算法（GA）和模糊C均值（FCM）聚类的WSN分簇路由算法GAFCMCR，采取"集中分簇，分布簇头选举"的方式。网络初始化时基站采用由GA优化的FCM聚类算法形成网络分簇。第一轮簇头由距簇中心最近的节点担任；从第二轮开始，簇头的选举由上一轮的簇头负责，选举过程综合考虑候选节点的剩余能量、与基站的距离、与簇内其他节点的平均距离三个因子，并根据网络状态实时调整三个因子的权重。在数据传输阶段，将轮询机制引入簇内通信。仿真结果表明，相同网络环境下，与LEACH算法和基于K-Means的均匀分簇路由（KUCR）算法相比，GAFCMCR将网络生命周期延长了105%和20%。GAFCMCR成簇效果良好，具有良好的能量均衡性和更高的吞吐量。     

Dynamic local search based immune automatic clustering algorithm and its applications

Based on clonal selection mechanism in immune system, a dynamic local search based immune automatic clustering algorithm (DLSIAC) is proposed to automatically evolve the number of clusters as well as a proper partition of datasets. The real based antibody encoding consists of the activation thresholds and the clustering centers. Then based on the special structures of chromosomes, a particular dynamic local search scheme is proposed to exploit the neighborhood of each antibody as much as possible so to realize automatic variation of the antibody length during evolution. The dynamic local search scheme includes four basic operations, namely, the external cluster swapping, the internal cluster swapping, the cluster addition and the cluster decrease. Moreover, a neighborhood structure based clonal mutation is adopted to further improve the performance of the algorithm. The proposed algorithm has been extensively compared with five state-of-the-art automatic clustering techniques over a suit of datasets. Experimental results indicate that the DLSIAC is superior to other five clustering algorithms on the optimum number of clusters found and the clustering accuracy. In addition, DLSIAC is applied to a real problem, namely image segmentation, with a good performance.     

A multiobjective spatial fuzzy clustering algorithm for image segmentation

This article describes a multiobjective spatial fuzzy clustering algorithm for image segmentation. To obtain satisfactory segmentation performance for noisy images, the proposed method introduces the non-local spatial information derived from the image into fitness functions which respectively consider the global fuzzy compactness and fuzzy separation among the clusters. After producing the set of non-dominated solutions, the final clustering solution is chosen by a cluster validity index utilizing the non-local spatial information. Moreover, to automatically evolve the number of clusters in the proposed method, a real-coded variable string length technique is used to encode the cluster centers in the chromosomes. The proposed method is applied to synthetic and real images contaminated by noise and compared with k-means, fuzzy c-means, two fuzzy c-means clustering algorithms with spatial information and a multiobjective variable string length genetic fuzzy clustering algorithm. The experimental results show that the proposed method behaves well in evolving the number of clusters and obtaining satisfactory performance on noisy image segmentation.     

创意FCM算法

针对现有模糊聚类方法仅仅是对已有数据点的聚类的不足,提出了在已有数据集的基础上找到新的一类集群的聚类方法 CFCM。该算法在FCM算法的基础上,通过引入观测点P作为聚类的先验知识,来大致确定未知集群的聚类中心,定义了权重系数λ来限定观测点对新的一类聚类中心形成的影响程度。人造数据集和UCI真实数据集的实验结果表明,该算法不仅对已知数据点有较好的聚类效果,并且可以在观测点P的作用下在特定区域创造出新的一类无已知数据点的集群中心点的大致位置,因而在实际中有潜在应用价值。     

Partition-and-merge based fuzzy genetic clustering algorithm for categorical data

Categorical data clustering is a difficult and challenging task due to the special characteristic of categorical attributes: no natural order. Thus, this study aims to propose a two-stage method named partition-and-merge based fuzzy genetic clustering algorithm (PM-FGCA) for categorical data. The proposed PM-FGCA uses a fuzzy genetic clustering algorithm to partition the dataset into a maximum number of clusters in the first stage. Then, the merge stage is designed to select two clusters among the clusters that generated in the first stage based on its inter-cluster distances and merge two selected clusters to one cluster. This procedure is repeated until the number of clusters equals to the predetermined number of clusters. Thereafter, some particular instances in each cluster are considered to be re-assigned to other clusters based on the intra-cluster distances. The proposed PM-FGCA is implemented on ten categorical datasets from UCI machine learning repository. In order to evaluate the clustering performance, the proposed PM-FGCA is compared with some existing methods such as k-modes algorithm, fuzzy k-modes algorithm, genetic fuzzy k-modes algorithm, and non-dominated sorting genetic algorithm using fuzzy membership chromosomes. Adjusted Ranked Index (ARI), Normalized Mutual Information (NMI), and Davies–Bouldin (DB) index are selected as three clustering validation indices which are represented to both external index (i.e., ARI and NMI) and internal index (i.e., DB). Consequently, the experimental result shows that the proposed PM-FGCA outperforms the benchmark methods in terms of the tested indices.