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.     

面向隶属度修正模糊聚类的参数选择方法

隶属度修正是模糊C-均值聚类算法改进的一个重要方向,该类改进算法引入模糊阈值修正隶属度,极大的加快了算法的收敛.然而其模糊阈值的自适应取值一直是一个较难解决的问题.针对这个问题,从数据对聚类中心的物理吸引和相似关系等角度提出了一种针对隶属度修正类FCM算法的模糊阈值参数选择方法,并从该参数选择公式的单调性、收敛性和鲁棒性等角度理论验证了该方法的有效性.仿真实验表明,该参数选择方法有效并具有较好的自适应效果,在加入离群点时也有着较强的鲁棒性,对于隶属度修正类FCM算法的参数选择有着较高的应用价值.     

结合Total-Bregman距离的模糊聚类算法

模糊C均值(fuzzy C-means,FCM)聚类算法是一种常用的基于目标函数最小化的聚类算法。目前已经提出了相当数量的聚类算法是对模糊C均值聚类算法的改进,例如AFCM算法、GK算法等。对最近发表的基于Bregman距离的模糊聚类算法进行了改进,通过在FCM模糊聚类框架中引入Total-Bregman距离提升了聚类算法的聚类性能。同时对基于Total-Bregman距离的模糊聚类算法的收敛性质进行了理论分析。实验部分对来自UCI数据库的几个数据集进行了聚类,证明了算法的有效性和收敛性。     

离群模糊核聚类算法

一般说来,离群点是远离其他数据点的数据,但很可能包含着极其重要的信息.提出了一种新的离群模糊核聚类算法来发现样本集中的离群点.通过Mercer核把原来的数据空间映射到特征空间,并为特征空间的每个向量分配一个动态权值,在经典的FCM模糊聚类算法的基础上得到了一个特征空间内的全新的聚类目标函数,通过对目标函数的优化,最终得到了各个数据的权值,根据权值的大小标识出样本集中的离群点.仿真实验的结果表明了该离群模糊核聚类算法的可行性和有效性.     

一种改进的模糊C均值聚类算法

针对数据集中若存在孤立点或者是噪声数据会影响模糊C均值聚类算法(FCM)的聚类性能问题,本文将离群点的辨认方法与FCM算法相结合,提出一种改进的FCM聚类算法。该算法有效地降低了孤立点或噪声数据对正常数据的影响,提高了FCM算法的聚类精度。将该算法在入侵检测系统中进行实验验证,通过与FCM算法进行对比分析,证明了该算法的有效性和可行性。     

基于模糊聚类的稳健支撑向量回归机及火焰图像处理

由于离群点会降低支撑向量回归机的性能,因此为了提高支撑向量回归机的图像处理性能,提出了一种具有抗离群点性能的模糊稳健支撑向量回归机（FRSVR）,并首先给出了在任意代价函数下支撑向量回归机的求解方法;然后讨论了构建稳健支撑向量机的代价函数所需的性质,并在此基础上,引入了损失代价函数族;接着根据支撑向量回归机的训练误差,用模糊C均值聚类（FCM）查找离群点;最后通过迭代的方法实现了模糊稳健支撑向量回归机。为了对火焰图像进行有效处理,还将FRSVR算法应用于乳化油燃烧火焰图像处理,以去除火焰图像上的离群点。实验结果表明,FRSVR算法处理图像的性能优于ε-SVR算法和自适应SVR滤镜（ASBF）,不仅能有效地查找离群点,而且可去除较大的离群点区域,还能显著的降低离群点的影响,并具有良好的泛化性能。     

基于共享反K近邻的局部离群点检测算法

离群点检测和分析离群模式隐含的特征是离群点挖掘的重要研究内容.现有离群点检测算法存在两个明显的不足:根据离群度检测离群点,难以确定离群点的数量;忽略了与离群点邻接的聚类信息,不能提供解析离群模式的有效证据.为此,提出一种基于共享反K近邻的离群点检测算法,首先定义了一种对密度和维数变化不敏感的共享反K近邻相似度,然后应用聚类方法将数据集划分为聚类簇和包含离群点的离群簇,从而获取数据集中的离群点及解析离群点的聚类结构.仿真结果表明,反K近邻算法比现有方法更能精确地检测数据集中的局部离群点,具有很好的控制性能.     

面向差分隐私保护的自适应谱聚类优化新算法

针对传统差分隐私保护的谱聚类算法存在聚类效果不理想的不足,提出一种面向差分隐私保护的自适应谱聚类优化新算法。采用互邻高斯核函数得到稀疏相似度矩阵,分析高维数据集的数据特征与聚类簇数的关系解决降维幅度和聚类簇数的不确定性;引入中间信息向量和中间性的概念来克服初始簇中心选取的盲目性;根据多维高斯分布离群点检验后的结果采用插补法解决离群点问题。仿真实验结果表明,该算法能够有效克服传统方法的不足,且在同一数据集相同隐私保护参数下,可以在保证数据隐私安全性的同时改善聚类效率并显著提高聚类可用性。     

融合最近邻矩阵与局部密度的自适应K-means聚类算法

针对传统K-means聚类算法对初始聚类中心和离群孤立点敏感的缺陷,以及现有引入密度概念优化的K-means算法均需要设置密度参数或阈值的缺点,提出一种融合最近邻矩阵与局部密度的自适应K-means聚类算法。受最邻近吸收原则与密度峰值原则启发,通过引入数据对象间的距离差异值构造邻近矩阵,根据邻近矩阵计算局部密度,不需要任何参数设置,采取最近邻矩阵与局部密度融合策略,自适应确定初始聚类中心数目和位置,同时完成非中心点的初分配。人工数据集和UCI数据集的实验测试,以及与传统K-means算法、基于离群点改进的K-means算法、基于密度改进的K-means算法的实验比较表明,提出的自适应K-means算法对人工数据集的孤立点免疫度较高,对UCI数据集具有更准确的聚类结果。     

基于划分自适应融合的多视角模糊聚类算法

针对多视角聚类任务如何更好地实现视角间的合作之挑战, 提出一种新的视角融合策略. 该策略首先为每个视角设置一个划分, 然后通过自适应学习获取一个融合权重矩阵对每个视角的划分进行自适应融合, 最终利用视角集成方法得到全局划分结果. 将上述策略应用到经典的FCM(Fuzzy ??-means) 模糊聚类框架, 提出相应的多视角模糊聚类算法. 在模拟数据集和UCI 数据集上的实验结果均显示, 所提出的算法较几种相关聚类算法在应对多视角聚类任务时具有更好的适应性和更好的聚类性能.

     

广义洛伦兹内核函数在模糊C均值聚类中的应用研究

模糊C均值(FCM)算法是数据聚类分析的主要算法。但在嘈杂环境下,对于抽样大小不一的聚类,数目越多准确性越低,上述弊端可通过替代性FCM(AFCM)的高斯内核映射来解决。鉴于AFCM的不足,提出了针对模糊C均值聚类的广义洛伦兹内核函数。利用该算法对鸢尾数据库进行聚类,将其划分成山鸢尾、变色鸢尾和维吉尼亚鸢尾3类。实验结果表明,广义洛伦兹模糊C均值(GLFCM)可实现对离群聚类和大小不等的聚类数据的分类,其结果优于K均值、FCM、替代性C均值(AFCM)、Gustafson-Kessel(GK)和 Gath-Geva(GG)方法,收敛迭代次数比AFCM的更少,其分区索引(SC)效果也好于其他方法。     

一种由FCM算法推导出的隶属函数研究

分析了Fuzzy C-Means算法中模糊指标m→1⁺和m→∞对隶属函数的模糊控制作用,据此提出一种带模糊指标的隶属函数,具有性质：（1）一个数据点对各个模式的隶属度和为1;（2）模糊指标m控制模糊程度。使用Iris数据集对样板法中新旧两种隶属函数做了实验对比。     

Intuitionistic fuzzy C-regression by using least squares support vector regression

This paper proposes a novel intuitionistic fuzzy c-least squares support vector regression (IFC-LSSVR) with a Sammon mapping clustering algorithm. Sammon mapping effectively reduces the complexity of raw data, while intuitionistic fuzzy sets (IFSs) can effectively tune the membership of data points, and LSSVR improves the conventional fuzzy c-regression model. The proposed clustering algorithm combines the advantages of IFSs, LSSVR and Sammon mapping for solving actual clustering problems. Moreover, IFC-LSSVR with Sammon mapping adopts particle swarm optimization to obtain optimal parameters. Experiments conducted on a web-based adaptive learning environment and a dataset of wheat varieties demonstrate that the proposed algorithm is more efficient than conventional algorithms, such as the k-means (KM) and fuzzy c-means (FCM) clustering algorithms, in standard measurement indexes. This study thus demonstrates that the proposed model is a credible fuzzy clustering algorithm. The novel method contributes not only to the theoretical aspects of fuzzy clustering, but is also widely applicable in data mining, image systems, rule-based expert systems and prediction problems.     

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.     

Analysis of parameter selections for fuzzy c-means

The weighting exponent m is called the fuzzifier that can influence the performance of fuzzy c-means (FCM). It is generally suggested that m∈[1.5,2.5]. On the basis of a robust analysis of FCM, a new guideline for selecting the parameter m is proposed. We will show that a large m value will make FCM more robust to noise and outliers. However, considerably large m values that are greater than the theoretical upper bound will make the sample mean a unique optimizer. A simple and efficient method to avoid this unexpected case in fuzzy clustering is to assign a cluster core to each cluster. We will also discuss some clustering algorithms that extend FCM to contain the cluster cores in fuzzy clusters. For a large theoretical upper bound case, we suggest the implementation of the FCM with a suitable large m value. Otherwise, we suggest implementing the clustering methods with cluster cores. When the data set contains noise and outliers, the fuzzifier m=4 is recommended for both FCM and cluster-core-based methods in a large theoretical upper bound case.     

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.     

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.     

基于连通核的鲁棒模糊C-均值聚类算法

提出一种新的鲁棒核模糊C-均值聚类算法.将连通核与AFCM(Alternative fuzzy C-means)聚类算法相结合,给出基于连通核的核AFCM:CRKFCM(Connectivity kernel based robust fuzzy C-means).CRKFCM一方面有效地利用了连通核,可以对任意形状数据聚类,且避免了核参数的选取问题;另一方面在特征空间使用非欧氏距离,可以有效地处理含噪声数据的聚类问题.实验结果表明,与原有的AFCM和连通核硬C-均值(CKHCM,Connectivity kernel based hard C-means)聚类算法相比,新算法在处理噪声环境中的任意形状聚类问题方面更有效.     

改进的FCM聚类算法在Weka平台的应用

模糊C-均值聚类算法是目前应用最广泛的聚类算法,但其仍然存在对孤立点敏感及对初始中心点依赖等问题.为此,提出了一种改进的基于样本加权的模糊聚类算法,该算法可以更加准确的获得初始中心点且去除噪声点.同时,针对Weka系统中聚类算法的薄弱性以及聚类问题在数据挖掘领域的广泛性,本文对此平台进行二次开发并对传统FCM算法与改进算法进行研究.研究发现,改进算法使得聚类结果稳定,且能准确获得聚类结果,提高了算法准确率.