Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization

The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of the components of the membership vector corresponding to an object are the membership degrees of the object in the various clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering methods generally find local optimum of their objective function.     

Robust fuzzy clustering of relational data

Popular relational-data clustering algorithms, relational dual of fuzzy c-means (RFCM), non-Euclidean RFCM (NERFCM) (both by Hathaway et al), and FANNY (by Kaufman and Rousseeuw) are examined. A new algorithm, which is a generalization of FANNY, called the fuzzy relational data clustering (FRC) algorithm, is introduced, having an identical objective functional as RFCM. However, the FRC does not have the restriction of RFCM, which is that the relational data is derived from Euclidean distance as the measure of dissimilarity between the objects, and it also does not have limitations of FANNY, including the use of a fixed membership exponent, or a fuzzifier exponent, m. The FRC algorithm is further improved by incorporating the concept of Dave's object data noise clustering (NC) algorithm, done by proposing a concept of noise-dissimilarity. Next, based on the constrained minimization, which includes an inequality constraint for the memberships and corresponding Kuhn-Tucker conditions, a noise resistant, FRC algorithm is derived which works well for all types of non-Euclidean dissimilarity data. Thus it is shown that the extra computations for data expansion (/spl beta/-spread transformation) required by the NERFCM algorithm are not necessary. This new algorithm is called robust non-Euclidean fuzzy relational data clustering (robust-NE-FRC), and its robustness is demonstrated through several numerical examples. Advantages of this new algorithm are: faster convergence, robustness against outliers, and ability to handle all kinds of relational data, including non-Euclidean. The paper also presents a new and better interpretation of the noise-class.     

基于模糊集的蚁群空间聚类方法研究

定义了对象间的平均距离,并将平均距离作为对象相似性的论域。通过隶属函数将对象间的相似性映射为论域上的一个模糊子集。由给定的置信水平λ,将模糊集分离为普通集,对蚂蚁是否拾起还是放下对象作出决策,实现对空间数据的聚类。并以矿山实际测量数据为空间数据源,采用基本的蚁群聚类算法和模糊蚁群空间聚类算法分别对其进行聚类。通过对这两种算法的实验结果进行分析比较,证明改进后的算法提高了聚类效果。     

基于模糊集的蚁群聚类算法的改进

改进了LF算法,提出了一种基于模糊集理论的蚁群聚类新方法。首先定义了平均距离,其次在“相似”的概念上引入模糊集理论,定义了数据对象与其邻域内对象相似程度的隶属函数,最后该数据对象的拾起或放下由隶属度与置信水平λ相比较来决定。该算法避免了LF算法中不相似的数据对象本该被拾起而可能未被拾起,相似的数据对象本该被放下而可能未被放下的弊端,并简化了LF算法。     

基于模糊极大似然估计聚类的点云数据分块

对散乱点云数据采用微切平面法进行法矢估计,对法矢方向进行全局协调性调整。采用稳定性较好的二次曲面拟合法估算点云数据的高斯曲率和平均曲率。将点的坐标、法矢和曲率合并为八维特征向量,通过模糊极大似然估计聚类技术,将具有类似几何特征的向量聚为一类,从而实现点云数据的分块。实验证明该方法有效。     

基于判断矩阵的专家模糊核聚类组合赋权方法

研究群决策中专家赋权问题.实际决策问题中,由于客体信息自身存在的不完备性和不确定性以及人们描述过程中的模糊性,更适合采用模糊聚类的分析方法,为此提出一种基于判断矩阵的专家模糊核聚类赋权方法.该方法运用模糊核聚类理论对专家排序向量进行分类,根据分类结果、判断矩阵一致性和排序向量的熵对各专家进行组合赋权.算例表明,所提出的方法是可行且有效的.     

网络入侵检测中的自动决定聚类数算法

针对模糊C均值算法(fuzzy C-means algorithm,简称FCM)在入侵检测中需要预先指定聚类数的问题,提出了一种自动决定聚类数算法(fuzzy C-means and support vector machine algorithm,简称F-CMSVM).它首先用模糊C均值算法把目标数据集分为两类,然后使用带有模糊成员函数的支持向量机(support vector machihe,简称SVM)算法对结果进行评估以确定目标数据集是否可分,再迭代计算,最终得到聚类结果.支持向量机算法引入模糊C均值算法得出的隶属矩阵作为模糊成员函数,使得不同的输入样本可以得到不同的惩罚值,从而得到最优的分类超平面.该算法既不需要对训练数据集进行标记,也不需要指定聚类数,因此是一种真正的无监督算法.在对KDD CUP 1999数据集的仿真实验结果表明,该算法不仅能够得到最佳聚类数,而且对入侵有较好的检测效果.     

Evolutionary fuzzy clustering of relational data

This paper is concerned with the computational efficiency of fuzzy clustering algorithms when the data set to be clustered is described by a proximity matrix only (relational data) and the number of clusters must be automatically estimated from such data. A fuzzy variant of an evolutionary algorithm for relational clustering is derived and compared against two systematic (pseudo-exhaustive) approaches that can also be used to automatically estimate the number of fuzzy clusters in relational data. An extensive collection of experiments involving 18 artificial and two real data sets is reported and analyzed.     

一种基于动态聚类的模糊分类规则的生成方法

介绍了一种基于动态聚类的模糊分类规则的生成方法，这种方法能决定规则数目，隶属函数的位置及形状．首先，介绍了基于超圆雏体隶属函数的模糊分类规则的基本形式；然后，介绍动态聚类算法，该算法能将每一类训练模式动态的分为成簇，对于每簇，则建立一个模糊规则；通过调整隶属函数的斜度，来提高对训练模式分类识别率，达到对模糊分类规则进行优化调整的目的；用两个典型的数据集评测了这篇文章研究的方法，这种方法构成的分类系统在识别率与多层神经网络分类器相当，但训练时间远少于多层神经网络分类器的训练时间．     

利用模糊神经网络实现逆向工程中的区域分割

论文提出了一种改进的模糊自组织特征映射网络(fuzzySOFM),它不仅显著加快了聚类的速度,而且算法简单。该网络采用由数据点的坐标、估算出的法矢量和曲率构成的八维特征向量作为输入,快速地实现了逆向工程中点云数据的区域分割。与现有方法相比,该方法具有以下优点:第一,具有更高的聚类速度,并可以直接处理含噪声数据;第二,聚类的结果与数据输入的顺序无关;第三,能利用数据的隶属度快速提取出特征线数据,从而将基于面的分割和基于线的分割结合起来。实验结果证明了这种方法的有效性。     

Dual-centers type-2 fuzzy clustering framework and its verification and validation indices

In this paper we present a clustering framework for type-2 fuzzy clustering which covers all steps of the clustering process including: clustering algorithm, parameters estimation, and validation and verification indices. The proposed clustering algorithm is developed based on dual-centers type-2 fuzzy clustering model. In this model the centers of clusters are defined by a pair of objects rather than a single object. The membership values of the objects to the clusters are defined by type-2 fuzzy numbers and there are not any type reduction or defuzzification steps in the proposed clustering algorithm. In addition, the relation among the size of the cluster bandwidth, distance between dual-centers and fuzzifier parameter are indicated and analyzed to facilitate the parameters estimation step. To determine the optimum number of clusters, we develop a new validation index which is compatible with the proposed model structure. A new compatible verification index is also defined to compare the results of the proposed model with existing type-1 fuzzy clustering model. Finally, the results of computational experiments are presented to show the efficiency of the proposed approach.     

鲁棒的交叉熵模糊聚类算法

针对模糊C-均值聚类(FCM)算法对噪声敏感、容易收敛到局部极小值的问题,提出一种基于交叉熵的模糊聚类算法。通过引入交叉熵重新定义了传统FCM算法的目标函数,利用交叉熵度量样本隶属度之间的差异性,并采用拉格朗日求解方法和朗伯W函数解决了目标函数的优化问题,此外,分析了样本划分矩阵的分布情况,依据分布特性对噪声样本进行识别。人工数据集合和标准数据集加噪的实验结果表明,该算法提高了传统FCM算法的抗干扰能力,具有更强的鲁棒性,噪声样本识别的准确率较高。     

一种基于区域的彩色图像分割方法

提出一种基于区域的彩色图像分割方法，该方法首先选用适当的彩色空间对图像中的每个像素抽取颜色、纹理及空间位置等综合特征，形成基于像素的综合特征空间；利用模糊C均值聚类方法，在综合特征空间中进行聚类，利用模糊熵的原理获得最佳聚类的簇数目，得到初步的区域分割，最后利用连接原理对图像区域进一步分割。该方法还提供了丰富的区域特征。     

基于模糊聚类的H.264压缩域视频对象分割

鉴于压缩域视频运动分割方法在分割速度上的优越性,提出一种基于H.264的压缩域视频运动对象分割方法,对初始的运动矢量场进行去噪、中值滤波、校正和累积处理,得到更可靠的运动矢量场,用改进的模糊C-均值聚类算法分割出视频序列中的运动对象。实验结果表明,该方法可以快速准确地提取出视频序列中的运动对象。     

Clustering and aggregation of relational data with applications to image database categorization

In this paper, we introduce a new algorithm for clustering and aggregating relational data (CARD). We assume that data is available in a relational form, where we only have information about the degrees to which pairs of objects in the data set are related. Moreover, we assume that the relational information is represented by multiple dissimilarity matrices. These matrices could have been generated using different sensors, features, or mappings. CARD is designed to aggregate pairwise distances from multiple relational matrices, partition the data into clusters, and learn a relevance weight for each matrix in each cluster simultaneously. The cluster dependent relevance weights offer two advantages. First, they guide the clustering process to partition the data set into more meaningful clusters. Second, they can be used in subsequent steps of a learning system to improve its learning behavior. The performance of the proposed algorithm is illustrated by using it to categorize a collection of 500 color images. We represent the pairwise image dissimilarities by six different relational matrices that encode color, texture, and structure information.     

EVCLUS: evidential clustering of proximity data

A new relational clustering method is introduced, based on the Dempster-Shafer theory of belief functions (or evidence theory). Given a matrix of dissimilarities between n objects, this method, referred to as evidential clustering (EVCLUS), assigns a basic belief assignment (or mass function) to each object in such a way that the degree of conflict between the masses given to any two objects reflects their dissimilarity. A notion of credal partition is introduced, which subsumes those of hard, fuzzy, and possibilistic partitions, allowing to gain deeper insight into the structure of the data. Experiments with several sets of real data demonstrate the good performances of the proposed method as compared with several state-of-the-art relational clustering techniques.     

融合KL信息的多视图模糊聚类算法

现有多视图模糊C均值聚类（FCM）算法通常将一个多视图分解为多个单视图进行数据处理,导致视图数据聚类精度降低,从而影响全局数据划分结果。为实现高维数据和多视图数据的高效聚类,提出一种基于KL信息的多视图自加权模糊聚类算法。将多个视图信息及其权重进行拟合融入标准FCM算法,求解多个隶属度矩阵和质心矩阵。在此基础上,通过附加KL信息作为模糊正则项进一步修正共识隶属度矩阵并保持权重分布的平滑性,其中KL信息是视图隶属度与其共识隶属度的比值,最小化KL信息会使每个视图的隶属度偏向于共识隶属度以得到更好的聚类结果。实验结果表明,该算法相比于传统聚类算法具有更好的聚类效果和更快的收敛速度,尤其在3-Sources数据集上相比于MVASM算法的聚类精度、标准化互信息和纯度分别提升了7.46、15.34和5.48个百分点。     

基于改进满意聚类的多模型建模方法

针对模糊聚类中普遍存在的聚类个数需要事先给定和收敛速度慢等问题,在原有聚类方法的基础上提出一种改进满意聚类算法。用该算法快速确定系统的模糊划分数目,进而用支持向量机算法建立每个聚类的子模型,将输入变量对各类别的隶属度作为权值,将多个子模型用加权方式组合。工业仿真实例验证了基于该方法的多模型建模方法的有效性、准确性和快速性。     

基于模糊聚类的汽车车内空气质量评价

在模糊聚类分析的基础上,提出一种适用于多项空气污染物的汽车车内空气质量评价的分类与评价方法。选取8种不同的汽车,测试其车内空气质量相关数据作为统计指标,利用最大最小法建立相似矩阵,用闭包法做出聚类分析,并分析聚类结果。结果表明:该方法对评价汽车车内空气质量具有实用性和普适性。