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.     

A grey-based clustering algorithm and its application on fuzzy system design

A grey-based clustering method was proposed and applied on fuzzy system design. A new grey-clustering algorithm using grey relational analysis as the similarity measure was developed for data clustering. It was more effective and accurate than C-Means like algorithms when dealing with data clustering issue, when the compact and complete separate data were considered. Some data clustering examples are presented to illustrate the effectiveness of the proposed clustering algorithm. Next, an application of the proposed method on fuzzy system design is presented. The procedure of fuzzy system design can be separated into two parts. In the first procedure, the grey-clustering algorithm was employed to form a rough fuzzy system only from gathered input-output data. Then, the gradient descent method was used to determine a suitable parameter set of the formed fuzzy system. A nonlinear system modelling and an inverted pendulum control problem were then used to illustrate the validity of the proposed fuzzy system design procedure.     

一种改进的相容关系聚类算法

聚类分析是数据挖掘中的一个重要研究内容。按照数据对象间的关系进行聚类在许多情况具有特殊的意义。提出一种相容关系数据对象的聚类算法。该算法首先对每个数据对象按字典排序,利用相容集的反单调性性质来产生极大相容簇,即通过相容集的连接产生更高层的相容集的候选,再通过剪枝的方法来得到更高层的相容集。该方法可以有效压缩算法的搜索空间,是现有相容关系聚类算法的有益改进和补充。     

基于λ-Warshall算法的聚类方法

根据数据之间的相似性,提出了一种基于改进Warshall算法的数据聚类方法.该方法在传统Warshall算法的基础上,引入聚类因子λ,构造模糊相似关系的传递闭包.由于相似性的自反性与对称性,该传递闭包就是模糊相似关系的等价闭包,把等价数据分到一类形成聚类.实验结果表明,该方法可得到与传统的K-均值聚类算法相同的聚类结果.     

模糊聚类分析系统的研究与实现

针对目前多种模糊聚类算法组合应用研究较少的现状,在分别对基于模糊等价关系和基于模糊等价划分这两种模糊聚类分析方法进行了较为深入研究的基础上,根据两种方法的特点,构建了一种组合式模糊聚类分析方法。采用VC++与Fortran6.5语言混合编程,开发了一套模糊聚类分析系统,分别实现了基于模糊等价关系法、基于模糊ISODATA法和基于组合式模糊聚类法的模糊聚类分析,并将其应用于电力系统中不良数据的辨识处理,取得了较为理想的效果。实例分析表明,组合式算法能够有效克服单独使用某种模糊聚类算法的缺点,同时也反映出该模糊聚类分析系统具有聚类方法选取灵活、软件界面友好、计算速度快等特点,有良好的应用前景。     

DF关系及其在数据聚类中的应用研究

基于DF关系,给出了DF关系截矩阵的定义,以及由DF相似关系构造DF等价关系的方法,并在此基础上结合数据挖掘中的分类技术,提出了一种面向DF数据的聚类算法,该算法的提出不但能拓宽聚类对象的范围,而且更符合实际需求。最后给出了运用该算法的示例。     

Fuzzy Clustering for Data Time Arrays With Inlier and Outlier Time Trajectories

In many knowledge discovery and data mining tasks, fuzzy clustering is one of the most common tools for data partitioning. In this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories (time series, sequences) are developed. In particular, by adopting an exploratory approach, based on a geometric-algebraic formulation of the data time array, different kinds of dynamic fuzzy clustering models, based on cross sectional and longitudinal aspects, are suggested. Furthermore, a modified version of the previous clustering models, that can be seen as a generalization of these models, is proposed. By utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories (trajectories with anomalous positions and slopes) are present in the dataset; in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure's domains and are characterized by strange slopes. In these models, the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given. Furthermore, some remarks on dynamic three-way extensions of a few robust fuzzy clustering models for two-way data are suggested. Demonstrative examples are shown and a comparison assessment based on artificial multivariate time-varying data is carried out     

基于主动学习的动态模糊聚类算法

聚类问题是近几年来机器学习和数据挖掘领域研究的热点问题,由于获取大量监督信息费时费力,目前国内外研究的重点是如何获得少量但对聚类性能提高显著的监督信息,再加上实际问题中存在的动态模糊性,故本文提出一种结合主动学习的动态模糊聚类算法DF-DBSCAN,通过引入动态模糊等价关系、动态模糊信任测度和动态模糊似然测度这3个约束信息来指导DBSCAN的聚类过程,以提高聚类的性能。实验结果表明,DF-DBSCAN算法不仅解决了实际问题中存在的动态模糊性数据的描述和表示问题,而且能够高效地进行数据聚类,显著地提高聚类性能。      

基于模糊商空间的聚类分析方法

在商空间理论基础上,提出了基于Fuzzy相似关系和归一化距离的聚类分析方法,用以解决复杂系统的数据结构分析问题.得到了如下结论:(1)通过引入基于Fuzzy相似关系和归一化距离的分层递阶结构,建立了严格的聚类分析理论描述;(2)给出了有效的分层递阶结构聚类的快速算法;(3)给出了两个Fuzzy相似关系或由两个归一化距离诱导的Fuzzy相似关系是同构的充分条件.其中所研究的理论和方法适应于建立在相似关系之上的任何复杂系统的数据结构分析.     

Cluster Analysis Based on T‐transitive Interval‐Valued Fuzzy Relations

In this paper, we consider cluster analysis based on T‐transitive interval‐valued fuzzy relations. A fuzzy relation with its partitional tree for obtaining an agglomerative hierarchical clustering has been studied and applied. In general, these fuzzy‐relation‐based clustering approaches are based on real‐valued memberships of fuzzy relations. Since interval‐valued memberships may be better than real‐valued memberships to represent higher order imprecision and vagueness for human perception, in this paper we first extend fuzzy relations to interval‐valued fuzzy relations and then construct a clustering algorithm based on the proposed T‐transitive interval‐valued fuzzy relations. We use two examples to demonstrate the efficiency and usefulness of the proposed method. In practical application, we apply the proposed clustering method to performance evaluations for academic departments of higher education by using actual engineering school data in Taiwan.     

检验双重性质特征的基因模糊聚类分析方法

针对基因序列分类的特点,结合模糊聚类分析方法,在原来的Markov链模型基因聚类方法的基础上,引入核酸碱基对的相互作用,得到具有双重性质特征的距离矩阵,并根据模糊聚类分析方法得到模糊相似性矩阵和其动态聚类图,从而实现基因序列的分类。通过对包括人类16个物种的16条p53基因序列进行模糊聚类得出,物种关系越相近,更容易聚成一类。此外,还检验双重性质的矩阵方法与原来的单一性质方法作聚类结果对比,发现具有双重性质的方法更准确。     

A clustering method to identify representative financial ratios

When companies evaluate their performance, it is impractical to take all of their financial ratios into consideration. To evaluate the financial performance of a company, only a fraction of the available financial ratios are considered and selected as evaluation criteria. In general, financial ratios presented as sequences (or called financial ratio sequences), are first clustered and then a representative indicator is chosen from each cluster to serve as an evaluation criterion. To cluster financial ratios, we propose a clustering method in which the financial ratios of different companies with similar variations are partitioned into the same cluster. In other words, a fuzzy relation is proposed to represent the similarity between the financial ratios, and a cluster validation index is also provided to determine the number of clusters. Once the financial ratios are clustered, the representative indicator for each cluster will be identified.     

混合属性对象的类别关系修正的模糊聚类方法

针对模糊聚类分析在处理混合条件属性数据时存在的不足,提出一种基于类别关系修正的集成方法。首先对分类条件属性特征参数采用熵表示类别隶属度,数值条件属性特征参数采用欧氏距离结合熵表示相似性;然后定义数据的混合类别模糊度及具体单个类别的模糊可信度,并由两者数值共同生成类别修正的线性、指数及对数变化的三种关系;最终通过类别关系修正值来衡量数据对象的类别模糊度。与多种已有的聚类集成方法对比实验表明,该方法具有优良的聚类性能。     

A new fuzzy relational clustering algorithm based on the fuzzy C-means algorithm

In this paper, we show how one can take advantage of the stability and effectiveness of object data clustering algorithms when the data to be clustered are available in the form of mutual numerical relationships between pairs of objects. More precisely, we propose a new fuzzy relational algorithm, based on the popular fuzzy C-means (FCM) algorithm, which does not require any particular restriction on the relation matrix. We describe the application of the algorithm to four real and four synthetic data sets, and show that our algorithm performs better than well-known fuzzy relational clustering algorithms on all these sets.     

并行分布式的Web访问模式双层聚类

Web日志挖掘可以通过对用户访问模式进行分析,以获取用户的访问兴趣程度。目前,大多数的web日志挖掘是基于频率的,其挖掘的信息没有太大的价值。而提出的聚类技术是基于访问时间的,使用模糊向量表示用户浏览模式,记录用户是否浏览过该页面以及停留的时间。通过不同的聚类方法对用户的访问序列进行聚类分析。将模糊粗糙[k]-均值和夹角余弦相结合,提出了一种双层聚类技术,减少了对初始聚类中心的敏感性,并且通过一系列实验,论证了该聚类方法的可行性。而且,实验通过使用Davies-Bouldin指标来验证不同聚类方法的效果并进行比较。由于数据量大时,仍然存在算法效率低的问题,因此,使用MapReduce实现双层聚类的并行化,提高了聚类的效率。     

Iterative Fuzzy Clustering Algorithm With Supervision to Construct Probabilistic Fuzzy Rule Base From Numerical Data

To deal with data patterns with linguistic ambiguity and with probabilistic uncertainty in a single framework, we construct an interpretable probabilistic fuzzy rule-based system that requires less human intervention and less prior knowledge than other state of the art methods. Specifically, we present a new iterative fuzzy clustering algorithm that incorporates a supervisory scheme into an unsupervised fuzzy clustering process. The learning process starts in a fully unsupervised manner using fuzzy c-means (FCM) clustering algorithm and a cluster validity criterion, and then gradually constructs meaningful fuzzy partitions over the input space. The corresponding fuzzy rules with probabilities are obtained through an iterative learning process of selecting clusters with supervisory guidance based on the notions of cluster-pureness and class-separability. The proposed algorithm is tested first with synthetic data sets and benchmark data sets from the UCI Repository of Machine Learning Database and then, with real facial expression data and TV viewing data.     

Video segmentation using a histogram-based fuzzy c-means clustering algorithm

The purpose of video segmentation is to segment video sequence into shots where each shot represents a sequence of frames having the same contents, and then select key frames from each shot for indexing. Existing video segmentation methods can be classified into two groups: the shot change detection (SCD) approach for which thresholds have to be pre-assigned, and the clustering approach for which a prior knowledge of the number of clusters is required. In this paper, we propose a video segmentation method using a histogram-based fuzzy c-means (HBFCM) clustering algorithm. This algorithm is a hybrid of the two approaches aforementioned, and is designed to overcome the drawbacks of both approaches. The HBFCM clustering algorithm is composed of three phases: the feature extraction phase, the clustering phase, and the key-frame selection phase. In the first phase, differences between color histogram are extracted as features. In the second phase, the fuzzy c-means (FCM) is used to group features into three clusters: the shot change (SC) cluster, the suspected shot change (SSC) cluster, and the no shot change (NSC) cluster. In the last phase, shot change frames are identified from the SC and the SSC, and then used to segment video sequences into shots. Finally, key frames are selected from each shot. Simulation results indicate that the HBFCM clustering algorithm is robust and applicable to various types of video sequences.     

模糊聚类分析在数据挖掘中的应用研究

数据挖掘是从大量数据中用平凡的方法发现有用的知识。聚类分析是数据挖掘的一个重要研究领域,它是按照一定的要求和规律将事物进行分类的一种数学方法。随着模糊数学的兴起,用精确的数学的方法研究模糊问题,人们逐渐将精确和模糊统一起来。论文将模糊数学的模糊理论应用于数据挖掘的聚类分析中,讨论了如何利用样本之间的模糊关系分析样本之间的关联程度,给出了模糊聚类分析在数据挖掘中的应用的主要步骤,以及相应的实例分析和程序设计。     

一种基于广义熵的模糊聚类算法

针对熵模糊聚类算法只考虑特殊的加权指数问题,将广义熵引入到模糊聚类的目标函数,获得一种基于广义熵的模糊聚类模型和模糊聚类算法。将核函数引入到该模糊聚类模型中,提出基于广义熵的核模糊聚类算法。实验研究广义熵模糊聚类算法与核模糊聚类算法,证明当使用熵模糊聚类算法对数据聚类时,选取加权指数大于2的值可获得较好的聚类结果,同时参数对核算法的聚类结果有较大的影响。     

Adaptive fuzzy systems for backing up a truck-and-trailer

Fuzzy control systems and neural-network control systems for backing up a simulated truck, and truck-and-trailer, to a loading dock in a parking lot are presented. The supervised backpropagation learning algorithm trained the neural network systems. The robustness of the neural systems was tested by removing random subsets of training data in learning sequences. The neural systems performed well but required extensive computation for training. The fuzzy systems performed well until over 50% of their fuzzy-associative-memory (FAM) rules were removed. They also performed well when the key FAM equilibration rule was replaced with destructive, or ;sabotage', rules. Unsupervised differential competitive learning (DCL) and product-space clustering adaptively generated FAM rules from training data. The original fuzzy control systems and neural control systems generated trajectory data. The DCL system rapidly recovered the underlying FAM rules. Product-space clustering converted the neural truck systems into structured sets of FAM rules that approximated the neural system's behavior.