基于相关随机子空间的分类数据聚类集成

为了提升分类数据聚类集成的效果,提出了一种新的相关随机子空间聚类集成模型。该模型利用粗糙集理论将分类属性分解成相关和不相关子集,在相关属性子集上随机生成多个相关子空间并对分类数据进行聚类,通过集成多个较优且具差异性的聚类结果以获得最终的聚类划分。此外,将粗糙集约简概念应用于相关子空间属性数目的确定,有效地避免了参数对聚类结果的影响。UCI数据集实验表明,新模型的性能优于其他已有模型,说明了其有效性。     

Clustering categorical data sets using tabu search techniques

Clustering methods partition a set of objects into clusters such that objects in the same cluster are more similar to each other than objects in different clusters according to some defined criteria. The fuzzy k-means-type algorithm is best suited for implementing this clustering operation because of its effectiveness in clustering data sets. However, working only on numeric values limits its use because data sets often contain categorical values. In this paper, we present a tabu search based clustering algorithm, to extend the k-means paradigm to categorical domains, and domains with both numeric and categorical values. Using tabu search based techniques, our algorithm can explore the solution space beyond local optimality in order to aim at finding a global solution of the fuzzy clustering problem. It is found that the clustering results produced by the proposed algorithm are very high in accuracy.     

Detecting outliers in categorical data through rough clustering

Outlier detection is an important data mining task with many contemporary applications. Clustering based methods for outlier detection try to identify the data objects that deviate from the normal data. However, the uncertainty regarding the cluster membership of an outlier object has to be handled appropriately during the clustering process. Additionally, carrying out the clustering process on data described using categorical attributes is challenging, due to the difficulty in defining requisite methods and measures dealing with such data. Addressing these issues, a novel algorithm for clustering categorical data aimed at outlier detection is proposed here by modifying the standard \(k\)-modes algorithm. The uncertainty regarding the clustering process is addressed by considering a soft computing approach based on rough sets. Accordingly, the modified clustering algorithm incorporates the lower and upper approximation properties of rough sets. The efficacy of the proposed rough \(k\)-modes clustering algorithm for outlier detection is demonstrated using various benchmark categorical data sets.     

A novel attribute weighting algorithm for clustering high-dimensional categorical data

Due to data sparseness and attribute redundancy in high-dimensional data, clusters of objects often exist in subspaces rather than in the entire space. To effectively address this issue, this paper presents a new optimization algorithm for clustering high-dimensional categorical data, which is an extension of the k-modes clustering algorithm. In the proposed algorithm, a novel weighting technique for categorical data is developed to calculate two weights for each attribute (or dimension) in each cluster and use the weight values to identify the subsets of important attributes that categorize different clusters. The convergence of the algorithm under an optimization framework is proved. The performance and scalability of the algorithm is evaluated experimentally on both synthetic and real data sets. The experimental studies show that the proposed algorithm is effective in clustering categorical data sets and also scalable to large data sets owning to its linear time complexity with respect to the number of data objects, attributes or clusters.     

基于混合蛙跳与阴影集优化的粗糙模糊聚类算法

针对粗糙模糊聚类算法对初值敏感、易陷入局部最优和聚类性能依赖阈值选择等问题, 提出一种混合蛙跳与阴影集优化的粗糙模糊聚类算法(SFLA-SRFCM). 通过设置自适应调节因子, 以增加混合蛙跳算法的局部搜索能力; 利用类簇上、下近似集的模糊类内紧密度和模糊类间分离度构造新的适应度函数; 采用阴影集自适应获取类簇阈值. 实验结果表明, SFLA-SRFCM 算法是有效的, 并且具有更好的聚类精度和有效性指标.

     

K-Harmonic means type clustering algorithm for mixed datasets

K-means type clustering algorithms for mixed data that consists of numeric and categorical attributes suffer from cluster center initialization problem. The final clustering results depend upon the initial cluster centers. Random cluster center initialization is a popular initialization technique. However, clustering results are not consistent with different cluster center initializations. K-Harmonic means clustering algorithm tries to overcome this problem for pure numeric data. In this paper, we extend the K-Harmonic means clustering algorithm for mixed datasets. We propose a definition for a cluster center and a distance measure. These cluster centers and the distance measure are used with the cost function of K-Harmonic means clustering algorithm in the proposed algorithm. Experiments were carried out with pure categorical datasets and mixed datasets. Results suggest that the proposed clustering algorithm is quite insensitive to the cluster center initialization problem. Comparative studies with other clustering algorithms show that the proposed algorithm produce better clustering results.     

动态的模糊K-Modes初始化算法

模糊-Modes聚类算法针对分类属性的数据进行聚类,使用爬山法来寻找最优解,因此该算法对初始值较为敏感。为了克服该缺点,提出一种动态的模糊K—Modes初始化算法,该方法能够自动确定聚类数目,以及对应的聚类中心;而且能够应用于数值属性和分类属性相混合的数据集。该初始化算法可以有效地克服模糊K—Modes算法对初值的敏感性。实验的结果表明了该初始化算法的可行性和有效性。     

Determining the number of clusters using information entropy for mixed data

In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numerical attributes and categorical attributes. To overcome this deficiency, a generalized mechanism is presented in this paper by integrating Rényi entropy and complement entropy together. The mechanism is able to uniformly characterize within-cluster entropy and between-cluster entropy and to identify the worst cluster in a mixed data set. In order to evaluate the clustering results for mixed data, an effective cluster validity index is also defined in this paper. Furthermore, by introducing a new dissimilarity measure into the k-prototypes algorithm, we develop an algorithm to determine the number of clusters in a mixed data set. The performance of the algorithm has been studied on several synthetic and real world data sets. The comparisons with other clustering algorithms show that the proposed algorithm is more effective in detecting the optimal number of clusters and generates better clustering results.     

基于新的相似性度量的加权粗糙聚类算法

聚类是数据挖掘中重要的研究方向。本文针对现有的聚类算法中相似度量的缺陷,提出了一种新的相似性度量方法。在此基础上,将粗糙集理论中的区分能力引入到聚类算法中,用来度量属性的重要性,进而提出了一种能够处理符号型数据的新的加权粗糙聚类算法。通过对UCI数据的实验表明,本文算法对数据输入顺序不敏感,且不需要预先给定簇的数目,提高了聚类的质量。     

A cluster centers initialization method for clustering categorical data

The leading partitional clustering technique, k-modes, is one of the most computationally efficient clustering methods for categorical data. However, the performance of the k-modes clustering algorithm which converges to numerous local minima strongly depends on initial cluster centers. Currently, most methods of initialization cluster centers are mainly for numerical data. Due to lack of geometry for the categorical data, these methods used in cluster centers initialization for numerical data are not applicable to categorical data. This paper proposes a novel initialization method for categorical data which is implemented to the k-modes algorithm. The method integrates the distance and the density together to select initial cluster centers and overcomes shortcomings of the existing initialization methods for categorical data. Experimental results illustrate the proposed initialization method is effective and can be applied to large data sets for its linear time complexity with respect to the number of data objects.     

Cluster center initialization algorithm for K-modes clustering

Partitional clustering of categorical data is normally performed by using K-modes clustering algorithm, which works well for large datasets. Even though the design and implementation of K-modes algorithm is simple and efficient, it has the pitfall of randomly choosing the initial cluster centers for invoking every new execution that may lead to non-repeatable clustering results. This paper addresses the randomized center initialization problem of K-modes algorithm by proposing a cluster center initialization algorithm. The proposed algorithm performs multiple clustering of the data based on attribute values in different attributes and yields deterministic modes that are to be used as initial cluster centers. In the paper, we propose a new method for selecting the most relevant attributes, namely Prominent attributes, compare it with another existing method to find Significant attributes for unsupervised learning, and perform multiple clustering of data to find initial cluster centers. The proposed algorithm ensures fixed initial cluster centers and thus repeatable clustering results. The worst-case time complexity of the proposed algorithm is log-linear to the number of data objects. We evaluate the proposed algorithm on several categorical datasets and compared it against random initialization and two other initialization methods, and show that the proposed method performs better in terms of accuracy and time complexity. The initial cluster centers computed by the proposed approach are close to the actual cluster centers of the different data we tested, which leads to faster convergence of K-modes clustering algorithm in conjunction to better clustering results.     

基于密度的混合属性数据流聚类算法

数据流聚类分析是当前数据挖掘研究的热点问题,为了克服数据流聚类框架CluStream算法不能处理混合属性数据流的缺陷,提出了基于密度的混合属性数据流聚类算法MCStream.在微聚类中使用面向维度的距离来度量对象之间的相似度,在宏聚类中使用改进的密度聚类算法M-DBSCAN对微簇进行聚类.实验结果表明,MCStream算法能快速有效地处理混合属性数据流聚类问题.     

A k-means type clustering algorithm for subspace clustering of mixed numeric and categorical datasets

Almost all subspace clustering algorithms proposed so far are designed for numeric datasets. In this paper, we present a k-means type clustering algorithm that finds clusters in data subspaces in mixed numeric and categorical datasets. In this method, we compute attributes contribution to different clusters. We propose a new cost function for a k-means type algorithm. One of the advantages of this algorithm is its complexity which is linear with respect to the number of the data points. This algorithm is also useful in describing the cluster formation in terms of attributes contribution to different clusters. The algorithm is tested on various synthetic and real datasets to show its effectiveness. The clustering results are explained by using attributes weights in the clusters. The clustering results are also compared with published results.     

Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values

The k-means algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the k-means algorithm to categorical domains and domains with mixed numeric and categorical values. The k-modes algorithm uses a simple matching dissimilarity measure to deal with categorical objects, replaces the means of clusters with modes, and uses a frequency-based method to update modes in the clustering process to minimise the clustering cost function. With these extensions the k-modes algorithm enables the clustering of categorical data in a fashion similar to k-means. The k-prototypes algorithm, through the definition of a combined dissimilarity measure, further integrates the k-means and k-modes algorithms to allow for clustering objects described by mixed numeric and categorical attributes. We use the well known soybean disease and credit approval data sets to demonstrate the clustering performance of the two algorithms. Our experiments on two real world data sets with half a million objects each show that the two algorithms are efficient when clustering large data sets, which is critical to data mining applications.     

一种基于多属性权重的分类数据子空间聚类算法

采用多属性频率权重以及多目标簇集质量聚类准则,提出一种分类数据子空间聚类算法.该算法利用粗糙集理论中的等价类,定义了一种多属性权重计算方法,有效地提高了属性的聚类区分能力;在多目标簇集质量函数的基础上,采用层次凝聚策略,迭代合并子簇,有效地度量了各类尺度的聚类簇;利用区间离散度,解决了使用阈值删除噪音点所带来的参数问题;利用属性对簇的依附程度,确定了聚类簇的属性相关子空间,提高了聚类簇的可理解性.最后,采用人工合成、UCI和恒星光谱数据集,实验验证了该聚类算法的可行性和有效性.     

不平衡数据的软子空间聚类算法

针对受均匀效应的影响,当前K-means型软子空间算法不能有效聚类不平衡数据的问题,提出一种基于划分的不平衡数据软子空间聚类新算法。首先,提出一种双加权方法,在赋予每个属性一个特征权重的同时,赋予每个簇反映其重要性的一个簇类权重;其次,提出一种混合型数据的新距离度量,以平衡不同类型属性及具有不同符号数目的类属型属性间的差异;第三,定义了基于双加权方法的不平衡数据子空间聚类目标优化函数,给出了优化簇类权重和特征权重的表达式。在实际应用数据集上进行了系列实验,结果表明,新算法使用的双权重方法能够为不平衡数据中的簇类学习更准确的软子空间;与现有的K-means型软子空间算法相比,所提算法提高了不平衡数据的聚类精度,在其中的生物信息学数据上可以取得近50%的提升幅度。     

DHCC: Divisive hierarchical clustering of categorical data

Clustering categorical data poses two challenges defining an inherently meaningful similarity measure, and effectively dealing with clusters which are often embedded in different subspaces. In this paper, we propose a novel divisive hierarchical clustering algorithm for categorical data, named DHCC. We view the task of clustering categorical data from an optimization perspective, and propose effective procedures to initialize and refine the splitting of clusters. The initialization of the splitting is based on multiple correspondence analysis (MCA). We also devise a strategy for deciding when to terminate the splitting process. The proposed algorithm has five merits. First, due to its hierarchical nature, our algorithm yields a dendrogram representing nested groupings of patterns and similarity levels at different granularities. Second, it is parameter-free, fully automatic and, in particular, requires no assumption regarding the number of clusters. Third, it is independent of the order in which the data is processed. Fourth, it is scalable to large data sets. And finally, our algorithm is capable of seamlessly discovering clusters embedded in subspaces, thanks to its use of a novel data representation and Chi-square dissimilarity measures. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.     

拓展集合差异度高维数据聚类*

提出度量多个集合之间总体差异程度的拓展集合差异度及相关定理,并给出一种新的解决分类属性高维数据聚类问题的CAESD算法。基于拓展集合差异度及拓展集合特征向量,在CABOSFV_C聚类的基础上通过两阶段聚类完成全部聚类过程。采用UCI数据集与K-modes及其改进算法、CABOSFV_C算法进行比较实验,结果表明CAESD算法具有较高的聚类正确率。     

一致性函数研究

通过把聚类集体当成一个概念型数据集,把聚类集体一致性函数问题转换成了一个普通的聚类问题,应用概念型数据聚类算法k-modes和LIMBO来进行聚类集成。实验结果证明用概念型数据聚类算法进行集成效果理想。     

基于EK-medoids聚类和邻域距离的特征选择方法

针对传统聚类算法中只注重数据间的距离关系,而忽视数据全局性分布结构的问题,提出一种基于EK-medoids聚类和邻域距离的特征选择方法。首先,用稀疏重构的方法计算数据样本之间的有效距离,构建基于有效距离的相似性矩阵;然后,将相似性矩阵应用到K-medoids聚类算法中,获取新的聚类中心,进而提出EK-medoids聚类算法,可有效对原始数据集进行聚类;最后,根据划分结果所构成簇的邻域距离给出确定数据集中的属性重要度定义,应用启发式搜索方法设计一种EK-medoids聚类和邻域距离的特征选择算法,降低了聚类算法的时间复杂度。实验结果表明,该算法不仅有效地提高了聚类结果的精度,而且也可选择出分类精度较高的特征子集。