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.     

方向相似性聚类方法DSCM

针对方向性数据提出了一种鲁棒的基于方向相似性度量的聚类方法DSCM．DSCM首先基于方向性度量构造目标函数，然后通过不动点迭代法对目标函数优化，获得各个样本的最终稳定状态，最后基于样本的最终状态集利用层次聚类技术实现聚类．DSCM的优势在于对方向性数据聚类时不依赖于具体的初始化参数，且能自组织地求解最优聚类划分因而有很好的鲁棒性．通过实验证实了DSCM的有效性以及对已有的两个传统方向性聚类算法的优越性．     

Clustering of the self-organizing map using a clustering validity index based on inter-cluster and intra-cluster density

The self-organizing map (SOM) has been widely used in many industrial applications. Classical clustering methods based on the SOM often fail to deliver satisfactory results, specially when clusters have arbitrary shapes. In this paper, through some preprocessing techniques for filtering out noises and outliers, we propose a new two-level SOM-based clustering algorithm using a clustering validity index based on inter-cluster and intra-cluster density. Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the SOM, and find an optimal number of clusters.     

聚类趋势问题的研究综述*

聚类算法的性能与数据集的结构是密切相关的,虽然目前已经研究出了很多聚类算法,但没有普遍适用的万能聚类算法,欠缺对数据集结构的有效解释。对聚类分析过程中重要的关键性问题,即聚类趋势问题进行了系统性的研究,从统计检验、可视化分析等角度给予了讨论,为数据集的无监督聚类分析提供了合理和有效的前期分析工具。     

Determining number of clusters and prototype locations via multi-scale clustering

In clustering algorithms, it is usually assumed that the number of clusters is known or given. In the absence of such a priori information, a procedure is needed to find an appropriate number of clusters. This paper presents a clustering algorithm that incorporates a mechanism for finding the appropriate number of clusters as well as the locations of cluster prototypes. This algorithm, called multi-scale clustering, is based on scale-space theory by considering that any prominent data structure ought to survive over many scales. The number of clusters as well as the locations of cluster prototypes are found in an objective manner by defining and using lifetime and drift speed clustering criteria. The outcome of this algorithm does not depend on the initial prototype locations that affect the outcome of many clustering algorithms. As an application of this algorithm, it is used to enhance the Hough transform technique.     

Self-Organizing-Map Based Clustering Using a Local Clustering Validity Index

Classical clustering methods, such as partitioning and hierarchical clustering algorithms, often fail to deliver satisfactory results, given clusters of arbitrary shapes. Motivated by a clustering validity index based on inter-cluster and intra-cluster density, we propose that the clustering validity index be used not only globally to find optimal partitions of input data, but also locally to determine which two neighboring clusters are to be merged in a hierarchical clustering of Self-Organizing Map (SOM). A new two-level SOM-based clustering algorithm using the clustering validity index is also proposed. Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data in a better way than classical clustering algorithms on an SOM.     

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。     

On biological validity indices for soft clustering algorithms for gene expression data

Unsupervised clustering methods such as K-means, hierarchical clustering and fuzzy c-means have been widely applied to the analysis of gene expression data to identify biologically relevant groups of genes. Recent studies have suggested that the incorporation of biological information into validation methods to assess the quality of clustering results might be useful in facilitating biological and biomedical knowledge discoveries. In this study, we generalize two bio-validity indices, the biological homogeneity index and the biological stability index, to quantify the abilities of soft clustering algorithms such as fuzzy c-means and model-based clustering. The results of an evaluation of several existing soft clustering algorithms using simulated and real data sets indicate that the soft versions of the indices provide both better precision and better accuracy than the classical ones. The significance of the proposed indices is also discussed.     

Distance and density based clustering algorithm using Gaussian kernel

Clustering is an important field for making data meaningful at various applications such as processing satellite images, extracting information from financial data or even processing data in social sciences. This paper presents a new clustering approach called Gaussian Density Distance (GDD) clustering algorithm based on distance and density properties of sample space. The novel part of the method is to find best possible clusters without any prior information and parameters. Another novel part of the algorithm is that it forms clusters very close to human clustering perception when executed on two dimensional data. GDD has some similarities with today’s most popular clustering algorithms; however, it uses both Gaussian kernel and distances to form clusters according to data density and shape. Since GDD does not require any special parameters prior to run, resulting clusters do not change at different runs. During the study, an experimental framework is designed for analysis of the proposed clustering algorithm and its evaluation, based on clustering performance for some characteristic data sets. The algorithm is extensively tested using several synthetic data sets and some of the selected results are presented in the paper. Comparative study outcomes produced by other well-known clustering algorithms are also discussed in the paper.     

新模糊聚类有效性指标

模糊聚类是模式识别、机器学习和图像处理等领域的重要研究内容。模糊C-均值聚类算法是最常用的模糊聚类实现算法,该算法需要预先给定聚类数才能对数据集进行聚类。提出了一种新的聚类有效性指标,对聚类结果进行有效性验证。该指标从划分熵、隶属度、几何结构角度,定义了紧凑度、分离度、重叠度三个重要特征测量。在此基础上,提出了一种最佳聚类数确定方法。将新聚类有效性指标和传统有效性指标在6个人工数据集和3个真实数据集进行实验验证。实验结果表明,所提出的指标和方法能够有效地对聚类结果进行评估,适合确定样本的最佳聚类数。