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.     

基于密度的聚类中心自动确定的混合属性数据聚类算法研究

面对广泛存在的混合属性数据,现有大部分混合属性聚类算法普遍存在聚类 质量低、聚类算法参数依赖性大、聚类类别个数和聚类中心无法准确自动确定等问题,针对 这些问题本文提出了一种基于密度的聚类中心自动确定的混合属性数据 聚类算法.该算法通过分析混合属性数据特征,将混合属性数据分为数 值占优、分类占优和均衡型混合属性数据三类,分析不同情况的特征选取 相应的距离度量方式.在计算数据集各个点的密度和距离分布图基础 上,深入分析获得规律: 高密度且与比它更高密度的数据点有较大距离的数 据点最可能成为聚类中心,通过线性回归模型和残差分析确定奇异 点,理论论证这些奇异点即为聚类中心,从而实现了自动确定聚类中心.采 用粒子群算法(Particle swarm optimization, PSO)寻找最优dc值,通过参数dc能够计算得到 任意数据对象的密度和到比它密度更高的点的最小距离,根据聚类 中心自动确定方法确定每个簇中心,并将其他点按到最近邻的更高 密度对象的最小距离划分到相应的簇中,从而实现聚类.最终将本文 提出算法与其他现有的多种混合属性聚类算法在多个数据集上进行 算法性能比较,验证本文提出算法具有较高的聚类质量.     

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.     

Non-dominated sorting genetic algorithm using fuzzy membership chromosome for categorical data clustering

In this research, a data clustering algorithm named as non-dominated sorting genetic algorithm-fuzzy membership chromosome (NSGA-FMC) based on K-modes method which combines fuzzy genetic algorithm and multi-objective optimization was proposed to improve the clustering quality on categorical data. The proposed method uses fuzzy membership value as chromosome. In addition, due to this innovative chromosome setting, a more efficient solution selection technique which selects a solution from non-dominated Pareto front based on the largest fuzzy membership is integrated in the proposed algorithm. The multiple objective functions: fuzzy compactness within a cluster (π) and separation among clusters (sep) are used to optimize the clustering quality. A series of experiments by using three UCI categorical datasets were conducted to compare the clustering results of the proposed NSGA-FMC with two existing methods: genetic algorithm fuzzy K-modes (GA-FKM) and multi-objective genetic algorithm-based fuzzy clustering of categorical attributes (MOGA (π, sep)). Adjusted Rand index (ARI), π, sep, and computation time were used as performance indexes for comparison. The experimental result showed that the proposed method can obtain better clustering quality in terms of ARI, π, and sep simultaneously with shorter computation time.     

An initialization method to simultaneously find initial cluster centers and the number of clusters for clustering categorical data

The leading partitional clustering technique, k-modes, is one of the most computationally efficient clustering methods for categorical data. However, in the k-modes-type algorithms, the performance of their clustering depends on initial cluster centers and the number of clusters needs be known or given in advance. This paper proposes a novel initialization method for categorical data which is implemented to the k-modes-type algorithms. The proposed method can not only obtain the good initial cluster centers but also provide a criterion to find candidates for the number of clusters. The performance and scalability of the proposed method has been studied on real data sets. The experimental results illustrate that the proposed method is effective and can be applied to large data sets for its linear time complexity with respect to the number of data points.     

采用离群点检测技术的混合型数据聚类初始化方法

近年来,混合型数据的聚类问题受到广泛关注。作为处理混合型数据的一种有效方法,K-prototype聚类算法在初始化聚类中心时通常采用随机选取的策略,然而这种策略在很多实际应用中难以保证聚类结果的质量。针对上述问题,采用基于离群点检测的策略来为K-prototype算法选择初始中心,并提出一种新的混合型数据聚类初始化算法(initialization of K-prototype clustering based on outlier detection and density, IKP-ODD)。给定一个候选对象,IKP-ODD通过计算其距离离群因子、加权密度以及与已有初始中心之间的加权距离来判断候选对象是否是一个初始中心。IKP-ODD通过采用距离离群因子和加权密度,防止选择离群点作为初始中心。在计算对象的加权密度以及对象之间的加权距离时,采用邻域粗糙集中的粒度邻域熵来计算每一个属性的重要性,并根据属性重要性的大小为不同属性赋予不同的权重,有效地反映不同属性之间的差异性。在多个UCI数据集上的实验表明,相对于现有的初始化方法,IKP-ODD能够更好地解决K-prototype聚类的初始化问题。     

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。     

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.     

针对混合型分类数据改进的[K]-modes算法距离公式

传统[K]-modes算法在分类属性聚类中有着广泛的应用,但是传统算法并不区分有序分类属性与无序分类属性。在区分这两种属性的基础上,提出了一种新的距离公式,并优化了算法流程。基于无序分类属性的距离数值,确定了有序分类属性相邻属性值之间距离数值的合理范围。借助有序分类属性蕴含的顺序关系,构建了有序分类属性的距离公式。计算样本点与质心距离之时,引入了簇内各属性值的比例作为总体距离公式的重要参数。综上,新的距离公式良好地刻画了有序分类属性的距离,并且平衡了两种不同分类属性距离公式之间的差异性。实验结果表明,提出的改进算法和距离公式在UCI真实数据集上比原始[K]-modes算法及其改进算法均有显著的效果。     

一种分类型矩阵数据的初始聚类中心选择算法

现有面向矩阵数据集的算法多数通过随机选取初始类中心得到聚类结果。为克服不同初始类中心对聚类结果的影响,针对分类型矩阵数据,提出一种新的初始聚类中心选择算法。根据属性值的频率定义矩阵对象的密度和矩阵对象间的距离,扩展最大最小距离算法,从而实现初始类中心的选择。在7个真实数据集上的实验结果表明,与初始类中心选择算法CAOICACD和BAIICACD相比,该算法均具有较优的聚类效果。     

Efficient algorithms based on the k-means and Chaotic League Championship Algorithm for numeric,categorical, and mixed-type data clustering

The success rates of the expert or intelligent systems depend on the selection of the correct data clusters. The k-means algorithm is a well-known method in solving data clustering problems. It suffers not only from a high dependency on the algorithm's initial solution but also from the used distance function. A number of algorithms have been proposed to address the centroid initialization problem, but the produced solution does not produce optimum clusters. This paper proposes three algorithms (i) the search algorithm C-LCA that is an improved League Championship Algorithm (LCA), (ii) a search clustering using C-LCA (SC-LCA), and (iii) a hybrid-clustering algorithm called the hybrid of k-means and Chaotic League Championship Algorithm (KSC-LCA) and this algorithm has of two computation stages. The C-LCA employs chaotic adaptation for the retreat and approach parameters, rather than constants, which can enhance the search capability. Furthermore, to overcome the limitation of the original k-means algorithm using the Euclidean distance that cannot handle the categorical attribute type properly, we adopt the Gower distance and the mechanism for handling a discrete value requirement of the categorical value attribute. The proposed algorithms can handle not only the pure numeric data but also the mixed-type data and can find the best centroids containing categorical values. Experiments were conducted on 14 datasets from the UCI repository. The SC-LCA and KSC-LCA competed with 16 established algorithms including the k-means, k-means++, global k-means algorithms, four search clustering algorithms and nine hybrids of k-means algorithm with several state-of-the-art evolutionary algorithms. The experimental results show that the SC-LCA produces the cluster with the highest F-Measure on the pure categorical dataset and the KSC-LCA produces the cluster with the highest F-Measure for the pure numeric and mixed-type tested datasets. Out of 14 datasets, there were 13 centroids produced by the SC-LCA that had better F-Measures than that of the k-means algorithm. On the Tic-Tac-Toe dataset containing only categorical attributes, the SC-LCA can achieve an F-Measure of 66.61 that is 21.74 points over that of the k-means algorithm (44.87). The KSC-LCA produced better centroids than k-means algorithm in all 14 datasets; the maximum F-Measure improvement was 11.59 points. However, in terms of the computational time, the SC-LCA and KSC-LCA took more NFEs than the k-means and its variants but the KSC-LCA ranks first and SC-LCA ranks fourth among the hybrid clustering and the search clustering algorithms that we tested. Therefore, the SC-LCA and KSC-LCA are general and effective clustering algorithms that could be used when an expert or intelligent system requires an accurate high-speed cluster selection.     

一种适用于混合型分类数据的聚类算法

传统的K-modes算法采用简单的属性匹配方式计算同一属性下不同属性值的距离，并且计算样本距离时令所有属性权重相等。在此基础上，综合考虑有序型分类数据中属性值的顺序关系、无序型分类数据中不同属性值之间的相似性以及各属性之间的关系等，提出一种更加适用于混合型分类数据的改进聚类算法，该算法对无序型分类数据和有序型分类数据采用不同的距离度量，并且用平均熵赋予相应的权重。实验结果表明，改进算法在人工数据集和真实数据集上均有比K-modes算法及其改进算法更好的聚类效果。     

基于相对密度和熵的混合属性聚类融合算法

混合属性聚类是近年来的研究热点,对于混合属性数据的聚类算法要求处理好数值属性以及分类属性,而现存许多算法没有很好得平衡两种属性,以至于得不到令人满意的聚类结果.针对混合属性,在此提出一种基于交集的聚类融合算法,算法单独用基于相对密度的算法处理数值属性,基于信息熵的算法处理分类属性,然后通过基于交集的融合算法融合两个聚类成员,最终得到聚类结果.算法在UCI数据集Zoo上进行验证,与现存k-prototypes与EM算法进行了比较,在聚类的正确率上都优于k-prototypes与EM算法,还讨论了融合算法中交集元素比的取值对算法结果的影响.     

类属型数据核子空间聚类算法

现有的类属型数据子空间聚类方法大多基于特征间相互独立假设,未考虑属性间存在的线性或非线性相关性.提出一种类属型数据核子空间聚类方法.首先引入原作用于连续型数据的核函数将类属型数据投影到核空间,定义了核空间中特征加权的类属型数据相似性度量.其次,基于该度量推导了类属型数据核子空间聚类目标函数,并提出一种高效求解该目标函数的优化方法.最后,定义了一种类属型数据核子空间聚类算法.该算法不仅在非线性空间中考虑了属性间的关系,而且在聚类过程中赋予每个属性衡量其与簇类相关程度的特征权重,实现了类属型属性的嵌入式特征选择.还定义了一个聚类有效性指标,以评价类属型数据聚类结果的质量.在合成数据和实际数据集上的实验结果表明,与现有子空间聚类算法相比,核子空间聚类算法可以发掘类属型属性间的非线性关系,并有效提高了聚类结果的质量.     

自适应聚合策略优化的密度峰值聚类算法

针对密度峰值聚类算法受人为干预影响较大和参数敏感的问题,即不正确的截断距离dc会导致错误的初始聚类中心,而且在某些情况下,即使设置了适当的dc值,仍然难以从决策图中人为选择初始聚类中心。为克服这些缺陷,提出一种新的基于密度峰值的聚类算法。该算法首先根据K近邻的思想来确定数据点的局部密度,然后提出一种新的自适应聚合策略,即首先通过算法给出阈值判断初始类簇中心,然后依据离初始类簇中心最近分配剩余点,最后通过类簇间密度可达来合并相似类簇。在实验中,该算法在合成和实际数据集中的表现比DPC、DBSCAN、KNNDPC和K-means算法要好,能有效提高聚类准确率和质量。     

基于密度的模糊代表点聚类算法

结合密度聚类和模糊聚类的特点,提出一种基于密度的模糊代表点聚类算法.首先利用密度对数据点成为候选聚类中心点的可能性进行处理,密度越高的点成为聚类中心点的可能性越大;然后利用模糊方法对聚类中心点进行确定;最后通过合并聚类中心点确定最终的聚类中心.所提出算法具有很好的自适应性,能够处理不同形状的聚类问题,无需提前规定聚类个数,能够自动确定真实存在的聚类中心点,可解释性好.通过结合不同聚类方法的优点,最终实现对数据的有效划分.此外,所提出的算法对于聚类数和初始化、处理不同形状的聚类问题以及应对异常值等方面具有较好的鲁棒性.通过在人工数据集和UCI真实数据集上进行实验,表明所提出算法具有较好的聚类性能和广泛的适用性.     

混合属性数据k-prototypes聚类算法

在现实世界中经常遇到混合数值属性和分类属性的数据, k-prototypes是聚类该类型数据的主要算法之一。针对现有混合属性聚类算法的不足,提出一种基于分布式质心和新差异测度的改进的 k-prototypes 算法。在新算法中,首先引入分布式质心来表示簇中的分类属性的簇中心,然后结合均值和分布式质心来表示混合属性的簇中心,并提出一种新的差异测度来计算数据对象与簇中心的距离,新差异测度考虑了不同属性在聚类过程中的重要性。在三个真实数据集上的仿真实验表明,与传统的聚类算法相比,本文算法的聚类精度要优于传统的聚类算法,从而验证了本文算法的有效性。     

A new initialization method for categorical data clustering

In clustering algorithms, choosing a subset of representative examples is very important in data set. Such “exemplars” can be found by randomly choosing an initial subset of data objects and then iteratively refining it, but this works well only if that initial choice is close to a good solution. In this paper, based on the frequency of attribute values, the average density of an object is defined. Furthermore, a novel initialization method for categorical data is proposed, in which the distance between objects and the density of the object is considered. We also apply the proposed initialization method to k-modes algorithm and fuzzy k-modes algorithm. Experimental results illustrate that the proposed initialization method is superior to random initialization method and can be applied to large data sets for its linear time complexity with respect to the number of data objects.     

基于Hub的高维数据初始聚类中心的选择策略

针对基于Hub的聚类算法K-hubs算法存在对初始聚类中心敏感的问题,提出一种基于Hub的初始中心选择策略。该策略充分利用高维数据普遍存在的Hubness现象,选择相距最远的K个Hub点作为初始的聚类中心。实验表明采用该策略的K-hubs算法与原来采用随机初始中心的K-hubs算法相比,前者拥有较好的初始中心分布,能够提高聚类准确率,而且初始中心所在的位置倾向于接近最终簇中心,有利于加快算法收敛。     

An initial seed selection algorithm for k-means clustering of georeferenced data to improve replicability of cluster assignments for mapping application

K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed to overcome this problem and has been shown to have better accuracy and computational efficiency than k-means. In many clustering problems though – such as when classifying georeferenced data for mapping applications – standardization of clustering methodology, specifically, the ability to arrive at the same cluster assignment for every run of the method i.e. replicability of the methodology, may be of greater significance than any perceived measure of accuracy, especially when the solution is known to be non-unique, as in the case of k-means clustering. Here we propose a simple initial seed selection algorithm for k-means clustering along one attribute that draws initial cluster boundaries along the “deepest valleys” or greatest gaps in dataset. Thus, it incorporates a measure to maximize distance between consecutive cluster centers which augments the conventional k-means optimization for minimum distance between cluster center and cluster members. Unlike existing initialization methods, no additional parameters or degrees of freedom are introduced to the clustering algorithm. This improves the replicability of cluster assignments by as much as 100% over k-means and k-means++, virtually reducing the variance over different runs to zero, without introducing any additional parameters to the clustering process. Further, the proposed method is more computationally efficient than k-means++ and in some cases, more accurate.