Chaotic ant swarm approach for data clustering

Clustering divides data into meaningful or useful groups (clusters) without any prior knowledge. It is a key technique in data mining and has become an important issue in many fields. This article presents a new clustering algorithm based on the mechanism analysis of chaotic ant swarm (CAS). It is an optimization methodology for clustering problem which aims to obtain global optimal assignment by minimizing the objective function. The proposed algorithm combines three advantages into one: finding global optimal solution to the objective function, not sensitive to clusters with different size and density and suitable to multi-dimensional data sets. The quality of this approach is evaluated on several well-known benchmark data sets. Compared with the popular clustering method named k-means algorithm and the PSO-based clustering technique, experimental results show that our algorithm is an effective clustering technique and can be used to handle data sets with complex cluster sizes, densities and multiple dimensions.     

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.     

A hybrid clustering procedure for concentric and chain-like clusters

K-means algorithm is a well known nonhierarchical method for clustering data. The most important limitations of this algorithm are that: (1) it gives final clusters on the basis of the cluster centroids or the seed points chosen initially, and (2) it is appropriate for data sets having fairly isotropic clusters. But this algorithm has the advantage of low computation and storage requirements. On the other hand, hierarchical agglomerative clustering algorithm, which can cluster nonisotropic (chain-like and concentric) clusters, requires high storage and computation requirements. This paper suggests a new method for selecting the initial seed points, so that theK-means algorithm gives the same results for any input data order. This paper also describes a hybrid clustering algorithm, based on the concepts of multilevel theory, which is nonhierarchical at the first level and hierarchical from second level onwards, to cluster data sets having (i) chain-like clusters and (ii) concentric clusters. It is observed that this hybrid clustering algorithm gives the same results as the hierarchical clustering algorithm, with less computation and storage requirements.     

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.     

一种带混合进化机制的膜聚类算法

膜计算(也称为P系统或膜系统)是一种新颖的分布式、并行计算模型.为了处理数据聚类问题,提出了一种采用混合进化机制的膜聚类算法.它使用了一个由3个细胞组成的组织P系统,为一个待聚类的数据集发现最优的簇中心.其对象表示候选的簇中心,并且这3个细胞分别使用了3种不同的进化机制:遗传算子、速度-位移模型和差分进化机制.然而,所使用的速度-位移模型和差分进化机制是结合了这个特殊膜结构和转运机制所提出的改进版本.这种混合进化机制能够增强系统中对象的多样性和改善收敛性能.在混合进化机制和转运机制控制下,这种膜聚类算法能够确定一个数据集的良好划分.所提出的膜聚类算法在3个人工数据集和5个真实数据集上被评估,并与k-means和几种进化聚类算法进行比较.统计显著性测试建立了所提出的膜聚类算法的优势.     

Efficient median based clustering and classification techniques for protein sequences

In this paper, an efficient K-medians clustering (unsupervised) algorithm for prototype selection and Supervised K-medians (SKM) classification technique for protein sequences are presented. For sequence data sets, a median string/sequence can be used as the cluster/group representative. In K-medians clustering technique, a desired number of clusters, K, each represented by a median string/sequence, is generated and these median sequences are used as prototypes for classifying the new/test sequence whereas in SKM classification technique, median sequence in each group/class of labelled protein sequences is determined and the set of median sequences is used as prototypes for classification purpose. It is found that the K-medians clustering technique outperforms the leader based technique and also SKM classification technique performs better than that of motifs based approach for the data sets used. We further use a simple technique to reduce time and space requirements during protein sequence clustering and classification. During training and testing phase, the similarity score value between a pair of sequences is determined by selecting a portion of the sequence instead of the entire sequence. It is like selecting a subset of features for sequence data sets. The experimental results of the proposed method on K-medians, SKM and Nearest Neighbour Classifier (NNC) techniques show that the Classification Accuracy (CA) using the prototypes generated/used does not degrade much but the training and testing time are reduced significantly. Thus the experimental results indicate that the similarity score does not need to be calculated by considering the entire length of the sequence for achieving a good CA. Even space requirement is reduced during both training and classification.     

A robust adaptive clustering analysis method for automatic identification of clusters

Identifying the optimal cluster number and generating reliable clustering results are necessary but challenging tasks in cluster analysis. The effectiveness of clustering analysis relies not only on the assumption of cluster number but also on the clustering algorithm employed. This paper proposes a new clustering analysis method that identifies the desired cluster number and produces, at the same time, reliable clustering solutions. It first obtains many clustering results from a specific algorithm, such as Fuzzy C-Means (FCM), and then integrates these different results as a judgement matrix. An iterative graph-partitioning process is implemented to identify the desired cluster number and the final result. The proposed method is a robust approach as it is demonstrated its effectiveness in clustering 2D data sets and multi-dimensional real-world data sets of different shapes. The method is compared with cluster validity analysis and other methods such as spectral clustering and cluster ensemble methods. The method is also shown efficient in mesh segmentation applications. The proposed method is also adaptive because it not only works with the FCM algorithm but also other clustering methods like the k-means algorithm.     

A symmetry based multiobjective clustering technique for automatic evolution of clusters

In this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization (MOO) problem, optimizing a set of cluster validity indices simultaneously. The proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy. Here variable number of cluster centers is encoded in the string. The number of clusters present in different strings varies over a range. The points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing Euclidean distance. Two cluster validity indices, one based on the Euclidean distance, XB-index, and another recently developed point symmetry distance based cluster validity index, Sym-index, are optimized simultaneously in order to determine the appropriate number of clusters present in a data set. Thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters. A new semi-supervised method is also proposed in the present paper to select a single solution from the final Pareto optimal front of the proposed multiobjective clustering technique. The efficacy of the proposed algorithm is shown for seven artificial data sets and six real-life data sets of varying complexities. Results are also compared with those obtained by another multiobjective clustering technique, MOCK, two single objective genetic algorithm based automatic clustering techniques, VGAPS clustering and GCUK clustering.     

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。     

A simulated annealing‐based maximum‐margin clustering algorithm

Maximum‐margin clustering is an extension of the support vector machine (SVM) to clustering. It partitions a set of unlabeled data into multiple groups by finding hyperplanes with the largest margins. Although existing algorithms have shown promising results, there is no guarantee of convergence of these algorithms to global solutions due to the nonconvexity of the optimization problem. In this paper, we propose a simulated annealing‐based algorithm that is able to mitigate the issue of local minima in the maximum‐margin clustering problem. The novelty of our algorithm is twofold, ie, (i) it comprises a comprehensive cluster modification scheme based on simulated annealing, and (ii) it introduces a new approach based on the combination of k‐means++ and SVM at each step of the annealing process. More precisely, k‐means++ is initially applied to extract subsets of the data points. Then, an unsupervised SVM is applied to improve the clustering results. Experimental results on various benchmark data sets (of up to over a million points) give evidence that the proposed algorithm is more effective at solving the clustering problem than a number of popular clustering algorithms.     

A design and analysis of objective function-based unsupervised neural networks for fuzzy clustering

Fuzzy clustering has played an important role in solving many problems. In this paper, we design an unsupervised neural network model based on a fuzzy objective function, called OFUNN. The learning rule for the OFUNN model is a result of the formal derivation by the gradient descent method of a fuzzy objective function. The performance of the cluster analysis algorithm is often evaluated by counting the number of crisp clustering errors. However, the number of clustering errors alone is not a reliable and consistent measure for the performance of clustering, especially in the case of input data with fuzzy boundaries. We introduce two measures to evaluate the performance of the fuzzy clustering algorithm. The clustering results on three data sets, Iris data and two artificial data sets, are analyzed using the proposed measures. They show that OFUNN is very competitive in terms of speed and accuracy compared to the fuzzy c-means algorithm.     

Gravitational clustering

This paper introduces and describes an algorithm or technique, called gravitational clustering, for performing cluster analysis on Euclidean data. The paper describes the physical gravitational model, an abstract generalized model, and several specific gravitational models. It illustrates clustering by one of these models using several sample data sets, and compares the results with those obtained using two other well-known nongravitational clustering methods. The paper also illustrates four graphical techniques to aid in the analysis of a clustering.     

An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis

Clustering is a popular data analysis and data mining technique. A popular technique for clustering is based on k-means such that the data is partitioned into K clusters. However, the k-means algorithm highly depends on the initial state and converges to local optimum solution. This paper presents a new hybrid evolutionary algorithm to solve nonlinear partitional clustering problem. The proposed hybrid evolutionary algorithm is the combination of FAPSO (fuzzy adaptive particle swarm optimization), ACO (ant colony optimization) and k-means algorithms, called FAPSO-ACO–K, which can find better cluster partition. The performance of the proposed algorithm is evaluated through several benchmark data sets. The simulation results show that the performance of the proposed algorithm is better than other algorithms such as PSO, ACO, simulated annealing (SA), combination of PSO and SA (PSO–SA), combination of ACO and SA (ACO–SA), combination of PSO and ACO (PSO–ACO), genetic algorithm (GA), Tabu search (TS), honey bee mating optimization (HBMO) and k-means for partitional clustering problem.     

SimClus: an effective algorithm for clustering with a lower bound on similarity

Clustering algorithms generally accept a parameter k from the user, which determines the number of clusters sought. However, in many application domains, like document categorization, social network clustering, and frequent pattern summarization, the proper value of k is difficult to guess. An alternative clustering formulation that does not require k is to impose a lower bound on the similarity between an object and its corresponding cluster representative. Such a formulation chooses exactly one representative for every cluster and minimizes the representative count. It has many additional benefits. For instance, it supports overlapping clusters in a natural way. Moreover, for every cluster, it selects a representative object, which can be effectively used in summarization or semi-supervised classification task. In this work, we propose an algorithm, SimClus, for clustering with lower bound on similarity. It achieves a O(log n) approximation bound on the number of clusters, whereas for the best previous algorithm the bound can be as poor as O(n). Experiments on real and synthetic data sets show that our algorithm produces more than 40% fewer representative objects, yet offers the same or better clustering quality. We also propose a dynamic variant of the algorithm, which can be effectively used in an on-line setting.     

基于扩展和网格的多密度聚类算法

提出了网格密度可达的聚类概念和边界处理技术,并在此基础上提出一种基于扩展的多密度网格聚类算法。该算法使用网格技术提高聚类的速度,使用边界处理技术提高聚类的精度,每次聚类均从最高的密度单元开始逐步向周围扩展形成聚类．实验结果表明,该算法能有效地对多密度数据集和均匀密度数据集进行聚类,具有聚类精度高等优点．     

半监督的仿射传播聚类

仿射传播聚类算法快速、有效,可以解决大数据集的聚类问题,但当数据的聚类结构比较松散时,聚类准确性不高。该文提出了半监督的仿射传播聚类算法,在迭代过程中嵌入了有效性指标以监督和引导算法向最优聚类结果的方向运行。实验结果表明,该方法对于聚类结构比较紧密和松散的数据集,均可以给出较为准确的聚类结果。     

k-ATTRACTORS: A PARTITIONAL CLUSTERING ALGORITHM FOR NUMERIC DATA ANALYSIS

Clustering is a data analysis technique, particularly useful when there are many dimensions and little prior information about the data. Partitional clustering algorithms are efficient but suffer from sensitivity to the initial partition and noise. We propose here k-attractors, a partitional clustering algorithm tailored to numeric data analysis. As a preprocessing (initialization) step, it uses maximal frequent item-set discovery and partitioning to define the number of clusters k and the initial cluster “attractors.” During its main phase the algorithm uses a distance measure, which is adapted with high precision to the way initial attractors are determined. We applied k-attractors as well as k-means, EM, and FarthestFirst clustering algorithms to several datasets and compared results. Comparison favored k-attractors in terms of convergence speed and cluster formation quality in most cases, as it outperforms these three algorithms except from cases of datasets with very small cardinality containing only a few frequent item sets. On the downside, its initialization phase adds an overhead that can be deemed acceptable only when it contributes significantly to the algorithm's accuracy.     

基于密度峰值和网格的自动选定聚类中心算法

针对快速搜索和发现密度峰值的聚类算法(DPC)中数据点之间计算复杂,最终聚类的中心个数需要通过决策图手动选取等问题,提出基于密度峰值和网格的自动选定聚类中心的改进算法GADPC。首先结合Clique网格聚类算法的思想,不再针对点对象进行操作,而是将点映射到网格,并将网格作为聚类对象,从而减少了DPC算法中对数据点之间的距离计算和聚类次数;其次通过改进后的聚类中心个数判定准则更精确地自动选定聚类中心个数;最后对网格边缘点和噪声点,采用网格内点对象和相邻网格间的相似度进行了处理。实验通过采用UEF(University of Eastern Finland)提供的数据挖掘使用的人工合成数据集和UCI自然数据集进行对比,其聚类评价指标(Rand Index)表明,改进的算法在计算大数据集时聚类质量不低于DPC和K-means算法,而且提高了DPC算法的处理效率。     

改进的蚂蚁聚类算法*

提出了一种改进的基于对称点距离的蚂蚁聚类算法。该算法不再采用Euclidean距离来计算类内对象的相似性,而是使用新的对称点距离来计算相似性,在处理带有对称性质的数据集时,可以有效地识别给定数据集的聚类数目和合适的划分。在该算法中,用人工蚂蚁代表数据对象,根据算法给定的聚类规则来寻找最合适的聚类划分。最后用本算法与标准的蚂蚁聚类算法分别对不同的数据集进行了聚类实验。实验结果证实了算法的有效性。     

A multi-prototype clustering algorithm

Clustering is an important unsupervised learning technique widely used to discover the inherent structure of a given data set. Some existing clustering algorithms uses single prototype to represent each cluster, which may not adequately model the clusters of arbitrary shape and size and hence limit the clustering performance on complex data structure. This paper proposes a clustering algorithm to represent one cluster by multiple prototypes. The squared-error clustering is used to produce a number of prototypes to locate the regions of high density because of its low computational cost and yet good performance. A separation measure is proposed to evaluate how well two prototypes are separated. Multiple prototypes with small separations are grouped into a given number of clusters in the agglomerative method. New prototypes are iteratively added to improve the poor cluster separations. As a result, the proposed algorithm can discover the clusters of complex structure with robustness to initial settings. Experimental results on both synthetic and real data sets demonstrate the effectiveness of the proposed clustering algorithm.