A Parameter-free Clustering Algorithm based K-means

Given the complexity of real-life event logs, several trace clustering techniques have been proposed to partition an event log into subsets with a lower degree of variation. In general, these techniques assume that the number of clusters is known in advance. However, this will rarely be the case in practice. Therefore, this paper presents approaches to determine the appropriate number of clusters in a trace clustering context. In order to fulfil the objective of identifying the most appropriate number of trace clusters, two approaches built on similarity are proposed: a stability- and a separation-based method. The stability-based method iteratively calculates the similarity between clustered versions of perturbed and unperturbed event logs. Alternatively, an approach based on between-cluster dissimilarity, or separation, is proposed. Regarding practical validation, both approaches are tested on multiple real-life datasets to investigate the complementarity of the different components. Our results suggest that both methods are successful in identifying an appropriate number of trace clusters.

The traditional K-means clustering algorithm has the problems that the number of clusters needs to be determined artificially, the clustering results are easily affected by the initial clustering centers and isolated points, and the iterative process is computationally complicated. To address above problems, an improved K-means clustering algorithm combining multi-point optimization(MFK-means) is proposed. The proposed algorithm is improved from the following four aspects. Firstly, the number of clusters is jointly determined by combining the contour coefficient method and the elbow rule. Secondly, the optimized outlier detection algorithm is used to exclude the influence of isolated points on the clustering results. Thirdly, the initial clustering centers are gradually determined based on the outlier candidate set and the maximum-minimum distance idea. Finally, the heuristic method is used to reduce the computational effort of the iterative process. The experimental results on the UCI dataset show that the proposed improved algorithm has higher clustering accuracy and better stability than the traditional K-means algorithm and another improved algorithm.

So far most of the K-means algorithms use the number of the labeled data as the K value, but sometimes it doesn’t work well. In this paper, we propose a semi-supervised K-means algorithm based on the global optimization. It can select an appropriate number of clusters as the K value directly and plan a great amount of supervision data by using only a small amount of the labeled data. Combining the distribution characteristics of data sets and monitoring information in each cluster after clustering, we use the voting rule to guide the cluster labeling in the data sets. The experiments indicated that the global optimization algorithm for semi-supervised K-means is quite helpful to improve the K-means algorithm, it can effectively find the best data sets for K values and clustering center and enhancing the performance of clustering.

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

Within the scope of cluster analysis of variables, the selection of the appropriate number of clusters is of paramount interest. The strategy of determination of the appropriate number of clusters adopted herein is based on a hypothesis testing approach. It consists in testing whether the variation of a partition quality criterion between two consecutive partitions is far removed from the expected variation under the null-hypothesis stipulating a lack of structure. Three hypothesis testing strategies are detailed and compared in the scope of clustering of variables: Gap, Weighted Gap and a statistic associated with CLV methodology. Finally, an illustration is presented based on data from a preference study.

Newman and Girvan [12] recently proposed an objective function for graph clustering called the Modularity function which allows automatic selection of the number of clusters. Empirically, higher values of the Modularity function have been shown to correlate well with good graph clustering. In this paper we propose an extended Modularity measure for categorical data clustering; first, we establish the connection with the Relational Analysis criterion. The proposed Modularity measure introduces an automatic weighting scheme which takes in consideration the profile of each data object. A modified Relational Analysis algorithm is then presented to search for the partitions maximizing the criterion. This algorithm deals linearly with large data set and allows natural clusters identification, i.e. doesn’t require fixing the number of clusters and size of each cluster. Experimental results indicate that the new algorithm is efficient and effective at finding both good clustering and the appropriate number of clusters across a variety of real-world data sets.

Clustering is a fundamental and widely used method for grouping similar records in one cluster and dissimilar records in the different cluster. In cluster analysis, a major problem is to determine the appropriate number of cluster in advance. It is difficult for a user (data miner) to estimate the appropriate number of clusters in advance. Another limitation of a well-known clustering technique called K-means is that it gets stuck at local optima. In order to overcome these limitations Genetic Algorithm (GA) based clustering techniques have been proposed in the 1990s. Since then many researchers have developed several evolutionary algorithm based clustering techniques, including GA and applied in various fields. This paper presents an up-to-date review of some major GA-based clustering techniques for the last twenty (20) years. A total of 45 ranked (i.e. based on citation reports and JCR/CORE rank) GA-based clustering approaches are reviewed, which are uses for real-life applications such as real-life data sets, highway construction projects, a Gas Company, cellular networks and satellite image segmentations. Almost two third of the techniques do not require any user to define the number of clusters. Finally, a thorough discussion and emerging research directions are presented.

There are some problems in the field of text clustering and particle swarm optimization (PSO) technology, for example, the researchers need to determine the appropriate number of clusters before clustering, the clustering results are sensitive to the initial cluster center, and the PSO algorithm has precocious convergence and easy to fall into local optimality defects. We propose a dynamic topology adaptive PSO (DTA-PSO) algorithm that combines the K-means algorithm PSO to realize automatic text clustering. In DTA-PSO, we adopt an improved comprehensive dynamic learning strategy from social group experience the source of the social experience of the particle group is not only the particle with the best performance among all its neighbors, according to the performance of all its neighbors and the relative position with the particle, the target position is calculated in the next iteration. We choose three data sets in the knowledge base of the machine learning open data set and part of the Chinese corpus of Fudan University. Many experiments are carried out on the automatic cluster of DTA-PSO, the text automatic clustering algorithm has a certain improvement on the K value determination and the clustering effect by the contrast analysis.

Clustering is a widely used technique in data mining applications and various pattern recognition applications, in which data objects are divided into groups. K-means algorithm is one of the most classical clustering algorithms. In this algorithm, the initial clustering centers are randomly selected, this results in unstable clustering results. To solve this problem, an optimized algorithm to select the initial centers is proposed. In the proposed algorithm, dispersion degree is defined, which is based on entropy. In the algorithm, all the objects are firstly grouped into a big cluster, and the object that has the maximum dispersion degree and the object that has the minimum dispersion degree are selected as the initial clustering centers from the initial big cluster. And then other objects in the biggest cluster are partitioned to the initial clusters to which the objects are nearest. The partition process will be repeated until the cluster number is equal to the specified value k. Finally, the partitioned k clusters and their cluster centers are applied to k-means algorithm as initial clusters and centers. Several experiments are conducted on real data sets to evaluate the proposed algorithm. The proposed algorithm is compared with traditional k-means algorithm and max-min distance clustering algorithm, and experimental results show that the improved k-means algorithm is stable in selecting initial clustering, because it can select unique initial clustering centers. The optimized algorithm’s effectiveness and feasibility are also verified by experiments, and the algorithm can reduce the times of iterations and has more stable clustering results and higher accuracy.

We propose a new principal component analysis (PCA) for interval-valued data by using a covariance involving a fuzzy classification structure based on dissimilarity in higher dimensional space in which objects exist. The covariance for interval-valued data is obtained adaptively by evaluating the validity of the fuzzy classification structure based on the selection of an appropriate number of clusters. In order to select an appropriate number of clusters, we propose an alignment criterion to evaluate the obtained classification structure and prove the concentration of the criterion around the expected value with respect to variation of similarity among clusters. The merit of this PCA is to consider not only the projection of objects to a lower dimensional space, but also the dissimilarity of objects in a higher dimensional space by using a weighted covariance matrix. The weight is estimated as the degree of contribution for the fuzzy classification structure based on dissimilarity of objects in the higher dimensional space. A numerical example of interval-valued data consisting of human based subjective decisions shows a better performance when compared with a result of an ordinary PCA.

In order to overcome the dimension problem of the traditional fuzzy clustering, we use kernel-based fuzzy c-means clustering (KFCM) to construct first-order TSK fuzzy models. The proposed algorithm is composed of two phases. In the first phase, the antecedent fuzzy sets are obtained by KFCM. We present the expression of the cluster prototypes of KFCM with different kernel functions in original input space. The use of cluster validity indices is a standard approach to determine an appropriate number of clusters in a data set. However, cluster validity index demands running the clustering algorithm for different number of clusters repeatedly. Therefore, a novel method specifying the number of clusters automatically is given for the purpose of reducing the computational complexity and eliminating the outliers. In the second phase, the consequent parameters can be identified by the least squares method. Experiment results show that the proposed method improves the generalization ability and robustness of fuzzy models compared with the traditional techniques.

The study of good governance over the past two decades has been at the forefront of the world's scientific and international circles, especially in developing countries. The purpose of this study is to evaluate the status of countries based on good governance and determine the ranking of Iran among other countries, using clustering techniques. In order to select an appropriate clustering method and the appropriate number of clusters, the Silhouette coefficient for each K-Means, Two Step and Kohonen method was calculated for the number of different clusters of each. Based on an assessment of these findings, the K-Means 12 cluster method was selected. The research findings show that, among the four countries of the world having common clusters with Iran in terms of the level of human development, Iran ranks among the 'Lowlevel developing countries' and 'Moderate developing countries'. This issue highlights the importance of improving the level of good governance indicators in the country in order to achieve a higher level of development.

In this paper, a new multi-objective (MO) fuzzy-clustering technique is developed for unsupervised land-cover classification in remote-sensing images. This technique automatically partitions the pixels in the spectral domain into several clusters. The new MO clustering algorithm uses the newly developed simulated-annealing-based multi-objective optimization technique (AMOSA) as the underlying optimization strategy. Centre-based cluster encoding is used. Each cluster is divided into several small hyperspherical sub-clusters, and the centres of all these small sub-clusters are encoded in a string to represent the whole cluster. For membership-value computation of points to different clusters, these sub-clusters are considered individually. However, for the purpose of objective-function evaluation, these sub-clusters are merged appropriately to form some variable number of whole clusters. Three objective functions, one reflecting the total compactness of the partitioning based on the Euclidean distance, one reflecting the total point-symmetrical compactness of the obtained partitioning and one reflecting the total line-symmetrical compactness of the obtained partitioning are considered here. These are optimized simultaneously using AMOSA in order to detect the appropriate number of clusters and the appropriate partitioning from remote-sensing image datasets. The point symmetry present in a particular partitioning is measured using a newly developed point-symmetry-based distance, whereas the line symmetry present in a particular partitioning is measured using a newly developed line-symmetry-based distance. Since AMOSA, as well as any other MO optimization technique, provides a set of Pareto-optimal solutions, a new method is also developed to determine a single solution from this set. Different land-cover regions in remote-sensing imagery have been classified using the proposed technique to establish its efficiency. Results are compared with those obtained by fuzzy C-means (FCM) clustering technique and a recently developed symmetry-based automatic clustering technique, the variable string length genetic point symmetry (VGAPS) technique, both qualitatively and quantitatively. Qualitative comparisons are also carried out with the segmentation results obtained by the mean-shift-based segmentation technique.

Data mining techniques are used to extract useful patterns from a large data set. k-mean algorithm is one of the most famous partitioning clustering algorithm. But, Euclidean distance is sensitive to outliers and is suitable to only numeric values. Real time datasets have mixed attribute values, missing values and measurements are not in the standard format.The proposed algorithm extends the ability of the kmean algorithm to use a mixed simil arity measure to find the similarity between data objects for clustering mixed datasets.For imp uting missing values, correlation based data imputation is used.In addition, k-mean output depends on the initial cluster centre and local optima suffers from the number of clusters(k). In order to improve the efficiency of the k-mean algorithm, Artificial Bee Colony Optimization (ABC) based clustering algorithm is suggested. ABC is successful at exploring the search space, but endures in leveraging the search space. Collaborative search is used to amplify the search quality of bees to amplify the search quality of bees employees. To determine the number of clusters for the given data set, the Elbow method is used. In order to evaluate the outcome of the proposed algorithm, real time datasets are used. The results showed that the proposed method performs well compared to comparative algorithms.

One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modelling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP-MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modelling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.