Developing an automatic fuzzy clustering algorithm for point data based on the circle similarity and applying to images

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.

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.

Categorical data clustering has been attracted a lot of attention recently due to its necessary in the real-world applications. Many clustering methods have been proposed for categorical data. However, most of the existing algorithms require the predefined number of clusters which is usually unavailable in real-world problems. Only a few works focused on automatic clustering, but mainly handled for numerical data. This study develops a novel automatic fuzzy clustering using non-dominated sorting particle swarm optimization (AFC-NSPSO) algorithm for categorical data. The proposed AFC-NSPSO algorithm can automatically identify the optimal number of clusters and exploit the clustering result with the corresponding selected number of clusters. In addition, a new technique is investigated to identify the maximum number of clusters in a dataset based on the local density. To select a final solution in the first Pareto front, some internal validation indices are used. The performance of the proposed AFC-NSPSO on the real-world datasets collected from the UCI machine learning repository exhibits effectiveness compared with some other existing automatic categorical clustering algorithms. Besides, this study also applies the proposed algorithm to analyze a real-world case study with an unknown number of clusters.

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

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.

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.

Clustering is one of the relevant data mining tasks, which aims to process data sets in an effective way. This paper introduces a new clustering heuristic combining the E-transitive heuristic adapted to quantitative data and the k-means algorithm with the goal of ensuring the optimal number of clusters and the suitable initial cluster centres for k-means. The suggested heuris-tic, called PFK-means, is a parameter-free clustering algorithm since it does not require the prior initialization of the number of clusters. Thus, it generates progressively the initial cluster centres until the appropriate number of clusters is automatically detected. Moreover, this paper exposes a thorough comparison between the PFK-means heuristic, its diverse variants, the E-Transitive heuristic for clustering quantitative data and the traditional k-means in terms of the sum of squared errors and accuracy using different data sets. The experiments results reveal that, in general, the proposed heuristic and its variants provide the appropriate number of clusters for different real-world data sets and give good clusters quality related to the traditional k-means. Furthermore, the experiments conducted on synthetic data sets report the performance of this heuristic in terms of processing time.

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.

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.

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.

This paper introduces a novel hierarchical fuzzy algorithm for clustering categorical attributes, which consists of three basic design steps. It incorporates a potential-based clustering scheme with a cluster validity index into a framework that is based on the use of the weighted fuzzy c-modes. The novelty of the contribution lies in the following properties: (a) the potential-based clustering scheme reduces the dependence of the algorithm on initialization, (b) the weighted fuzzy c-modes provides flexibility in detecting the real data structure, and (c) the cluster validity index determines the appropriate number of clusters. The algorithm is applied to model (classify) cultural data related to a number of painters of the seventeenth century, where its performance is compared to the respective performance of an agglomerative hierarchical clustering algorithm.

Determination of the appropriate number of clusters is a big challenge for the bi-clustering method of the non-negative matrix factorization (NMF). The conventional determination method may be to test a number of candidates and select the optimal one with the best clustering performance. However, such strategy of repetition test is obviously time-consuming. In this paper, we propose a novel efficient algorithm called the automatic NMF clustering method with competitive sparseness constraints (autoNMF) which can perform the reasonable clustering without pre-assigning the exact number of clusters. It is demonstrated by the experiments that the autoNMF has been significantly improved on both clustering performance and computational efficiency.

Although clustering is an unsupervised learning approach, most clustering algorithms require setting several parameters (such as the number of clusters, minimum density or distance threshold) in advance to work properly. In this paper, we eliminate the necessity of setting the minimum cluster size parameter of the Randomized Gravitational Clustering algorithm proposed by Gomez et al. Basically, the minimum cluster size is estimated using a heuristic that takes in consideration the functional relation between the number of clusters and the clusters with at least a given number of points. Then a data point’s region of action (region of the space assigned to a point) is defined and a cluster refinement process is proposed in order to merge overlapping clusters. Our experimental results show that the proposed algorithm is able to deal with noise, while finding an appropriate number of clusters without requiring a manual setting of the minimum cluster size.

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.

Data clustering describes a set of frequently employed techniques in exploratory data analysis to extract "natural" group structure in data. Such groupings need to be validated to separate the signal in the data from spurious structure. In this context, finding an appropriate number of clusters is a particularly important model selection question. We introduce a measure of cluster stability to assess the validity of a cluster model. This stability measure quantifies the reproducibility of clustering solutions on a second sample, and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm. The preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters. Convincing results are achieved on simulated as well as gene expression data sets. Comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real-world problems.