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One of the most popular clustering techniques is the k-means clustering algorithm. However, the utilization of the k-means is severely limited by its high computational complexity. In this study, we propose a new strategy to accelerate the k-means clustering algorithm through the Partial Distance (PD) logic. The proposed strategy avoids many unnecessary distance calculations by applying efficient PD strategy. Experiments show the efficiency of the proposed strategy when applied to different data sets. Clustering, k-means algorithm, pattern recognition, partial distance, INTRODUCTION Clustering techniques have become very popular in a number of areas, such as engineering, medicine, biology and data mining (1), (2). A good survey on clustering algorithms can be [...]

We consider the problem of variable or feature selection for model-based clustering. The problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate Bayes factors. A greedy search algorithm is proposed for finding a local optimum in model space. The resulting method selects variables (or features), the number of clusters, and the clustering model simultaneously. We applied the method to several simulated and real examples and found that removing irrelevant variables often improved performance. Compared with methods based on all of the variables, our variable selection method consistently yielded more accurate estimates of the number of groups and lower classification error rates, as well as more parsimonious clustering models and easier visualization of results. KEY WORDS: Bayes factor; BIC; Feature selection; Model-based clustering; Unsupervised learning; Variable selection.

Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates (p [much greater than] n). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a multivariate normal mixture model with an unknown number of components and use the reversible-jump Markov chain Monte Carlo technique to define a sampler that moves between different dimensional spaces. We handle the problem of selecting a few predictors among the prohibitively vast number of variable subsets by introducing a binary exclusion/inclusion latent vector, which gets updated via stochastic search techniques. We specify conjugate priors and exploit the conjugacy by integrating out some of the parameters. We describe strategies for posterior inference and explore the performance of the methodology with simulated and real datasets. KEY WORDS: Bayesian variable selection; Bayesian clustering; Label switching; Reversible-jump Markov chain Monte Carlo.

1. OVERVIEW It is truly a delight for us to read the inspirational work by Morris, Vannucci, Brown, and Carroll (abbreviated as MVBC hereafter). To the best of our knowledge, [...]

A new approach for the defuzzification process, based on the Most Typical Value (MTV) concept, is being introduced and investigated. It assumes that the single decision, based on the output fuzzy subset, should represent a typical value of this set, rather than a numerical "central tendency" of its elements. The MTV defuzzification method is compared with previous defuzzification procedures and its applicability is illustrated. Index Terms - Defuzzification, fuzzy set theory, fuzzy systems, most typical value, typicality theory.

In this paper, we discuss a fuzzy classifier with ellipsoidal regions that dynamically generates clusters. First, for the data belonging to a class we define a fuzzy rule with an ellipsoidal region. Namely, using the training data for each class, we calculate the center and the covariance matrix of the ellipsoidal region for the class. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. Then if the number of the data belonging to a class that are misclassified into another class exceeds a prescribed number, we define a new cluster to which those data belong and the associated fuzzy rule. Then we tune the newly defined fuzzy rules in the similar way as stated above, fixing the already obtained fuzzy rules. We iterate generation of clusters and tuning of the newly generated fuzzy rules until the number of the data belonging to a class that are misclassified into another class does not exceed the prescribed number. We evaluate our method using thyroid data, Japanese Hiragana data of vehicle license plates, and blood cell data. By dynamic cluster generation, the generalization ability of the classifier is improved and the recognition rate of the fuzzy classifier for the test data is the best among the neural network classifiers and other fuzzy classifiers if there are no discrete input variables. Index Terms - Blood cell data, cluster generation, fuzzy classifiers, license plate recognition, membership function, neural networks, rule extraction, thyroid data, tuning.

An efficient multidimensional extension to Belkhale and Banerjee's Quad algorithm for connected component labeling is described. The technique deals with abstract spatial connectivity information and considerably simplifies implementations in more than two dimensions. Two optimizations to the basic algorithm that effectively exploit locality in Ising model cluster configurations are introduced. Results indicate that the optimizations are critical in more than two dimensions where the surface area-to-volume ratio is high.

Experimentation with a support vector (SV) machine, a classical radial basis function (RBF) with a Gaussian kernel and a hybrid system revealed that the SV machine provides a foundation for a superior and practical application. Testing on the US postal service database of handwritten digits show that SV delivers lower error rates that k-means and allows a training error of zero. Data show that SV centers are chosen for the classification task while k-means does not choose centers that make the problem separable.

The concept of polarization is profoundly different from the concept of inequality. The importance of this polarization concept lies in its intimate relationship with the rise of social tensions, the occurence of revolution as a result of these tensions and the recurrence of social unrest if such polarization goes unresolved. A theory for measuring degrees of polarization is proposed and applications for the study of income and wealth distribution are discussed.

Dave's version of fuzzy c-shells is an iterative clustering algorithm which requires the application of Newton's method or a similar general optimization technique at each half step in any sequence of iterates for minimizing the associated objective function. An important computational question concerns the accuracy of the solution required at each half step within the overall iteration. This note applies the general convergence theory for grouped coordinate minimization to this question to show that numerically exact solution of the half-step subproblems in Dave's algorithm is not necessary. We show that one iteration of Newton's method in each coordinate minimization half step yields a sequence of iterates with the same local convergence properties as sequences obtained using the fuzzy c-shells algorithm with numerically exact coordinate minimization at each half step. Finally, we show that fuzzy c-shells generates hyperspherical prototypes to the clusters it finds for certain special cases of the measure of dissimilarity used.

Several generalizations of the fuzzy c-shells (FCS) algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells. An earlier generalization, called the adaptive fuzzy c-shells (AFCS) algorithm, is examined in detail, and is found to have global convergence problems when the shapes to be detected are partial. New formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the AFCS algorithm. The resulting algorithm, called the AFCS-U algorithm, is shown to perform better for partial shapes. Another formulation is also considered, which is based on the second-order quadrics equation, resulting in a linear system of equations. These algorithms are shown to be able to detect ellipses and circles in two - dimensional data. Their performance is compared with the Hough transform (HT) based methods for ellipse detection. Existing HT-based methods for ellipse detection are evaluated, and a multistage method incorporating the good features of all the methods is used for comparison. It is demonstrated through numerical examples of real image data that the AFCS algorithm requires less memory than the HT based methods, and it is at least an order of magnitude faster than the HT approach. It is also shown that the use of fuzzy memberships improves the ability to attain global optima compared with the use of hard memberships.

The fuzzy c spherical shells (FCSS) algorithm is specially designed to search for clusters that can be described by circular arcs or, more generally, by shells of hyperspheres. In this paper, a new approach to the FCSS algorithm is presented. This algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose. An unsupervised algorithm which automatically finds the optimum number of clusters is also proposed. This algorithm can be used when the number of clusters is not known. It uses a cluster validity measure to identify good clusters, merges all compatible clusters, and eliminates spurious clusters to achieve the final result. Experimental results on several data sets are presented.

Byline: Elisabeth T. Pereira, Antonio Jorge Fernandes This study examines the cluster concept and the importance of developing clusters to obtain and sustain competitive advantages, either as a regional competitive factor or to the level of industrial competitiveness.

The implementation on a graph of the maximin power clustering criterion to partition observations into groups of near replicates has been studied. The graph is specified on the predictor settings r(sub i), where i = 1, .... n. A procedure has also been developed for determining the collection of candidate groupings to which the maximin criterion can be used. The criterion chooses near replicate clusters for use with Christensen's tests for orthogonal between and within cluster of lack of fit., 1. INTRODUCTION One of the most important aspects of a regression analysis is determining departure from a proposed model. Failure to do so can result in incorrect conclusions about the [...]