• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.343-352
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• 2000

In this study. the author proposes a nonhierarchical clustering method. called the "Double K-Means Clustering", which performs clustering of multivariate observations with the following algorithm: Step I: Carry out the ordinary K-means clmitering and obtain k temporary clusters with sizes $n_1$,... , $n_k$, centroids $c_$1,..., $c_k$ and pooled covariance matrix S. $\bullet$ Step II-I: Allocate the observation x, to the cluster F if it satisfies ..... where N is the total number of observations, for -i = 1, . ,N. $\bullet$ Step II-2: Update cluster sizes $n_1$,... , $n_k$, centroids $c_$1,..., $c_k$ and pooled covariance matrix S. $\bullet$ Step II-3: Repeat Steps II-I and II-2 until the change becomes negligible. The double K-means clustering is nearly "optimal" under the mixture of k multivariate normal distributions with the common covariance matrix. Also, it is nearly affine invariant, with the data-analytic implication that variable standardizations are not that required. The method is numerically demonstrated on Fisher's iris data.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• Korean Journal of Remote Sensing
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• v.1 no.1
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• pp.5-27
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• 1985

A hill-sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimates of sample data for the first step of iterative unsupervised classification. The underlying assumption in this approach was that each cluster possessed a unimodal normal distribution. The key idea was that a clustering function proposed could distinguish elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill-sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with Landsat multispectral scanner (MSS) data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill-sliding clustering technique developed herein has the potential applicability to decomposition of any multivariate mixture distribution into a number of unimodal distributions when an appropriate diatribution function to the data set is employed.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.9-14
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• 2003

A Bayesian model-based clustering method is proposed for clustering objects on the basis of dissimilarites. This combines two basic ideas. The first is that tile objects have latent positions in a Euclidean space, and that the observed dissimilarities are measurements of the Euclidean distances with error. The second idea is that the latent positions are generated from a mixture of multivariate normal distributions, each one corresponding to a cluster. We estimate the resulting model in a Bayesian way using Markov chain Monte Carlo. The method carries out multidimensional scaling and model-based clustering simultaneously, and yields good object configurations and good clustering results with reasonable measures of clustering uncertainties. In the examples we studied, the clustering results based on low-dimensional configurations were almost as good as those based on high-dimensional ones. Thus tile method can be used as a tool for dimension reduction when clustering high-dimensional objects, which may be useful especially for visual inspection of clusters. We also propose a Bayesian criterion for choosing the dimension of the object configuration and the number of clusters simultaneously. This is easy to compute and works reasonably well in simulations and real examples.