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A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling

Title
A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling
Authors
Oh M.-S.
Ewha Authors
오만숙
SCOPUS Author ID
오만숙scopus
Issue Date
2012
Journal Title
Journal of Multivariate Analysis
ISSN
0047-259XJCR Link
Citation
vol. 107, pp. 200 - 209
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Multidimensional scaling (MDS) is a technique which retrieves the locations of objects in a Euclidean space (the object configuration) from data consisting of the dissimilarities between pairs of objects. An important issue in MDS is finding an appropriate dimensionality underlying these dissimilarities. In this paper, we propose a simple and efficient Bayesian approach for selecting dimensionality in MDS. For each column (attribute) vector of an MDS configuration, we assume a prior that is a mixture of the point mass at 0 and a continuous distribution for the rest of the parameter space. Then the marginal posterior distribution of each column vector is also a mixture of the same form, in which the mixing weight of the continuous distribution is a measure of significance for the column vector. We propose an efficient Markov chain Monte Carlo (MCMC) method for estimating the mixture posterior distribution.The proposed method is fully Bayesian. It takes parameter estimation error into account when computing penalties for complex models and provides an uncertainty measure for the choice of dimensionality. Also, the MCMC algorithm is computationally very efficient since it visits various dimensional models in one MCMC procedure. A simulation study compares the proposed method with the Bayesian method of Oh and Raftery (2001). Three real data sets are analysed by using the proposed method. © 2012 Elsevier Inc.
DOI
10.1016/j.jmva.2012.01.012
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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