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

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  • Oh, Man-Suk

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.

Suggested Citation

  • Oh, Man-Suk, 2012. "A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 200-209.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:200-209
    DOI: 10.1016/j.jmva.2012.01.012
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    References listed on IDEAS

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    1. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    2. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
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    Cited by:

    1. Lin, L. & Fong, D.K.H., 2019. "Bayesian multidimensional scaling procedure with variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 1-13.

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