Title
A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling
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.
Year
DOI
Venue
2012
10.1016/j.jmva.2012.01.012
J. Multivariate Analysis
Keywords
Field
DocType
efficient bayesian procedure,continuous distribution,appropriate dimensionality,mcmc algorithm,mixture posterior distribution,multidimensional scaling,column vector,mcmc procedure,marginal posterior distribution,mds configuration,bayesian method,parameter space,markov chain monte carlo,mixture,data consistency,euclidean space,bayesian approach,model selection,posterior distribution
Econometrics,Multidimensional scaling,Markov chain Monte Carlo,Model selection,Posterior probability,Euclidean space,Curse of dimensionality,Estimation theory,Statistics,Mathematics,Bayesian probability
Journal
Volume
ISSN
Citations 
107,
0047-259X
1
PageRank 
References 
Authors
0.40
4
1
Name
Order
Citations
PageRank
Man-Suk Oh184.10