Abstract:
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Bayesian approach for multidimensional scaling (MDS) models using Markov Chain Monete Carlo (MCMC) method appears to be promising alternative to the commonly used least-squared or maximum likelihood type methods, because it provides a general scheme of probabilistic inference, prediction, and model evaluation. However, MCMC estimation in MDS suffers from identification problem: the center and the direction of the configuration matrix at each iteration are arbitrary due to the rotational invariance of Euclidean distance. In this study, a new post-processing method is proposed to maximize the congruence between each MCMC samples and the average configuration. This optimization problem is solved using generalized Procrustes analysis, which is a generalization of the Procrustes rotation to more than two matrices. Efficacy of the proposed method is investigated by numerical experiments. Performance comparisons with existing methods indicate that the proposed method is effective and applicable to practical problems.
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