Choice of Dimension Using Reversible Jump Markov Chain Monte Carlo in the Multidimensional Scaling

Abstract

Multidimensional scaling is a powerful tool for dimensionality reduction in the field of pattern recognition and data mining. Based on the bayesian multidimensional scaling (MDS), we consider the problem of determining the number of intrinsic low dimensions of MDS as a model selection problem. A Reversible Jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed for performing low-dimensional coordinate and choice of dimension simultaneously within the bayesian framework. Experiments results on simulated data and real data are presented to demonstrate the effectiveness of our RJMCMC method.