Bayesian Multidimensional Scaling and Choice of Dimension

Abstract

Multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects. We deal with two major problems in metric multidimensional scaling–configuration of objects and determination of the dimension of object configuration–within a Bayesian framework. A Markov chain Monte Carlo algorithm is proposed for object configuration, along with a simple Bayesian criterion, called MDSIC, for choosing their dimension. Simulation results are presented, as are real data. Our method provides better results than does classical multidimensional scaling and ALSCAL for object configuration, and MDSIC seems to work well for dimension choice in the examples considered.

KEY WORDS:

• Clustering
• Dimensionality
• Dissimilarity
• Markov chain Monte Carlo
• Metric scaling
• Model selection