University of Washington - Department of Statistics
Multidimensional scaling is widely used to handle data which consist of dissimilarity measures between pairs of objects or people, and consists of estimating an object configuration in Euclidean space such that the estimated distances are related to the dissimilarities. Problems of this kind are pervasive in psychology and social science, and have arisen recently in areas such as document clustering, classification of Web sites, gene expression data, and datamining. One major practical problem in MDS to which only ad hoc solutions seem to be available is that of choosing the dimension of the space. 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 for choosing their dimension, called MDSIC. Simulation results are presented, as well as examples on real data. We compare our method to standard MDS methods: classical MDS (the only one available in Splus), and ALSCAL (available in SAS and SPSS). The method appears to perform well for estimating the object configuration, and also seems to work well for dimension choice in the examples considered.
This is joint work with Man-Suk Oh, Ewha Women's University, Seoul, Korea.