Using Support Vector Machines for Facet Partitioning in Multidimensional Scaling

Abstract

In this article we focus on interpreting multidimensional scaling (MDS) configurations using facet theory. The facet theory approach is attempting to partition a representational space, facet by facet, into regions with certain simplifying constraints on the regions’ boundaries (e.g., concentric circular sub-spaces). A long-standing problem has been the lack of computational methods for optimal facet-based partitioning. We propose using support vector machines (SVM) to perform this task. SVM is highly attractive for this purpose as they allow for linear as well as nonlinear classification boundaries in any dimensionality. Using various classical examples from the facet theory literature we elaborate on the combined use of MDS and SVM for facet-based partitioning. Different types of MDS are discussed, and options for SVM kernel specification, tuning, and performance evaluation are illustrated.