Development of an agreement metric based upon the RAND index for the evaluation of dimensionality reduction techniques, with applications to mapping customer data

Abstract

We develop a metric ψ based upon the RAND index, for the comparison and evaluation of dimensionality reduction techniques. This metric is designed to test the preservation of neighborhood structure in derived lower dimensional configurations. We use a customer information data set to show how ψ can be used to compare dimensionality reduction methods, tune method parameters, and choose solutions when methods have a local optimum problem. We show that ψ is highly negatively correlated with an alienation coefficient K that is designed to test the recovery of relative distances. In general a method with a good value of ψ also has a good value of K. However the monotonic regression used by Nonmetric MDS produces solutions with good values of ψ, but poor values of K. © Springer-Verlag Berlin Heidelberg 2007.