DEMscale: Large scale MDS accounting for a ridge operator and demographic variables

Abstract

In this paper, a method called DEMScale is introduced for large scale MDS. DEMScale can be used to reduce MDS problems into manageable sub-problems, which are then scaled separately. The MDS items can be split into sub-problems using demographic variables in order to choose the sections of the data with optimal and sub-optimal mappings. The lower dimensional solutions from the scaled sub-problems are recombined by taking sample points from each sub-problem, scaling the sample points, and using an affine mapping with a ridge operator to map the non-sample points. DEMScale builds upon the methods of distributional scaling and FastMDS, which are used to split and recombine MDS mappings. The use of a ridge regression parameter enables DEMScale to achieve stronger solution stability than the basic distributional scaling and FastMDS techniques. The DEMScale method is general, and is independent of the MDS technique and optimization method used. © 2009 Springer Berlin Heidelberg.