Multidimensional analysis of complex structure: Mixtures of class and quantitative variation

For certain kinds of structure consisting of quantitative dimensions superimposed on a discrete class structure, spatial representations can be viewed as being composed of two subspaces, the first of which reveals the discrete classes as isolated clusters and the second of which contains variation along the quantitative attributes. A numerical method is presented for rotating a multi-dimensional configuration or factor solution so that the first few axes span the space of classes and the remaining axes span the space of quantitative variation. The use of this method is then illustrated in the analysis of some experimental data.The author is particulary indebted to Dr. W. S. Torgerson for many valuable suggestions. In addition, Mr. M. David Todd and Mr. Joseph Young provided technical assistance in developing several assembly language routines, and Dr. James E. Deese made a number of helpful comments. This research was undertaken in partial fulfillment of the doctoral requirements at Johns Hopkins University, and was financed in part by the National Science Foundation.