Visualization and self-organization of multidimensional data through equalized orthogonal mapping

A new approach to dimension-reduction mapping: of multidimensional pattern data is presented. The motivation for this work is to provide a computation ally efficient method for visualizing large bodies of complex multidimensio nal data as a relatively "topologically correct" lower dimensional approxim ation. Examples of the use of this approach in obtaining meaningful two-dim ensional (2-D) maps and comparisons with those obtained by the self-organiz ing map (SOM) and the neural-net implementation of Sammon's approach are al so presented and discussed. In this method, the mapping equalizes and ortho gonalizes the lower dimensional outputs by reducing the covariance matrix o f the outputs to the form of a constant times the identity matrix. This new method is computationally efficient and "topologically correct" in interes ting and useful ways.