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

An approach to dimension-reduction mapping of multidimensional pattern data is presented. The motivation for this work is to provide a computationally efficient method for visualizing large bodies of complex multidimensional data as a relatively "topologically correct" lower dimensional approximation. Examples of the use of this approach in obtaining meaningful two-dimensional (2-D) maps and comparisons with those obtained by the self-organizing map (SOM) and the neural-net implementation of Sammon's approach are also presented and discussed. In this method, the mapping equalizes and orthogonalizes the lower dimensional outputs by reducing the covariance matrix of the outputs to the form of a constant times the identity matrix. This new method is computationally efficient and "topologically correct" in interesting and useful ways.