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