Minimum mean-square error transformations of categorical data to target positions

摘要

A new algorithm is described for transforming multidimensional data such that all the data points in each of several predefined categories map toward a category target position in the transformed space. The procedure is based on minimizing the mean-square error between specified category target positions and actual transformed locations of the data. Least squares estimation techniques are used to derive linear equations for computing the transformation coefficients and for determining an origin offset in the transformed space. However, for additional flexibility in the transformation, a method is presented for combining the linear transformation with a nonlinear connectionist network transformation. This procedure can, among other things, be used as a tool to evaluate the precision with which physical measurements of psychophysical stimuli correlate with the perceptual configuration of those stimuli. Potential speech science applications are identified. Experimental results illustrate some of these applications with vowel data.