A dimensionality reduction technique based on a least squared error criterion

A method of achieving dimensionality reduction is presented. The reduced dimensionality is achieved by utilizing a least squared error technique under the assumption that the goodness criterion is the maximum separation of classes. The criterion is met by first maximizing the spread of the cluster centers, and then minimizing the within class scatter. The derivation of the desired transformation from an arbitrary p-space to a space of lower dimension, say l, is completed with the assumption that the cluster centers are known. The criterion for the cluster center location is the minimization of the variance of the distance between the cluster center and the transformed pattern. It is demonstrated that the resulting cluster center set is similar to the simplex signal set in communication theory, which is a minimum energy signal set.