Sigma-pi implementation of a Gaussian classifier

In practical pattern-recognition applications, the Gaussian classifier is often suboptimal because some features are non-Gaussian or even discrete valued, the class statistics are only estimated, and the covariance matrix inversions can be ill-conditioned. The authors presently deal with these problems by mapping the Gaussian classifier to a sigma-pi neural network, to which it is isomorphic. Back-propagation learning is then used to improve classifier performance. This approach is applied to the problem of hand-printed numeral recognition and to the problem of image texture classification. For both problems, significant improvement in classification error percentages is observed for the training data and the testing data, and weights due to the mapping procedure are found to be better than purely random initial weights