212 Nonlinear discriminant analysis – projection methods
Stopping criterion The most common stopping criterion used in the nonlinear opti-misation schemes is to terminate the algorithm when the relative change in the error is less than a specified amount (or the maximum number of allowed iterations has been exceeded).
klog.n/ k ! 1 n ! 0
as n ! 1, then
n!1L.gkn/ D LŁ
with probability 1. Thus, the classification error approaches the Bayes error as the number of training samples becomes large, provided k is chosen to satisfy the conditions above. However, although this result is attractive, the problem of choosing the parameters of gkn to give minimum errors on a training set is computationally difficult.
The aim of the study is to investigate how well neural networks can approximate an optimum (Bayesian) classification. What form of preprocessing should be performed prior to network training? How should the network be constructed?
The data In terms of synthetic aperture radar imagery, a correlated K distribution pro-vides a reasonable description of natural clutter textures arising from fields and woods. However, an analytical expression for correlated multivariate K distributions is not avail-able. Therefore, the approach taken in this work is to develop methodology on simulated uncorrelated K-distributed data, before application to correlated data.