# The order parameter and the modified bessel function order

212 **Nonlinear discriminant analysis – projection
methods**

Stopping criterionThe 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).

6.2.4Properties

klog.n/k! 1n! 0

as *n* ! 1, then

*n*!1*L*.*gkn*/ D *L*Ł

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.