  Linear discrimination, from the point of view of numerical linear algebra,
can be treated as solving an ill-posed system of linear equations. In order to
generate a solution that is robust in the presence of noise, these problems
require regularization. Here, we examine the ill-posedness involved in the
linear discrimination of cancer gene expression data with respect to outcome
and tumor subclasses. We show that a filter factor representation, based upon
Singular Value Decomposition, yields insight into the numerical ill-posedness
of the hyperplane-based separation when applied to gene expression data. We
also show that this representation yields useful diagnostic tools for guiding
the selection of classifier parameters, thus leading to improved performance.
