Regularization Strategies for Hyperplane Classifiers: Application to Cancer Classification with Gene Expression Data

摘要

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 togenerate a solution that is robust in the presence of noise, these problemsrequire regularization. Here, we examine the ill-posedness involved in thelinear discrimination of cancer gene expression data with respect to outcomeand tumor subclasses. We show that a filter factor representation, based uponSingular Value Decomposition, yields insight into the numerical ill-posednessof the hyperplane-based separation when applied to gene expression data. Wealso show that this representation yields useful diagnostic tools for guidingthe selection of classifier parameters, thus leading to improved performance.