Margin Based Dimensionality Reduction and Generalization

ABSTRACT

Linear discriminant analysis (LDA) for dimension reduction has been applied to a wide variety of problems such as face recognition. However, it has a major computational difficulty when the number of dimensions is greater than the sample size. In this paper, we propose a margin based criterion for linear dimension reduction that addresses the above problem associated with LDA. We establish an error bound for our proposed technique by showing its relation to least squares regression. In addition, there are well established numerical procedures such as semi-definite programming for optimizing the proposed criterion. We demonstrate the efficacy of our proposal and compare it against other competing techniques using a number of examples.

Keywords:

Dimensionality reduction, linear discriminent analysis, Margin criterion, semi-definite programming, Small sample size problem.