Robust discriminant analysis using multi-directional projection pursuit

Abstract

Abstract While linear discriminant analysis (LDA) is a widely used classification method, it is highly affected by outliers which commonly occur in various real datasets. Therefore, several robust LDA methods have been proposed. However, they either rely on robust estimation of the sample means and covariance matrix which may have noninvertible Hessians or can only handle binary classes or low dimensional cases. The proposed robust discriminant analysis is a multi-directional projection-pursuit approach which can classify multiple classes without estimating the covariance or Hessian matrix and work for high dimensional cases. The weight function effectively gives smaller weights to the points more deviant from the class center. The discriminant vectors and scoring vectors are solved by the proposed iterative algorithm. It inherits good properties of the weight function and multi-directional projection pursuit for reducing the influence of outliers on estimating the discriminant directions and producing robust classification which is less sensitive to outliers. We show that when a weight function is appropriately chosen, then the influence function is bounded and discriminant vectors and scoring vectors are both consistent as the percentage of outliers goes to zero. The experimental results show that the robust optimal scoring discriminant analysis is effective and efficient.