Robust Estimation for Fisher Discriminant Analysis

Fisher Linear Discriminant Analysis (LDA) is a well-known classification method, but it is also well-known for not being robust against outliers. This paper investigates the uses of two methods for data classification including outliers. One method alleviates data sensitivity by incorporating data uncertainty and subsequently optimizes the worst-case scenario of the Fisher discriminant ratio, which appears to be ineffective. The use of the second method does seem to be effective. It directly attempts to remove outliers by removing those points that lie furthest from the sample mean in the Mahalanobis distance sense. Additionally, this paper provides a proof for a general tolerance ellipsoid for multivariate normally distributed data which is used in the second method. This technique is also well-known and a rather obvious one, yet most papers do not provide a general proof for this concept.