Localized linear discriminant analysis

Abstract

Despite its age, the Linear Discriminant Analysis performs well even in situations where the underlying premises like normally distributed data with constant covariance matrices over all classes are not met. It is, however, a global technique that does not regard the nature of an individual observation to be classified. By weighting each training observation according to its distance to the observation of interest, a global classifier can be transformed into an observation specific approach. So far, this has been done for logistic discrimination. By using LDA instead, the computation of the local classifier is much simpler. Moreover, it is ready for applications in multi-class situations.