Universum linear discriminant analysis

Universum learning has been used for classification and clustering, and obtains favourable improvements with the help of Universum - the samples that do not belong to either class of interest. In this reported work, universum learning is extended to dimensionality reduction by incorporating it with linear discriminant analysis (LDA). However, for the C-class problem, LDA can get at most C-1 projection directions due to the rank limitation. The C-1 directions are not enough for sufficient discrimination, which has motivated the adaption of the one-against-one trick to decompose the original C-class LDA into 0.5C(C-1) binary LDA ones for getting more directions. Uiniversum learning is then introduced to each binary LDA and the method is termed as universum linear discriminant analysis (ULDA). ULDA aims to find discriminant directions by maximising the distance between two target classes and simultaneously minimising the distance between the Universum and the mean of the target classes. The experiments on UCI datasets demonstrate the advantages and effectiveness of the ULDA.