Power linear discriminant analysis

Dimensionality reduction is one of the important preprocessing steps to handle high-dimensional data. Linear discriminant analysis (LDA) is a classical and popular approach for this purpose. LDA finds an optimal linear transformation, which maximizes the ratio of the variance in the between-class distance to the variance in the within-class distance. On the other hand, in order to overcome the limitation in LDA resulting from the assumption of equal covariance, several heteroscedastic extensions, such as heteroscedastic discriminant analysis (HDA), have been proposed. However, it is difficult to find one particular criterion suitable for any kind of data set in carrying out dimensionality reduction while preserving discriminative information. In this paper, we propose a new generalized framework which we call power linear discriminant analysis (PLDA). PLDA can describe various criteria including LDA and HDA with one parameter. Numerical results show that the PLDA is effective for various data sets.