A minimax probabilistic approach to feature transformation for multi-class data

Feature transformation (FT) for dimensionality reduction has been deeply studied in the past decades. While the unsupervised FT algorithms cannot effectively utilize the discriminant information between classes in classification tasks, existing supervised FT algorithms have not yet caught up with the advances in classifier design. In this paper, based on the idea of controlling the probability of correct classification of a future test point as big as possible in the transformed feature space, a new supervised FT method called minimax probabilistic feature transformation (MPFT) is proposed for multi-class dataset. The experimental results on the UCI benchmark datasets and the high dimensional cancer gene expression datasets demonstrate that the proposed feature transformation methods are superior or competitive to several classical FT methods.