Representative null space LDA for discriminative dimensionality reduction

Abstract Null space Linear Discriminant Analysis (NLDA) was proposed twenty years ago to overcome the singularity problem of LDA in practical applications. With two decades of technique development, many Discriminative Dimensionality Reduction (DDR) methods that outperform NLDA have been proposed. This paper provides new insight into NLDA and illustrates that NLDA is much more powerful after solving its inherent problem. The main problem of NLDA is the intrinsic overfitting problem. An ideal NLDA model is proposed to analyze its overfitting problem. Based on the ideal NLDA model, a more reasonable Representative NLDA (RNLDA) method is proposed to prevent overfitting. Two simple but efficient RNLDA algorithms are proposed to implement the RNLDA method with a theoretical proof. This study theoretically analyzed and indicated that applying the classical but simple hold-out pretraining method can automatically set the only parameter to achieve high performance. Extensive experiments with eight databases demonstrate the superior performance of the RNLDA method over state-of-the-art DDR methods.