Transformation Technique for Null Space-Based Linear Discriminant Analysis with Lagrange Method

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.