The linear discriminant analysis (LDA), aiming at maximizing the ratio of the betweenclass
distance to the within-class distance of data, is one of the most fundamental and
powerful feature extraction methods. The LDA has been successfully applied in many
applications such as facial recognition, text recognition, and image retrieval. However,
due to the singularity of the within-class scatter, the LDA becomes ill-posed for small
sample size (SSS) problems where the dimension of data is larger than the number of data.
To extend the applicability of LDA in SSS problems, the null space-based LDA (NLDA)
was proposed as an extension of the LDA. The NLDA has been shown in the literature to
provide a good discriminant performance for SSS problems: Yet, as the original scheme
for the feature extractor (FE) of the NLDA suffers from a complexity burden, a number
of modified schemes based on QR factorization and eigen-decomposition have since been
proposed for complexity reduction. In this dissertation, by transforming the problem of
finding the FE of the NLDA into a linear equation problem, a novel scheme is derived,
offering a further reduction of the complexity.