Linear discriminant analysis with spectral regularization

Abstract

Linear discriminant analysis (LDA) is a popular technique that works for both dimensionality reduction and classification. However, LDA faces the problem of small sample size in dealing with high dimensional data. Several approaches have been proposed to overcome this issue, but the resulting transformation matrix fails to extract shared structures among data samples. In this paper, we propose trace norm regularized LDA that not only tackles the problem of small sample size but also uncover the underlying structures between target classes. Specifically, our formulation characterizes the intrinsic dimensionality of a transformation matrix owing to the appealing property of trace norm. Evaluations over nine real data sets deliver the effectiveness of our algorithm.