Abstract: In this paper, we propose a scale invariant linear discriminant analysis classifier for high-dimensional data with dense signals. The method is valid for both cases that the data dimension is smaller or greater than the sample size. Based on recent advances of the sample correlation matrix in random matrix theory, we derive the asymptotic limits of the error rate which characterizes the influences of the data dimension and the tuning parameter. The major advantage of our proposed classifier is scale invariant and it is applicable to any variances of the feature. Several numerical studies are investigated and our proposed classifier performs favorably in comparison to some existing methods.

Key words and phrases: Dimension effect, discriminant analysis, random matrix theory, sample correlation matrix, scale invariant.