16 - Covariance Discriminant Analysis

Summary

This chapter discusses a procedure for quantifying differences between two covariance matrices. Despite being applicable to a range of statistical problems, the general procedure has no standard name. In this chapter, we call it Covariance Discriminant Analysis (CDA). CDA finds the linear combination of variables that maximizes the ratio of variances. More generally, CDA decomposes two multivariate time series, separately, into components ordered such that the variance ratio of the first component is maximized, and each succeeding component maximizes the variance ratio under the constraint that it is uncorrelated with the preceding components. This technique is used in numerous other multivariate techniques, including canonical correlation analysis, predictable component analysis, and multivariate ANOVA. CDA also is used to identify low-frequency components that maximize the ratio of low-frequency to high-frequency variance. To mitigate overfitting, the standard approach is to apply CDA to a few principal components. No standard criterion exists for choosing the number of principal components. A new criterion is proposed in this chapter.