Polynomial whitening for high-dimensional data

Abstract The inverse square root of a covariance matrix is often desirable for performing data whitening in the process applying many common multivariate analysis methods. Direct calculation not available when either singular or nearly singular, as occurs high dimensions. We develop new methods, which we broadly call polynomial , to construct low-degree empirical has similar properties true (should it exist). Our method does suffer near-singular settings, and computationally tractable demonstrate that our construction polynomials provides good substitute high-dimensional matrices, both $$d < N$$ d < N \ge ≥ cases. offer examples on whitening, outlier detection principal component performance proposed method.