Comparing two basic approaches to decorrelation transforms

Kristopher A. Innanen, Marcelo Guarido, Daniel O. Trad

Statistical decorrelation transforms map clusters of multivariate data to domains in which they are uncorrelated. In 2020 an algorithm was introduced to decorrelate deterministic optimization problems. In the approach, a given model space is re-parameterized such that a quadratic objective function defined on that space maps to one whose Hessian matrix is the unit; this procedure is immediately applicable to statistical decorrelation problems. The approach is essentially geometrical, in that involves designing the re-parameterization as a coordinate transform involving oblique-rectilinear basis vectors. In this paper the approach, which is procedurally very different from other decorrelation approaches, is investigated to understand what relationship it bears to standard methods, which are generally based on factorization algorithms. The results are suggestive that the geometric approach and its various realizations are different from existing methods, they may represent a generalization of the ZCA approach. The algorithm meanwhile may have some advantages, in that once one instance of the transform is constructed, alternate versions can be computed with little additional calculation.