Decorrelation of Neutral Vector Variables: Theory and Applications

TL;DR

This paper introduces novel invertible transformations for decorrelating neutral vector variables, enabling the conversion of negatively correlated vectors into mutually independent scalar variables, with applications demonstrated on Dirichlet-distributed data.

Contribution

The paper proposes two new invertible nonlinear transformations for decorrelating neutral vector variables, addressing limitations of PCA for non-Gaussian distributions.

Findings

Transformations achieve mutual independence verified by distance correlation

Effective decorrelation demonstrated on Dirichlet and mixture distributions

Enhanced data processing for non-Gaussian neutral vectors

Abstract

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations.