Decorrelation of Neutral Vector Variables: Theory and Applications

Area of Science:

• Statistics
• Data Analysis
• Information Theory

Background:

• Conventional principal component analysis (PCA) fails to achieve mutual independence for non-multivariate-Gaussian distributed neutral vector variables.
• Decorrelation is crucial for simplifying complex datasets and improving downstream analysis.

Purpose of the Study:

• To propose and evaluate novel invertible nonlinear transformations for decorrelating neutral vector variables.
• To achieve mutual independence of scalar variables from non-Gaussian neutral vectors.

Main Methods:

• Development of two fundamental invertible transformations: serial nonlinear transformation and parallel nonlinear transformation.
• Application of these transformations to neutral vector variables, including those from Dirichlet and mixture of Dirichlet distributions.
• Verification of mutual independence using distance correlation measurements.

Main Results:

• The proposed transformations successfully decorrelate highly negatively correlated neutral vectors into mutually independent scalar variables.
• The transformed variables retain the same degrees of freedom as the original vector.
• Demonstrated effectiveness on synthesized data and in practical applications.

Conclusions:

• The novel nonlinear transformation strategies provide an effective method for achieving mutual independence in decorrelated neutral vector variables.
• These methods offer advantages over conventional techniques, particularly for non-Gaussian data distributions.