Decorrelation of Neutral Vector Variables: Theory and Applications

• Published in: IEEE transaction on neural networks and learning systems Vol. 29; no. 1; pp. 129 - 143
• Main Authors: Zhanyu Ma, Jing-Hao Xue, Leijon, Arne, Zheng-Hua Tan, Zhen Yang, Jun Guo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Correlation analysis; Covariance matrices; Data processing; Decorrelation; Dirichlet problem; Dirichlet variable; Distributed databases; Genetic transformation; Image color analysis; Independent variables; Kernel; neutral vector; neutrality; non-Gaussian; Pattern recognition; Principal component analysis; Principal components analysis; Variables
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2016.2616445

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 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.