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Decorrelation of Neutral Vector Variables: Theory and Applications

Ma, Z; Xue, J-H; Leijon, A; Tan, Z-H; Yang, Z; Guo, J; (2016) Decorrelation of Neutral Vector Variables: Theory and Applications. IEEE Transactions on Neural Networks and Learning Systems 10.1109/TNNLS.2016.2616445. (In press). Green open access

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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 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.

Type: Article
Title: Decorrelation of Neutral Vector Variables: Theory and Applications
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TNNLS.2016.2616445
Publisher version: http://dx.doi.org/10.1109/TNNLS.2016.2616445
Language: English
Additional information: Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Keywords: Decorrelation, Principal component analysis, Kernel, Distributed databases, Image color analysis, Covariance matrices, Pattern recognition, non-Gaussian, Decorrelation, Dirichlet variable, neutral vector, neutrality
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1524856
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