Articles | Volume 22, issue 1
https://doi.org/10.5194/npg-22-87-2015
https://doi.org/10.5194/npg-22-87-2015
Research article
 | 
03 Feb 2015
Research article |  | 03 Feb 2015

Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance

C. A. L. Pires and R. A. P. Perdigão

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Cited articles

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Almeida, L. B.: MISEP – linear and nonlinear ICA based on mutual information, J. Mach. Learn. Res., 4, 1297–1318, 2003.
Almeida, L. B.: Nonlinear Source Separation, Synthesis Lectures on Signal Processing, Morgan and Claypool Publishers, San Rafael, California (USA), 114 pp., https://doi.org/10.2200/S00016ED1V01Y200602SPR002, 2006.
Bailey, R. A.: Orthogonal partitions for designed experiments, Design Code Cryptogr., 8, 45–77, 1996.
Ball, F. K.: Energy transfer between external and internal gravity waves, J. Fluid Mech., 19, 465–478, 1964.
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Short summary
Non-Gaussian joint PDFs and Shannon negentropies allow for nonlinear correlations and synergetic interaction information among random variables. Third-order cross-cumulants (triadic correlations -- TCs) under pair-wise (total or partial) independence are maximized on projections and orthogonal rotations of the full PDF. Fourier analysis allows decomposing TCs as wave resonant triads working as non-Gaussian sources of dynamical predictability. An illustration is given in a minimal fluid model.