Decomposing data sets into skewness modes

Details Decomposing data sets into skewness modes Decomposing data sets into skewness modes

2009-08-24

arxiv.org/abs/0908.3400v1

Physica D, 239 (2010), 1503-1508

Physics

Data Analysis, Statistics and Probability

Submitted for publication, 12 pages, 4 figures

Scientific paper

10.1016/j.physd.2010.01.024

We derive the nonlinear equations satisfied by the coefficients of linear combinations that maximize their skewness when their variance is constrained to take a specific value. In order to numerically solve these nonlinear equations we develop a gradient-type flow that preserves the constraint. In combination with the Karhunen-Lo\`eve decomposition this leads to a set of orthogonal modes with maximal skewness. For illustration purposes we apply these techniques to atmospheric data; in this case the maximal-skewness modes correspond to strongly localized atmospheric flows. We show how these ideas can be extended, for example to maximal-flatness modes.

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