Principal dynamical components

Details Principal dynamical components Principal dynamical components

2010-12-17

arxiv.org/abs/1012.3963v1

Mathematics

Statistics Theory

29 pages, 14 figures

Scientific paper

A new procedure is proposed for the dimensional reduction of time series. Similarly to principal components, the procedure seeks a low-dimensional manifold that minimizes information loss. Unlike principal components, however, the new procedure involves dynamical considerations, through the proposal of a predictive dynamical model in the reduced manifold. Hence the minimization of the uncertainty is not only over the choice of a reduced manifold, as in principal components, but also over the parameters of the dynamical model. Further generalizations are provided to non-autonomous and non-Markovian scenarios, which are then applied to historical sea-surface temperature data.

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