Principal dynamical components
Statistics Theory
2010-12-20 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.1012.3963,
title = {Principal dynamical components},
author = {Manuel D. de la Iglesia and Esteban G. Tabak},
journal= {arXiv preprint arXiv:1012.3963},
year = {2010}
}
Comments
29 pages, 14 figures