Principal dynamical components

TL;DR

This paper introduces a novel dimensionality reduction method for time series that incorporates dynamical modeling, aiming to find a low-dimensional manifold that minimizes information loss while capturing the underlying dynamics.

Contribution

The paper presents a new procedure combining manifold reduction with predictive dynamical models, extending principal components to dynamical systems for time series analysis.

Findings

Effective reduction of sea-surface temperature data dimensions

Incorporation of non-autonomous and non-Markovian dynamics

Improved predictive modeling of time series

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.