Dynamical Component Analysis (DYCA): Dimensionality Reduction for High-Dimensional Deterministic Time-Series

Abstract

Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and -for a certain type of dynamics -to a signal subspace representing the dynamics of the data. In this paper the algorithm is derived leading to a generalized eigenvalue problem of correlation matrices. The application of the DyCA on high-dimensional chaotic signals is presented both for simulated data as well as real EEG data of epileptic seizures.

Analytic Quantification of Shilnikov Chaos in Epileptic EEG Data

“…Further work will focus on the development of projection algorithms independent of choosing a set of ODEs obtained by solving a generalized eigenvalue problem as presented in Seifert et al [21].…”

Cognitive Robotics & Control

“…Note that in this case, the temporal sequences are just considered as long feature vectors, so that the temporal relation between subsequent signal measurements is not explicitly considered. However, dimensionality reduction has proven to be an effective technique in time series analysis, in which data are remarkably high dimensional [37][38][39].…”

“…Knowing the physics of a self-balancing robot [39] and aiming to solve the classic problem of the inverted pendulum, the mechanical structure of the Figure 17, designed with SolidWorks [39], is proposed to integrate and assemble the rest of the components. Different aspects of the design of this structure are considered, which are directly related to the physics of a self-balancing robot, and with it, of the inverted pendulum.…”

Dynamical Component Analysis (DYCA) and Its Application on Epileptic EEG

“…Dynamical Component Analysis (DyCA) is a recentlyproposed [7] method for dimensionality reduction of deterministic time-series and can be derived as follows. Assume, given a high-dimensional deterministic time-series q(t) ∈ R N with dynamics governed by a low-dimensional system of ordinary differential equations, the signal can be decomposed into…”

“…Presumably due to the lack of better matching techniques they are often used for dimensionality reduction of deterministic time-series even if its assumptions are not fulfilled. Recently [7] the authors proposed a new method for dimensionality reduction of deterministic time-series: dynamical component analysis (DyCA). This method relys on a determinacy assumption on the time-series.…”