Dynamical Component Analysis (DyCA): Dimensionality Reduction For High-Dimensional Deterministic Time-Series

TL;DR

Dynamical Component Analysis (DyCA) is a novel dimensionality reduction method designed for high-dimensional deterministic time-series, enabling classification of underlying dynamics and extraction of a signal subspace, demonstrated on chaotic and EEG data.

Contribution

DyCA introduces a new approach to reduce dimensionality in deterministic time-series by formulating a generalized eigenvalue problem, improving dynamic classification.

Findings

Effective in identifying underlying dynamics in chaotic signals

Successfully applied to EEG data of epileptic seizures

Provides a signal subspace representing data dynamics

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.