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.

Published in Proc. 2018 IEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING; 7 figures; Corrected formula (16)

References in corpus (4)

• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Data-driven model reduction and transfer operator approximation
• Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography
• Dimensionality reduction for time series data

Cited by in corpus (2)

• Dynamical Component Analysis (DyCA) and its application on epileptic EEG
• Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis