Dynamical Component Analysis (DYCA): Dimensionality Reduction for High-Dimensional Deterministic Time-Series
Authors:
- 1 September 2018
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-6
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.Keywords
All Related Versions
This publication has 11 references indexed in Scilit:
- Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing ApproachPhysical Review Letters, 2018
- Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from dataChaos: An Interdisciplinary Journal of Nonlinear Science, 2017
- Time-Series Dimensionality Reduction via Granger CausalityIEEE Signal Processing Letters, 2012
- Dimension Reduction in Multivariate Time Series2007
- Chaos via Shilnikov’s Saddle-Node Bifurcation in a Theory of the ElectroencephalogramPhysical Review Letters, 2006
- Independent component analysis: algorithms and applicationsNeural Networks, 2000
- Spatio-temporal analysis of human electroencephalograms: Petit-mal epilepsyPhysica D: Nonlinear Phenomena, 1996
- PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patternsJournal of Geophysical Research: Atmospheres, 1988
- An equation for continuous chaosPhysics Letters A, 1976
- LIII. On lines and planes of closest fit to systems of points in spaceJournal of Computers in Education, 1901