Dynamical Component Analysis (DyCA): Dimensionality Reduction For High-Dimensional Deterministic Time-Series
This method addresses dimensionality reduction in multivariate signal processing for applications like EEG analysis, but it appears incremental as it builds on existing techniques without claiming broad breakthroughs.
The authors tackled the problem of dimensionality reduction for high-dimensional deterministic time-series by proposing Dynamical Component Analysis (DyCA), which classifies underlying dynamics and identifies signal subspaces, demonstrating its application on simulated chaotic signals and real EEG data from epileptic seizures.
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.