Subspace Detection and Blind Source Separation of Multivariate Signals by Dynamical Component Analysis (DyCA)

The decomposition of a multivariate signal is an important tool for the analysis of measured or simulated data leading to possible detection of the relevant subspace or the sources of the signal. A new method - dynamical component analysis (DyCA) - is based on modeling the signal by a set of coupled ordinary differential equations. Its derivation and its features are presented in-depth. The corresponding algorithm is nearly as simple as principal component analysis (PCA). The results obtained by DyCA however yield a deeper insight into the underlying dynamics of the data. To illustrate the broad area of possible applications a set of examples of analyzing data by DyCA is presented - involving both measured EEG, motion and ECG data as well as data obtained from stochastic differential equations. Thereby our alternative tool for dimensionality reduction is compared to results obtained PCA and ICA and demonstrate the gain of this approach.