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

Abstract

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 toresults obtained PCA and ICA and demonstrate the gain of this approach.

Source Detection With Multi-Label Classification

“…We live in an increasingly connected environment fueled by hand held devices, household appliances, autonomous vehicles, and wearable devices; the ease of connectivity provided by multi-input multi-output (MIMO) systems and fast data rates of modern communication protocols. As a result, radio source detection has received significant attention over the years [1], [2], [3], [4], [5], and made its way into applications across various domains of science and engineering [2], [6], [7], [8], [9], [10]. High resolution direction of arrival (DoA) estimation algorithms such as MuSiC, root-MuSiC, ESPRIT and several others including non-parametric machine learning and deep learning methods require the knowledge of the number of sources to compute a viable localization estimation [1], [2], [11], [12], [13], [14].…”