Cost Function Approach for Dynamical Component Analysis: Full Recovery of Mixing and State Matrix

Abstract

A reformulation of the dynamical component analysis (DyCA) via an optimization-free approach is presented. The original cost function approach is converted into a numerical linear algebra problem, i.e., the computation of coupled singular-value decompositions. A simple algorithm is presented together with numerical experiments to document the feasability of the approach. This methodology is able to recover the mixing and state matrices of multivariate signals from high-dimensional measured data fully.

Keywords

• dynamical component analysis
• system of ordinary differential equations
• singular-value decomposition