Christian Uhl: Extracting Dynamical Systems-Based Signals from Noisy and Incomplete Datasets скачать в хорошем качестве

Christian Uhl: Extracting Dynamical Systems-Based Signals from Noisy and Incomplete Datasets

Title: Extracting Dynamical Systems-Based Signals from Noisy and Incomplete Datasets Speaker: Christian Uhl (Ansbach University of Applied Sciences) Abstract: We present the theory and applications of a new signal decomposition algorithm called Dynamical Component Analysis (DyCA). DyCA optimizes the least-squares cost function of the linear portion of an assumed set of differential equations, representing a Koopman-based approach. This yields a generalized eigenvalue problem involving the correlation matrices of the original and time-shifted signals. Thus, deterministic signals can be extracted from data corrupted by component noise. Additionally, we present a robust version of DyCA that couples it with L2-based regularization. This enables the simultaneous reconstruction of data and extraction of dynamical components in the presence of additive noise or incomplete data.