Manifold Learning for Latent Variable Inference in Dynamical Systems

We study the inference of latent intrinsic variables of dynamical systems from output signal measurements. The primary focus is the construction of an intrinsic distance between signal measurements, which is independent of the measurement device. This distance enables us to infer the latent intrinsic variables through the solution of an eigenvector problem with a Laplace operator based on a kernel. The signal geometry and its dynamics are represented with nonlinear observers. An analysis of the properties of the observers that allow for accurate recovery of the latent variables is given, and a way to test whether these properties are satisfied from the measurements is proposed. Scattering and window Fourier transform observers are compared. Applications are shown on simulated data, and on real intracranial Electroencephalography (EEG) signals of epileptic patients recorded prior to seizures.