Nonlinear dynamical factor analysis
Xavier Giannakopoulos · AIP conference proceedings · 2001
A general method for state space analysis is presented where not only underlying factors generating the data are estimated, but also the dynamics behind time series in factor space are modeled. The mappings and the states are all unknown. The nonlinearity of the mappings makes the problem highly underdetermined and thus challenging. The Bayesian approach is able to find a set of mappings which has a high posterior probability. The model is very general: in principle any dynamical process can be modeled as a nonlinear state space model, and long-term dependencies can always be transformed into a model with more states and one-step dynamics. Potential applications are abundant. We present the results of experiments on real-world data.