Towards independent subspace analysis in controlled dynamical systems
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In this paper we extend Independent Component Analysis (ICA) task to controlled dynamical systems. To our best knowledge this is the first work that considers the control task in this field, which may open the door for extended ICA applications. We treat Independent Subspace Analysis (ISA) task, the multidimensional generalization of ICA. In particular, we consider the identification problem of ARX models, i.e., hidden AutoRegressive dynamical systems subject to eXogenous control inputs. In our case, these ARX models are driven by independent multidimensional noise processes. The goal is the estimation of the hidden variables, that is, the parameters of the system and the driving noise. We aim efficient estimation by choosing suitable control values. For the optimal choice of the control we adapt the D-optimality principle, also known as 'InfoMax method'. To this end, we decouple the problem into a fully observable one and an ISA task. We solve the two problems and join the results to estimate the hidden variables. Numerical examples illustrate the efficiency of our method.
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