An Algebraic Approach to Efficient Identification of a Class of Wiener Systems. Issue 2 (2020) - Ozbay, B.; Sznaier, M.; Camps, O.
Abstract: This paper considers the problem of identifying the linear portion of a Wiener system, for the case of a known, but non-invertible non-linearity. It is well known that this scenario, common in many practical applications, leads to NP-hard problems in the number of experiments. Thus, existing techniques scale poorly and are typically limited to relatively few points. We show that this difficulty can be circumvented by considering an algebraic motivated approach. Specifically, we show that it is equivalent to identification of a switched linear system generated from the data. In turn, we can solve this problem by recasting it as the problem of finding the vanishing ideal of an arrangement of subspaces, a task that reduces to finding the null space of an embedded data matrix constructed from observed data.