This chapter addresses the problem of nonparametric identification of Wiener systems using a Kernel-based approach. Salient features of the proposed framework are its ability to exploit both positive and negative samples, and the fact that it does not require prior knowledge of the dimension of the output of the linear subsystem. Thus, it can be considered as a generalization to dynamical systems of kernel-based nonlinear manifold embedding methods recently developed in the machine-learning field. The main result of the chapter shows that while in principle, the proposed approach results in a non-convex problem, a tractable convex relaxation can be obtained by using a combination of polynomial optimization and rank-minimization techniques. The main advantage of the proposed algorithm stems from the fact that, since it is based on kernel ideas, it uses scalar inner products of the observed data, rather than the data itself. Hence, it can comfortably handle cases involving systems with high dimensional outputs. A practical scenario where such situation arises is activity classification from video data, since here each data point is a frame in a video sequence, and hence its dimension is typically O(103) even when using low resolution videos.
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