Set membership identification using S-Isomap and K-NNC

A set membership identification method by pattern classification is proposed for nonlinear-in-parameter regression models with unknown but bounded (UBB) noises. Suppose that the points in the parameter space can be divided into two classes according to whether they are in the feasible solution set or not, the problem of set membership identification is to construct a pattern classifier to decide which class a point belongs to. The method has three steps. Firstly, the training data are selected uniformly in the parameter space, and are decided by equation error whether they are in the feasible solution set. Secondly, supervised Isomap (S-Isomap) is used to map the training data into low-dimensional space. Thirdly, k-nearest neighbor classifier (k-NNC) is trained on the mapped training data. This method not only can describe the feasible solution set approximately in the high-dimensional parameter space, but also can characterize it in the low-dimensional feature space. Simulation results show the effectiveness of the proposed method.