Manifold-Constrained Regressors in System Identification, Report no. LiTH-ISY-R-2859

High-dimensional regression problems are becoming more and more common with emerging technologies. However, in many cases data are constrained to a low dimensional manifold. The information about the output is hence contained in a much lower dimensional space, which can be expressed by an intrinsic description. By rst nding the intrinsic description, a low dimensional mapping can be found to give us a two step mapping from regressors to output. In this paper a methodology aimed at manifoldconstrained identi cation problems is proposed. A supervised and a semisupervised method are presented, where the later makes use of given regressor data lacking associated output values for learning the manifold. As it turns out, the presented methods also carry some interesting properties also when no dimensional reduction is performed.