Revisiting robustness of the union-of-subspaces model for data-adaptive learning of nonlinear signal models

This paper revisits the problem of data-adaptive learning of geometric signal structures based on the Union-of-Subspaces (UoS) model. In contrast to prior work, it motivates and investigates an extension of the classical UoS model, termed the Metric-Constrained Union-of-Subspaces (MC-UoS) model. In this regard, it puts forth two iterative methods for data-adaptive learning of an MC-UoS in the presence of complete and missing data. The proposed methods outperform existing approaches to learning a UoS in numerical experiments involving both synthetic and real data, which demonstrates effectiveness of both an MC-UoS model and the proposed methods.