NON-LINEAR SINGULAR VALUE DECOMPOSITION

In data mining, machine learning, and signal processing, among others, many tasks such as dimensionality reduction, feature extraction, and classification are often based on the singular value decomposition (SVD). As a result, the usage and computation of the SVD have been extensively studied and well understood. However, as current approaches take into account the non-linearity of the world around us, non-linear generalizations of the SVD are needed. We present our ideas on this topic. As it turns out, the so-called decoupling problem is a promising non-linear generalization of the SVD, and can be solved by tensor techniques. We briefly discuss the potential of this approach for inverting nonlinear functions and for defining a nonlinear modal canonical form in the context of state-space modeling.