Inexact Generalized Gauss–Newton for Scaling the Canonical Polyadic Decomposition With Non-Least-Squares Cost Functions

The canonical polyadic decomposition (CPD) allows one to extract compact and interpretable representations of tensors. Several optimization-based methods exist fit the CPD a tensor for standard least-squares (LS) cost function. Extensions have been proposed more general functions such as β-divergences well. For these non-LS functions, generalized Gauss-Newton (GGN) method has developed. This is second-order that uses an approximation Hessian function determine next iterate with this algorithm, fast convergence can be achieved close solution. While it possible construct full small tensors, exact GGN approach becomes too expensive tensors larger dimensions, found in typical applications. In paper, we therefore propose use inexact provide several strategies make scalable large First, only used implicitly its multilinear structure exploited during Hessian-vector products, which greatly improves scalability method. Next, show by using compressed instance approximation, computation time lowered even more, limited influence on speed. We also dedicated preconditioners problem. Further, maximum likelihood estimator Rician distributed data examined detail example alternative useful analysis moduli complex data, functional magnetic resonance imaging, instance. compare existing demonstrate method's speed effectiveness synthetic simulated real-life data. Finally, scale randomized block sampling.