Scaled Tucker manifold and its application to large-scale machine learning

摘要

We propose a novel geometry for dealing with low-rank Tucker decomposition of tensors. The geometry of the scaled Tucker manifold readily allows to develop algorithms for a number of regression problems. Specifically, we propose a novel scaled Riemannian metric (an inner product) that suits well to least-squares cost. The simulation experiments on the tensor completion problem show that our proposed nonlinear conjugate gradient algorithm outperforms state-of-the-art algorithms.