Tensor completion using geodesics on Segre manifolds

We propose a Riemannian conjugate gradient algorithm for approximating incomplete tensors by canonical polyadic decompositions of low rank. Our main contribution consists an explicit expression almost everywhere complete set geodesics the Segre manifold rank-1 tensors. These are leveraged in our optimization over geometrically convenient parametrization rank- r $$ to move direction tangent vector -fold product manifolds. apply method movie rating predictions recommender system MovieLens dataset, and identifying pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we can recover tensor decomposition from only 6 . 5 % 6.5\% numerical experiments, proposed was competitive state-of-the-art quasi-Newton truncated inner solves Tensorlab terms accuracy could reduce computation time half.