  Multi-relational learning has received lots of attention from researchers in
various research communities. Most existing methods either suffer from
superlinear per-iteration cost, or are sensitive to the given ranks. To address
both issues, we propose a scalable core tensor trace norm Regularized
Orthogonal Iteration Decomposition (ROID) method for full or incomplete tensor
analytics, which can be generalized as a graph Laplacian regularized version by
using auxiliary information or a sparse higher-order orthogonal iteration
(SHOOI) version. We first induce the equivalence relation of the Schatten
p-norm (0<p<\infty) of a low multi-linear rank tensor and its core tensor. Then
we achieve a much smaller matrix trace norm minimization problem. Finally, we
develop two efficient augmented Lagrange multiplier algorithms to solve our
problems with convergence guarantees. Extensive experiments using both real and
synthetic datasets, even though with only a few observations, verified both the
efficiency and effectiveness of our methods.
