Title: Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squares,
Abstract: We consider the asymmetric orthogonal tensor decomposition problem, and
present an orthogonalized alternating least square algorithm that converges to
rank-$r$ of the true tensor factors simultaneously in
$O(\log(\log(\frac{1}{\epsilon})))$ steps under our proposed Trace Based
Initialization procedure. Trace Based Initialization requires $O(1/{\log
(\frac{\lambda_{r}}{\lambda_{r+1}})})$ number of matrix subspace iterations to
guarantee a "good" initialization for the simultaneous orthogonalized ALS
method, where $\lambda_r$ is the $r$-th largest singular value of the tensor.
We are the first to give a theoretical guarantee on orthogonal asymmetric
tensor decomposition using Trace Based Initialization procedure and the
orthogonalized alternating least squares. Our Trace Based Initialization also
improves convergence for symmetric orthogonal tensor decomposition.