Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squares

05/25/2018

∙

by   Jialin Li, et al.

∙

0

∙

share

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(((1/ϵ))) steps under our proposed Trace Based Initialization procedure. Trace Based Initialization requires O(1/ (λ_r/λ_r+1)) number of matrix subspace iterations to guarantee a "good" initialization for the simultaneous orthogonalized ALS method, where λ_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.