Title: Efficient Constrained Tensor Factorization by Alternating Optimization with Primal-Dual Splitting,
Abstract: Tensor factorization with hard and/or soft constraints has played an
important role in signal processing and data analysis. However, existing
algorithms for constrained tensor factorization have two drawbacks: (i) they
require matrix-inversion; and (ii) they cannot (or at least is very difficult
to) handle structured regularizations. We propose a new tensor factorization
algorithm that circumvents these drawbacks. The proposed method is built upon
alternating optimization, and each subproblem is solved by a primal-dual
splitting algorithm, yielding an efficient and flexible algorithmic framework
to constrained tensor factorization. The advantages of the proposed method over
a state-of-the-art constrained tensor factorization algorithm, called AO-ADMM,
are demonstrated on regularized nonnegative tensor factorization.