Efficient algorithms for ‘universally’ constrained matrix and tensor factorization

We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in unsupervised learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in turn, using ADMM. This combination can naturally accommodate a great variety of constraints on the factor matrices, hence the term `universal'. Computation caching and warm start strategies are used to ensure that each update is evaluated efficiently, while the outer AO framework guarantees that the algorithm converges monotonically. Simulations on synthetic data show significantly improved performance relative to state-of-the-art algorithms.