  There is growing interest to extend low-rank matrix decompositions to
multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is
the canonical polyadic decomposition (CPD). The challenge of fitting a
low-rank, nonnegative CPD model to Poisson-distributed count data is of
particular interest. Several popular algorithms use local search methods to
approximate the maximum likelihood estimator (MLE) of the Poisson CPD model.
This work presents two new algorithms that extend state-of-the-art local
methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical
Decomposition (GCP) with stochastic optimization and CP Alternating Poisson
Regression (CPAPR), a deterministic algorithm, to increase the probability of
converging to the MLE over either method used alone. Restarted CPAPR with
SVDrop uses a heuristic based on the singular values of the CPD model
unfoldings to identify convergence toward optimizers that are not the MLE and
restarts within the feasible domain of the optimization problem, thus reducing
overall computational cost when using a multi-start strategy. We provide
empirical evidence that indicates our approaches outperform existing methods
with respect to converging to the Poisson CPD MLE.
