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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.

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse structure and the tensor elements are nonnegative count data. SparTen is a high-performance C++ library which computes a low-rank decomposition using different solvers: a first-order quasi-Newton or a second-order damped Newton method, along with the appropriate choice of runtime parameters. Since default parameters in SparTen are tuned to experimental results in prior published work on a single real-world dataset conducted using MATLAB implementations of these methods, it remains unclear if the parameter defaults in SparTen are appropriate for general tensor data. Furthermore, it is unknown how sensitive algorithm convergence is to changes in the input parameter values. This report addresses these unresolved issues with large-scale experimentation on three benchmark tensor data sets. Experiments were conducted on several different CPU architectures and replicated with many initial states to establish generalized profiles of algorithm convergence behavior., Comment: 33 pages, 13 figures