Tensor factorizations with nonnegative constraints have found application in
analyzing data from cyber traffic, social networks, and other areas. We
consider application data best described as being generated by a Poisson
process (e.g., count data), which leads to sparse tensors that can be modeled
by sparse factor matrices. In this paper we investigate efficient techniques
for computing an appropriate canonical polyadic tensor factorization based on
the Kullback-Leibler divergence function. We propose novel subproblem solvers
within the standard alternating block variable approach. Our new methods
exploit structure and reformulate the optimization problem as small independent
subproblems. We employ bound-constrained Newton and quasi-Newton methods. We
compare our algorithms against other codes, demonstrating superior speed for
high accuracy results and the ability to quickly find sparse solutions.

本文探讨了基于 Kullback-Leibler divergence 函数的适当的标准交替块变量方法的正定多项式张量分解的有效技术，并提出了新的子问题解算器来利用结构并将优化问题重新表述为小的独立子问题，使用有界的 Newton 和拟牛顿方法。与其他代码比较，表明我们的算法具有更快的速度，能够获得高精度的结果，并迅速找到稀疏解。