# Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations

### Abstract

Tensor factorizations with nonnegativity 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.

Type
Publication
Optimization Methods and Software
Date
Tags
Citation
S. Hansen, T. Plantenga, T. G. Kolda. Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations. Optimization Methods and Software, Vol. 30, No. 5, pp. 1002-1029, 28 pages, 2015. https://doi.org/10.1080/10556788.2015.1009977

### Keywords

tensor factorization, multilinear algebra, nonlinear optimization, poisson, Kullback-Leibler

### BibTeX

@article{HaPlKo15,
author = {Samantha Hansen and Todd Plantenga and Tamara G. Kolda},
title = {Newton-Based Optimization for {Kullback-Leibler} Nonnegative Tensor Factorizations},
journal = {Optimization Methods and Software},
volume = {30},
number = {5},
pages = {1002-1029},
pagetotal = {28}
month = {April},
year = {2015},
doi = {10.1080/10556788.2015.1009977},
eprint = {1304.4964},
}