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Title: Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

Tensor factorizations with nonnegativity constraints have found application in analysing 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 modelled 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. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.
 [1] ;  [1] ;  [2]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Northwestern Univ., Evanston, IL (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1055-6788; 533741
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Optimization Methods and Software
Additional Journal Information:
Journal Volume: 30; Journal Issue: 5; Journal ID: ISSN 1055-6788
Taylor & Francis
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
Work for Others (WFO)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; tensor factorization; multilinear algebra; nonlinear optimization; Poisson; Kullback–Leibler