Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations

TL;DR

This paper introduces Newton-based algorithms for efficient Kullback-Leibler divergence tensor factorizations, particularly suited for sparse, count-based data, outperforming existing methods in speed and accuracy.

Contribution

It develops novel Newton and quasi-Newton subproblem solvers that exploit problem structure, enabling faster and more accurate tensor factorizations for sparse, Poisson-like data.

Findings

Superior speed for high accuracy factorizations

Effective in finding sparse solutions quickly

Outperforms existing algorithms in benchmarks

Abstract

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.