Quasi-orthogonalization for alternating non-negative tensor factorization

ETNA - Electronic Transactions on Numerical Analysis, vol. 62, pp. 22–57

Abstract

Low-rank tensor formats allow for efficient handling of high-dimensional objects. In many applications, it is crucial to preserve the non-negativity in the approximation, for instance, by constraining all cores to be non-negative. Common alternating strategies reduce the high-dimensional problem to a sequence of low-dimensional subproblems but often suffer from slow convergence and persistence in local minima. In order to counteract this, we propose a new quasi-orthogonalization strategy as an intermediate step between the alternating minimization steps that preserves non-negativity. It allows one to improve the expressivity in each individual factor by modifying the current factorization within the equivalence class representing the same tensor.

Authors 3

1. Lars Grasedyck Aachen Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Applied Mathematics , RWTH Aachen University , Templergraben 55 , 52056 Aachen , Germany

2. Maren Klever Aachen Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Applied Mathematics , RWTH Aachen University , Templergraben 55 , 52056 Aachen , Germany

3. Sebastian Krämer Aachen Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Applied Mathematics , RWTH Aachen University , Templergraben 55 , 52056 Aachen , Germany