Randomshot, a fast nonnegative Tucker factorization approach

Abraham Traoré (1) , Maxime Berar (1) , Alain Rakotomamonjy (2)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
2 DocApp - LITIS - Equipe Apprentissage

Nonnegative Tucker decomposition is a powerful tool for the extraction of nonnegative and meaningful latent components from a positive multidimensional data (or tensor) while preserving the natural multilinear structure. However, as a tensor data has multiple modes, the existing approaches suffer from a high complexity in terms of computation time since they involve intermediate computations that can be time consuming. Besides, most of the existing approaches for nonnega-tive Tucker decomposition, inspired from well-established Nonnegative Matrix Factorization techniques, do not actually address the convergence issue. Most methods with a convergence rate guarantee assume restrictive conditions for their theoretical analyses (e.g. strong convexity, update of all of the block variables at least once within a fixed number of iterations). Thus, there still exists a theoretical vacuum for the convergence rate problem under very mild conditions. To address these practical (computation time) and theoretical (conver-gence rate under mild conditions) challenges , we propose a new iterative approach named Randomshot, which principle is to update one latent factor per iteration with a theoretical guarantee: we prove, under mild conditions, the convergence of our approach to the set of minimizers with high probability at the rate O 1 k , k being the iteration number. The effectiveness of the approach in terms of both running time and solution quality is proven via experiments on real and synthetic data.

Domaines: Intelligence artificielle [cs.AI]

Abraham Traoré, Maxime Berar, Alain Rakotomamonjy. Randomshot, a fast nonnegative Tucker factorization approach. 2019. ⟨hal-02288293⟩