EXTRAPOLATED ALTERNATING ALGORITHMS FOR APPROXIMATE CANONICAL POLYADIC DECOMPOSITION

Andersen Man Shun Ang , Andersen Man , Shun Ang , Jérémy E Cohen (1) , Le Thi Khanh , Nicolas Gillis (2)

1 IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires
2 UMONS - University of Mons [Belgium]

Tensor decompositions have become a central tool in machine learning to extract interpretable patterns from multiway arrays of data. However, computing the approximate Canonical Polyadic Decomposition (aCPD), one of the most important tensor decomposition model, remains a challenge. In this work, we propose several algorithms based on extrapolation that improve over existing alternating methods for aCPD. We show on several simulated and real data sets that carefully designed extrapolation can significantly improve the convergence speed hence reduce the computational time, especially in difficult scenarios.

Mots clés: Canonical Polyadic Decomposition; Block-coordinate Descent; Tensor; Acceleration; Non-convex Optimization

Domaines: Optimisation et contrôle [math.OC]; Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]

Andersen Man Shun Ang, Andersen Man, Shun Ang, Jérémy E Cohen, Le Thi Khanh, et al.. EXTRAPOLATED ALTERNATING ALGORITHMS FOR APPROXIMATE CANONICAL POLYADIC DECOMPOSITION. ICASSP, May 2020, Barcelone, Spain. ⟨10.1109/ICASSP40776.2020.9053849⟩. ⟨hal-02330641v2⟩