Séminaire Konstantin Usevich


10 juin 2024    
14h00 - 15h00

CRAN - FST - 4ème
Campus Sciences, Boulevard des Aiguillettes, Vandoeuvre-lès-Nancy, 54506

Type d’évènement

Speaker: Konstantin Usevich (CRAN)
Title: Algebraic Algorithms for the ParaTuck-2 Decomposition
Abstract: ParaTuck-2 decomposition (PT2D) of 3-rd order tensors is a 2-level extension of the well-known CP (canonical polyadic) decomposition (CPD). It is relevant in several applications, such as chemometrics, telecommunications, and machine learning. As shown in (Harshman, Lundy, 1996), the PT2D enjoys strong uniqueness properties (up to scaling/permutation ambiguities, similarly to the CPD). However, there are very few results on theory and algorithms for the PT2D. In particular, common strategies, such as the alternating least squares, suffer from convergence and initialization issues. We propose an algebraic algorithm for the PT2D decomposition in the case when the ParaTuck-2 ranks are smaller than the frontal dimensions of the tensor. Our approach relies only on linear algebra operations and is based on finding the kernel of a structured matrix constructed from the tensor. It refines the previously known identifiability conditions. Yet another algorithm is proposed for the symmetric case, which appears in the implicit approach to the PARAFAC-2 model.

Teams link: https://teams.microsoft.com/l/meetup-join/19%3aaa79c15ac331466aa8ad98cbecb29ab2%40thread.tacv2/1717591833486?context=%7b%22Tid%22%3a%22158716cf-46b9-48ca-8c49-c7bb67e575f3%22%2c%22Oid%22%3a%22c4a8aea2-7ce5-4ee9-b6c5-9fee62ad0257%22%7d

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