Study of performance of low-rank nonnegative tensor factorization methods

Author:

Shcherbakova Elena M.1,Matveev Sergey A.12,Smirnov Alexander P.1,Tyrtyshnikov Eugene E.12

Affiliation:

1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University , Moscow , Russia .

2. Marchuk Insitute of Numerical Mathematics, Russian Academy of Sciences , Moscow , Russia

Abstract

Abstract In the present paper we compare two different iterative approaches to constructing nonnegative tensor train and Tucker decompositions. The first approach is based on idea of alternating projections and randomized sketching for factorization of tensors with nonnegative elements. This approach can be useful for both TT and Tucker formats. The second approach consists of two stages. At the first stage we find the unconstrained tensor train decomposition for the target array. At the second stage we use this initial approximation in order to fix it within moderate number of operations and obtain the factorization with nonnegative factors either in tensor train or Tucker model. We study the performance of these methods for both synthetic data and hyper-spectral image and demonstrate the clear advantage of the latter technique in terms of computational time and wider range of possible applications.

Publisher

Walter de Gruyter GmbH

Subject

Modeling and Simulation,Numerical Analysis

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