Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1863–1872 | Cite as

Nonnegative Tensor Train Factorization with DMRG Technique

  • E. M. ShcherbakovaEmail author


Tensor train is one of the modern decompositions used as low-rank tensor approximations of multidimensional arrays. If the original data is nonnegative we sometimes want the approximant to keep this property. In this work new methods for nonnegative tensor train factorization are proposed. Low-rank approximation approach helps to speed up the computations whereas DMRG technique allows to adapt nonnegative TT ranks for better accuracy. The performance analysis of the proposed algorithms as well as comparison with other nonnegative TT factorization method are presented.

Keywords and phrases

nonnegative tensor train multiplicative updates DMRG 


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The author thanks E. E. Tyrtyshnikov for useful advices and participation in discussions of the results.


This article contains the results of the project performed in the framework of the implementation of the programs of the Central Competences of the National Technological Database “Center for Big Data Storage and Analysis” (project “Tensor methods for processing and analysis of Big Data”) of Lomonosov MSU with the Project Support Funding of the National Technological Reporting dated December 11, 2018, no. 13/1251/2018.


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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Marchuk Institute of Numerical Mathematics of Russian Academy of SciencesMoscowRussia

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