Nesterov-Based Alternating Optimization for Nonnegative Tensor Factorization: Algorithm and Parallel Implementation

Athanasios P. Liavas, Georgios Kostoulas, Georgios Lourakis, Kejun Huang, Nicholas D. Sidiropoulos

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25 Scopus citations


We consider the problem of nonnegative tensor factorization. Our aim is to derive an efficient algorithm that is also suitable for parallel implementation. We adopt the alternating optimization framework and solve each matrix nonnegative least-squares problem via a Nesterov-Type algorithm for strongly convex problems. We describe a parallel implementation of the algorithm and measure the attained speedup in a multicore computing environment. It turns out that the derived algorithm is a competitive candidate for the solution of very large-scale dense nonnegative tensor factorization problems.

Original languageEnglish (US)
Article number8119874
Pages (from-to)944-953
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - Feb 15 2018

Bibliographical note

Funding Information:
Manuscript received April 27, 2017; revised September 12, 2017; accepted November 5, 2017. Date of publication November 24, 2017; date of current version January 16, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Tsung-Hui Chang. This work was supported in part by NSF, under Grants IIS-1447788 and IIS-1704074, and in part by computational time granted from the Greek Research & Technology Network in the National HPC facility—ARIS—under project pa170403. Part of this work was presented at IEEE International Conference on Acoustics, Speech and Signal Processing, New Orleans, LA, USA, March 2017. (Corresponding author: Athanasios P. Liavas.) A. P. Liavas, G. Kostoulas, and G. Lourakis are with the School of Electrical and Computer Engineering, Technical University of Crete, Chania 73100, Greece (e-mail:;; glourakis@isc.

Publisher Copyright:
© 1991-2012 IEEE.


  • Tensors
  • nonnegative tensor factorization
  • optimal first-order optimization algorithms
  • parallel algorithms


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