Adaptive Rank Selection for Tensor Ring Decomposition

Farnaz Sedighin, Andrzej Cichocki, Huy ANH Phan

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Optimal rank selection is an important issue in tensor decomposition problems, especially for Tensor Train (TT) and Tensor Ring (TR) (also known as Tensor Chain) decompositions. In this paper, a new rank selection method for TR decomposition has been proposed for automatically finding near optimal TR ranks, which result in a lower storage cost, especially for tensors with inexact TT or TR structures. In many of the existing approaches, TR ranks are determined in advance or by using truncated Singular Value Decomposition (t-SVD). There are also other approaches for selecting TR ranks adaptively. In our approach, the TR ranks are not determined in advance, but are increased gradually in each iteration until the model achieves a desired approximation accuracy. For this purpose, in each iteration, the sensitivity of the approximation error to each of the core tensors is measured and the core tensors with the highest sensitivity measures are selected and their sizes are increased. Simulation results confirmed that the proposed approach reduces the storage cost considerably and allows us to find optimal model in TR format, while preserving the desired accuracy of the approximation.

Original languageEnglish
Article number9321501
Pages (from-to)454-463
Number of pages10
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number3
Publication statusPublished - Apr 2021


  • Approximation algorithms
  • Approximation error
  • Matrix decomposition
  • Rank incremental
  • Rank selection
  • Sensitivity
  • Signal processing algorithms
  • Simulation
  • Tensor ring decomposition
  • Tensors


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