First-order perturbation analysis of low-rank tensor approximations based on the truncated HOSVD

Emilio Rafael Balda, Sher Ali Cheema, Jens Steinwandt, Martin Haardt, Amir Weiss, Arie Yeredor

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The truncated version of the higher-order singular value decomposition (HOSVD) has a great significance in multi-dimensional tensor-based signal processing. It allows to extract the principal components from noisy observations in order to find a low-rank approximation of the multi-dimensional data. In this paper, we address the question of how good the approximation is by analytically quantifying the tensor reconstruction error introduced by the truncated HOSVD. We present a first-order perturbation analysis of the truncated HOSVD to obtain analytical expressions for the signal subspace error in each dimension as well as the tensor reconstruction error induced by the low-rank approximation of the noise corrupted tensor. The results are asymptotic in the signal-to-noise ratio (SNR) and expressed in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. Empirical simulation results verify the obtained analytical expressions.

Original languageEnglish
Title of host publicationConference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1723-1727
Number of pages5
ISBN (Electronic)9781538639542
DOIs
StatePublished - 1 Mar 2017
Event50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, United States
Duration: 6 Nov 20169 Nov 2016

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers

Conference

Conference50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
Country/TerritoryUnited States
CityPacific Grove
Period6/11/169/11/16

Keywords

  • Perturbation analysis
  • higher-order singular value decomposition (HOSVD)
  • tensor signal processing

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

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