Robust tensor decomposition with gross corruption

Quanquan Gu, Huan Gui, Jiawei Han

Research output: Contribution to journalConference articlepeer-review


In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensor W and an entrywise sparse corruption tensor ν. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We show that under certain conditions, the true low-rank tensor as well as the sparse corruption tensor can be recovered simultaneously. Our theory yields nonasymptotic Frobenius-norm estimation error bounds for each tensor separately. We show through numerical experiments that our theory can precisely predict the scaling behavior in practice.

Original languageEnglish (US)
Pages (from-to)1422-1430
Number of pages9
JournalAdvances in Neural Information Processing Systems
Issue numberJanuary
StatePublished - 2014
Event28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada
Duration: Dec 8 2014Dec 13 2014

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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