Uni-mode and partial uniqueness conditions for Candecomp/Parafac of three-way arrays with linearly dependent loadings.

Xijing Guo*, Sebastian Miron, David Brie, Alwin Stegeman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

33 Citations (Scopus)
243 Downloads (Pure)

Abstract

In this paper, three sufficient conditions are derived for the three-way CANDECOMP/PARAFAC (CP) model, which ensure uniqueness in one of the three modes ("uni-mode-uniqueness"). Based on these conditions, a partial uniqueness condition is proposed which allows collinear loadings in only one mode. We prove that if there is uniqueness in one mode, then the initial CP model can be uniquely decomposed in a sum of lower-rank tensors for which identifiability can be independently assessed. This condition is simpler and easier to check than other similar conditions existing in the specialized literature. These theoretical results are illustrated by numerical examples.

Original languageEnglish
Pages (from-to)111 - 129
Number of pages19
JournalSIAM Journal on Matrix Analysis and Applications
Volume33
Issue number1
DOIs
Publication statusPublished - 2012

Keywords

  • uni-mode uniqueness
  • partial uniqueness
  • CANDECOMP/PARAFAC
  • parallel profiles with linear dependencies
  • PARALIND
  • constrained factors
  • CONFAC
  • SIMULTANEOUS MATRIX DIAGONALIZATION
  • HIGHER-ORDER TENSOR
  • MULTIWAY DATA
  • SENSOR ARRAY
  • DECOMPOSITION
  • TERMS
  • IDENTIFICATION
  • SYSTEMS

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