Stability analysis and fast damped-gauss-newton algorithm for INDSCAL tensor decomposition

Zbyněk Koldovsky, Petr Tichavský, Anh Huy Phan

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

4 Citations (Scopus)

Abstract

INDSCAL is a special case of the CANDECOMP-PARAFAC (CP) decomposition of three or more-way tensors, where two factor matrices are equal. This paper provides a stability analysis of INDSCAL that is done by deriving the Cramér-Rao lower bound (CRLB) on variance of an unbiased estimate of the tensor parameters from its noisy observation (the tensor plus an i.i.d. Gaussian random tensor). The existence of the bound reveals necessary conditions for the essential uniqueness of the INDSCAL decomposition. This is compared with previous results on CP. Next, analytical expressions for the inverse of the Hessian matrix, which is needed to compute the CRLB, are used in a damped Gaussian (Levenberg-Marquardt) algorithm, which gives a novel method for INDSCAL having a lower computational complexity.

Original languageEnglish
Title of host publication2011 IEEE Statistical Signal Processing Workshop, SSP 2011
Pages581-584
Number of pages4
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event2011 IEEE Statistical Signal Processing Workshop, SSP 2011 - Nice, France
Duration: 28 Jun 201130 Jun 2011

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings

Conference

Conference2011 IEEE Statistical Signal Processing Workshop, SSP 2011
Country/TerritoryFrance
CityNice
Period28/06/1130/06/11

Keywords

  • CANDECOMP
  • Cramér-Rao lower bound
  • INDSCAL
  • Levenberg-Marquardt algorithm
  • PARAFAC
  • tensor decomposition

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