Two-factor degeneracies and a stabilization of PARAFAC

William S. Rayens, Benjamin C. Mitchell

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


Mitchell and Burdick (B.C. Mitchell, D.S. Burdick, An empirical comparison of resolution methods for three-way arrays, Chemom. Intell. Lab. Syst. 20 (1993) 149-161; B.C. Mitchell, D.S. Burdick, Slowly converging PARAFAC sequences: Swamps and two-factor degeneracies, J. Chemom. 8 (1994) 155-168.) uncovered an intriguing correspondence between the existence of PARAFAC swamps and the presence of two-factor degeneracies (2FDs). This observation, coupled with the recognition that post-swamp resolutions were generally better than pre-swamp resolutions allowed the user a method of detecting when a swamp had likely been encountered and, hence, when it was safe to assume that PARAFAC had converged to a suitable resolution. Still, this correspondence alone did not suggest how one might reduce the number of PARAFAC iterations required to move through a swamp. In this paper, it is noted that serious 2FDs must produce an identifiable ill-conditioning in the least squares estimation step in PARAFAC. Moreover, a serious 2FD is only one way this ill-conditioning may occur and, hence, it is more correct to say that swamps correspond to this ill-conditioning in general, rather than to the presence of 2FDs in particular. In an attempt to reduce the number of iterations that PARAFAC spends in a swamp, a particular method of stabilization is employed and results are presented which suggest that the number iterations can often be greatly reduced.

Original languageEnglish
Pages (from-to)173-181
Number of pages9
JournalChemometrics and Intelligent Laboratory Systems
Issue number2
StatePublished - Oct 1997

Bibliographical note

Funding Information:
During the preparation of this manuscript Professor Rayens was supported by NSF Grant ATM 9108177.


  • Two-factor degeneracies (2FDs)

ASJC Scopus subject areas

  • Analytical Chemistry
  • Software
  • Process Chemistry and Technology
  • Spectroscopy
  • Computer Science Applications


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