Abstract
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 language | English |
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Pages (from-to) | 173-181 |
Number of pages | 9 |
Journal | Chemometrics and Intelligent Laboratory Systems |
Volume | 38 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1997 |
Bibliographical note
Funding Information:During the preparation of this manuscript Professor Rayens was supported by NSF Grant ATM 9108177.
Keywords
- PARAFAC
- Two-factor degeneracies (2FDs)
ASJC Scopus subject areas
- Analytical Chemistry
- Software
- Process Chemistry and Technology
- Spectroscopy
- Computer Science Applications