Two-factor degeneracies and a stabilization of PARAFAC

✍ Scribed by William S. Rayens; Benjamin C. Mitchell

• Book ID: 104309490
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 807 KB
• Volume: 38
• Category: Article
• ISSN: 0169-7439
• DOI: 10.1016/s0169-7439(97)00033-6

✦ Synopsis

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 PAWAC 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 PAWAC.

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.