Solving the sign indeterminacy for multiway models. (18th March 2013)

• Record Type: Journal Article
• Authors: Bro, Rasmus; Leardi, Riccardo; Johnsen, Lea Giørtz
• Is Part Of: Journal of chemometrics. Volume 27:Number 3/4(2013:Apr.)
• Page Start: 70
• Page End: 75
• Publication Date: 2013-03-18
• Subjects: sign flip -- tensor models -- PARAFAC -- Tucker3 -- PARAFAC2; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.2493
• Languages: English
• ISSNs: 0886-9383

Abstract

Abstract : Bilinear and multilinear models such as principal component analysis and PARAFAC have intrinsic sign indeterminacies. For example, any loading vector can be multiplied by −1 if another vector of that particular component is also multiplied by −1 without affecting the loss function values. This sometimes causes problems, for example, with respect to interpretation. In this paper, a method is developed to fix the sign indeterminacy for the PARAFAC, Tucker3 and PARAFAC2 models. Copyright © 2013 John Wiley & Sons, Ltd. Abstract : Bilinear and multilinear models such as principal component analysis and PARAFAC have intrinsic sign indeterminacies. For example, any loading vector can be multiplied by −1 if another vector of that particular component is also multiplied by −1 without affecting the loss function values. This sometimes causes problems, for example, with respect to interpretation. In this paper, a method is developed to fix the sign indeterminacy for the PARAFAC, Tucker3 and PARAFAC2 models.