A constrained PARAFAC method for positive manifold data

Krijnen, Wim P.
Ten Berge, Jos M. F.
1992
Thumbnail Image

View/Download File

v16n3p295.pdf (1.06 MB)

Persistent link to this item

https://hdl.handle.net/11299/116152
Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

A constrained PARAFAC method for positive manifold data

Authors

Published Date

1992

Publisher

Type

Article

Abstract

A set of non-negatively correlated variables, referred to as positive manifold data, display a peculiar pattern of loadings in principal components analysis (PCA). If a small set of principal components is rotated to a simple structure, the variables correlate positively with all components, thus displaying positive manifold. However, this phenomenon is critically dependent on the freedom of rotation, as is evident from the unrotated loadings. That is, although the first principal component is without contrast (which means that all variables correlate either positively or negatively with the first component), subsequent components have mixtures of positive and negative loadings-which means that positive manifold is absent. PARAFAC is a generalization of PCA that has unique components, which means that rotations are not allowed. This paper examines how PARAFAC behaves when applied to positive manifold data. It is shown that PARAFAC does not always produce positive manifold solutions. For cases in which PARAFAC does not produce a positive manifold solution, a constrained PARAFAC method is offered that restores positive manifold by introducing non-negativity constraints. Thus, noncontrast PARAFAC components can be found that explain only a negligible amount of variance less than the PARAFAC components. These noncontrast components cannot be degenerate and cannot be partially unique in the traditional sense. Index terms: degenerate components; noncontrast components; non-negativity constraints; PARAFAC; positive manifold.

Keywords

Description

Related to

Replaces

License

Collections

Applied Psychological Measurement, Volume 16, 1992

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Krijnen, Wim P & ten Berge, Jos M. (1992). A constrained PARAFAC method for positive manifold data. Applied Psychological Measurement, 16, 295-305. doi:10.1177/014662169201600310

Suggested citation

Krijnen, Wim P.; Ten Berge, Jos M. F.. (1992). A constrained PARAFAC method for positive manifold data. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/116152.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.