It was developed from Cattell's
idea of Parallel Proportional Profiles]
Parallel Proportional Profiles.
Harshman & Lundy [1984a],
- as a statistical/data analysis model, it is a three-way
generalization of Factor Analysis
and Principal Components Analysis (PCA);
- as an array/tensor decomposition, it is a
three-way generalization of singular value
decomposition and principal components
- as an array/tensor decomposition PARAFAC, also but seldomly referred to as
PARAFAC1, is equal to
CANDECOMP, which underlies the INDSCAL model for multidimensional scaling.
generalization PARAFAC2 allows oblique
axis analysis (but see also direct fitting
method by Kiers and Bro) that maintains uniqueness
property due to fixed angles among factors (cf.
- Parafac and its
generalizations encompass one of the two major families
of higher-way multilinear analysis methods, the other being
the family of Tucker Models for
Three-Mode Principal Component Analysis (TMPCA) or
Three-mode Factor Analysis as it was initially called by Tucker. The most prominent member of this
family is the Tucker3 model (T3), but other types of
component models exist as well, along with confirmatory factor analysis variants.
- Current key application areas include Chemometrics, Psychometrics,
Electrical Engineering signal processing, Physics,
Linguistics, and Neuroscience, also Marketing.
Please note that most links in this entry are not
operational. Links between square bracket [ ] refer to entries in the Three-Mode Bibliography,
i.e. outside the Encyclopedia.