How 3-MFA data can cause degenerate parafac solutions, among other relationships
Multiway data analysis
A two-stage procedure incorporating good features of both trilinear and quadrilinear models
Multiway data analysis
PARAFAC: parallel factor analysis
Computational Statistics & Data Analysis - Special issue on multiway data analysis—software and applications
Three-factor association models for three-way contingency tables
Computational Statistics & Data Analysis
Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure
Computational Statistics & Data Analysis
Tensor-based techniques for the blind separation of DS-CDMA signals
Signal Processing
Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
SIAM Journal on Matrix Analysis and Applications
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Unsupervised Multiway Data Analysis: A Literature Survey
IEEE Transactions on Knowledge and Data Engineering
A comparison of algorithms for fitting the PARAFAC model
Computational Statistics & Data Analysis
SIAM Journal on Matrix Analysis and Applications
Tensor Decompositions and Applications
SIAM Review
Blind PARAFAC receivers for DS-CDMA systems
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
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Three-way Candecomp/Parafac (CP) is a three-way generalization of principal component analysis (PCA) for matrices. Contrary to PCA, a CP decomposition is rotationally unique under mild conditions. However, a CP analysis may be hampered by the non-existence of a best-fitting CP decomposition with R=2 components. In this case, fitting CP to a three-way data array results in diverging CP components. Recently, it has been shown that this can be solved by fitting a decomposition with several interaction terms, using initial values obtained from the diverging CP decomposition. The new decomposition is called CP"l"i"m"i"t, since it is the limit of the diverging CP decomposition. The practical merits of this procedure are demonstrated for a well-known three-way dataset of TV-ratings. CP"l"i"m"i"t finds main components with the same interpretation as Tucker models or when imposing orthogonality in CP. However, CP"l"i"m"i"t has higher joint fit of the main components than Tucker models, contains only one small interaction term, and does not impose the unnatural constraint of orthogonality. The uniqueness properties of the CP"l"i"m"i"t decomposition are discussed in detail.