Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis

Keywords

Uniqueness, Mathematics, Rotation (mathematics), Oblique case, Simple (philosophy)

References

• Testing a simple structure hypothesis in factor analysisD.A. Dingee, H. M. Epstein, J.W. Chastain — 1966
• Three areas of experimental phoneticsPeter Ladefoged — 1967
• Acoustic Theory Of Speech ProductionGunnar Fant — 1960
• Some mathematical notes on three-mode factor analysisLedyard R Tucker — 1966
• The Measurement of Phonetic SimilarityPeter Ladefoged — 1969
• “Parallel proportional profiles” and other principles for determining the choice of factors by rotationRaymond B. Cattell — 1944
• Factor analysis by minimizing residuals (minres)Harry H. Harman, Wayne H. Jones — 1966
• Problems in measuring changeArdie Lubin, Chester W. Harris — 1965
• The varimax criterion for analytic rotation in factor analysisHenry F. Kaiser — 1958
• Tandem criteria for analytic rotation in factor analysisAndrew L. Comrey — 1967
• Factor interaction in nonlinear factor analysis.Roderick P. McDonald — 1967
• Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decompositionJ. Douglas Carroll, Jih-Jie Chang — 1970
• Three-Mode Factor Analysis Of Parker-Fleishman Complex Tracking Behavior Data.Ledyard R Tucker — 1967
• The approximation of one matrix by another of lower rankCarl Eckart, Gale Young — 1936
• FACTOR ROTATION FOR PROPORTIONAL PROFILES: ANALYTICAL SOLUTION AND AN EXAMPLERaymond B. Cattell, Alan Cattell — 1955
• Methods Factors In Multitrait-Multimethod Matrices : Multiplicative Rather Than Additive?Donald T. Campbell, Edward J. O’Connell — 1967
• Moderator Variables in PredictionDavid Saunders — 1956
• THE INFLUENCE OF MULTIVARIATE SELECTION ON THE FACTORIAL ANALYSIS OF ABILITYGodfrey H. Thomson — 1938
• The Vectors of MindL. L. Thurstone — 1935
• Factor analysis of data matricesRichard B. Darlington, Paul Horst — 1965

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• Properties of and Algorithms for Fitting Three-Way Component Models with Offset TermsBernardo. Ibáñez de Echávarri — 2006
• Linked matrix factorizationLuis Manuel Estalayo — 2017
• Causality and Similarity in Autobiographical Event Structure: An Investigation Using Event Cueing and Latent Semantic AnalysisChristopher M. O’Connor — 2010
• Variational Bayesian LearningZoubin Ghahramani — 2000
• Infinite Positive Semidefinite Tensor Factorization for Source Separation of Mixture SignalsKazuyoshi Yoshii, Ryota Tomioka, Daichi Mochihashi — 2013
• Recherche linéaire optimisée : Une nouvelle méthode pour accélérer PARAFACMyriam Rajih, Pierre Comon — 2005
• Canonical Variate Analysis and Related Methods with Longitudinal DataMichael Beaghen — 1997
• CPOPT : optimization for fitting CANDECOMP/PARAFAC models.Daniel Dunlavy, Tamara G. Kolda, Evrim Acar — 2008
• Variational Inference For Probabilistic Latent Tensor Factorization with KL DivergenceBeyza Ermiş, Yusuf Kenan Yilmaz, Ali Taylan Cemgil — 2014
• Simultaneous Matrix Diagonalization : the Overcomplete CaseLieven De Lathauwer — 2003
• On asymptotic tests in three-factor factorial designs with no replicationsKyoungah See — 1999
• Modeling Wavelength-dependent BRDFs as Factored Tensors for Real-time Spectral RenderingKarsten Schwenk, Arjan Kuijper, Ulrich Bockholt — 2010
• The opioid peptide dynorphin A : Biophysical studies of peptide–receptor and peptide–membrane interactionsJohannes Björnerås — 2014
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Related papers

• The Expression of a Tensor or a Polyadic as a Sum of ProductsFrank L. Hitchcock — 1927
• On the uniqueness of multilinear decomposition of N‐way arraysNicholas D. Sidiropoulos, Rasmus Bro — 2000
• Blind PARAFAC receivers for DS-CDMA systemsNicholas D. Sidiropoulos, Georgios B. Giannakis, Rasmus Bro — 2000
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation ProblemVin de Silva, Lek‐Heng Lim — 2006
• PARAFAC. Tutorial and applicationsRasmus Bro — 1997
• Parallel factor analysis in sensor array processingNicholas D. Sidiropoulos, Rasmus Bro, Georgios B. Giannakis — 2000
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statisticsJoseph B. Kruskal — 1977
• A comparison of algorithms for fitting the PARAFAC modelGiorgio Tomasi, Rasmus Bro — 2006
• The N-way Toolbox for MATLABClaus A. Andersson, Rasmus Bro — 2000
• Multi-way Analysis with Applications in the Chemical SciencesAge K. Smilde, Rasmus Bro, Paul Geladi — 2004