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Simultaneous Component Analysis by Means of Tucker3

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  • Alwin Stegeman

    (KU Leuven – Kulak
    KU Leuven)

Abstract

A new model for simultaneous component analysis (SCA) is introduced that contains the existing SCA models with common loading matrix as special cases. The new SCA-T3 model is a multi-set generalization of the Tucker3 model for component analysis of three-way data. For each mode (observational units, variables, sets) a different number of components can be chosen and the obtained solution can be rotated without loss of fit to facilitate interpretation. SCA-T3 can be fitted on centered multi-set data and also on the corresponding covariance matrices. For this purpose, alternating least squares algorithms are derived. SCA-T3 is evaluated in a simulation study, and its practical merits are demonstrated for several benchmark datasets.

Suggested Citation

  • Alwin Stegeman, 2018. "Simultaneous Component Analysis by Means of Tucker3," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 21-47, March.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:1:d:10.1007_s11336-017-9568-7
    DOI: 10.1007/s11336-017-9568-7
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    References listed on IDEAS

    as
    1. Alwin Stegeman & Tam Lam, 2014. "Three-Mode Factor Analysis by Means of Candecomp/Parafac," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 426-443, July.
    2. Stegeman, Alwin, 2014. "Finding the limit of diverging components in three-way Candecomp/Parafac—A demonstration of its practical merits," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 203-216.
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    10. Nathaniel Helwig, 2013. "The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 725-739, October.
    11. Alwin Stegeman, 2006. "Degeneracy in Candecomp/Parafac explained for p × p × 2 arrays of rank p + 1 or higher," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 483-501, September.
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