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Explicit Candecomp/Parafac Solutions for a Contrived 2 × 2 × 2 Array of Rank Three

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge ,
Henk A. L. Kiers  and
Jan de Leeuw
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Henk A. L. Kiers
Affiliation:
University of Groningen
Jan de Leeuw
Affiliation:
University of Leiden
*
Requests for reprints should be sent to Jos M.F. ten Berge, Vakgroep Psychologic, RU Groningen, Grote Markt 32, 9712 HV Groningen, THE NETHERLANDS.
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Abstract

Kruskal, Harshman and Lundy have contrived a special 2 × 2 × 2 array to examine formal properties of degenerate Candecomp/Parafac solutions. It is shown that for this array the Candecomp/Parafac loss has an infimum of 1. In addition, the array will be used to challenge the tradition of fitting Indscal and related models by means of the Candecomp/Parafac process.

Keywords

Degenerate Parafac Solutionstrilinear modelscomponent analysis of n-way arrays
Type
Notes And Comments
Information
Psychometrika , Volume 53 , Issue 4 , December 1988 , pp. 579 - 583
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

Jan de Leeuw is now at the University of California at Los Angeles.

References

Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via anN-way generalization of “Eckart-Young” decomposition. Psychometrika, 35, 283–319.CrossRefGoogle Scholar
Carroll, J. D., & Pruzansky, S. (1984). The CANDECOMP-CANDELINC family of Models and Methods for Multidimensional Data Analysis. In Law, H. G., Snyder, C. W. Jr., Hattie, J. A., & McDonald, R. P. (Eds.), Research methods for multimode data analysis (pp. 372–402). New York: Praeger.Google Scholar
Harshman, R. A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multi-mode factor analysis. UCLA Working Papers in Phonetics, 16, 1–84.Google Scholar
Harshman, R. A., & Lundy, M. E. (1984). The PARAFAC model. In Law, H. G., Snyder, C. W. Jr., Hattie, J. A., & McDonald, R. P. (Eds.), Research methods for multimode data analysis (pp. 122–215). New York: Praeger.Google Scholar
Kruskal, J. B. (1977). Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra and its Applications, 18, 95–138.CrossRefGoogle Scholar
Kruskal, J. B., Harshman, R. A., & Lundy, M. E. (1983). Some relationships between Tucker's three-mode factor analysis and PARAFAC/CANDECOMP. Paper presented at the annual meeting of the Psychometric Society, Los Angeles.Google Scholar
Kruskal, J. B., Harshman, R. A., & Lundy, M. E. (1985). Several mathematical relationships between PARAFAC-CANDECOMP and three-mode factor analysis. Paper presented at the annual meeting of the Classification Society, St. John's, Newfoundland.Google Scholar
Schur, J. (1911). Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen [Comments on the theory of bounded bilinear forms with infinite numbers of variables]. Journal für die reine und angewandte Mathematik, 140, 1–28.CrossRefGoogle Scholar