Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms |
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| Authors: | Jos M. F. ten Berge Jan de Leeuw Pieter M. Kroonenberg |
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| Affiliation: | (1) University of Groningen, The Netherlands;(2) University of Leiden, The Netherlands;(3) Subfakulteit Psychologie, RU Groningen, Grote Markt 32, 9712 HV Groningen, The Netherlands |
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| Abstract: | Kroonenberg and de Leeuw (1980) have developed an alternating least-squares method TUCKALS-3 as a solution for Tucker's three-way principal components model. The present paper offers some additional features of their method. Starting from a reanalysis of Tucker's problem in terms of a rank-constrained regression problem, it is shown that the fitted sum of squares in TUCKALS-3 can be partitioned according to elements of each mode of the three-way data matrix. An upper bound to the total fitted sum of squares is derived. Finally, a special case of TUCKALS-3 is related to the Carroll/Harshman CANDECOMP/PARAFAC model. |
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| Keywords: | partitioning of least-squares fit rank-constrained regression Candecomp Parafac |
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