Some New Results on Orthogonally Constrained Candecomp |
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Authors: | Mohammed Bennani Dosse Jos MF ten Berge Jorge N Tendeiro |
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Institution: | (1) Statistics Research Team, University of Rennes 2, Rennes, France;(2) University of Groningen, Groningen, The Netherlands |
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Abstract: | The use of Candecomp to fit scalar products in the context of Indscal is based on the assumption that, due to the symmetry
of the data matrices involved, two components matrices will become equal when Candecomp converges. Bennani Dosse and Ten Berge
(2008) have shown that, in the single component case, the assumption can only be violated at saddle points in the case of
Gramian matrices. This paper again considers Candecomp applied to symmetric matrices, but with an orthonormality constraint
on the components. This constrained version of Candecomp, when applied to symmetric matrices, has long been known under the
acronym Indort. When the data matrices are positive definite, or have become positive semidefinite due to double centering,
and the saliences are nonnegative – by chance or by constraint –, the component matrices resulting from Indort are shown to
be equal. Because Indort is also free from so-called degeneracy problems, it is a highly attractive alternative to Candecomp
in the present context. We also consider a well-known successive approach to the orthogonally constrained Indscal problem
and we compare, from simulated and real data sets, its results with those given by the simultaneous (Indort) approach. |
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