P. Giaquinto
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RePub, Erasmus University RepositoryWeighted Majorization Algorithms for Weighted Least Squares Decomposition Models
http://repub.eur.nl/pub/1700/
Wed, 26 Mar 2003 00:00:01 GMT<div>P.J.F. Groenen</div><div>P. Giaquinto</div><div>H.A.L. Kiers</div>
For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal components analysis with missing data. Kiers (1997) discusses an algorithm for minimizing weighted
decomposition models by iterative majorization. In this paper, we for computing a solution. We will show that the algorithm by Kiers is a special case of our algorithm. Here, we will apply weighted majorization to weighted principal components analysis, robust Procrustes analysis, and logistic bi-additive models of which the two parameter logistic model in item response theory is a special
case. Simulation studies show that weighted majorization is generally faster than the method by Kiers by a factor one to four and obtains the same or better quality solutions. For logistic bi-additive models, we propose a new iterative majorization algorithm called logistic majorization.