The CANDECOMP algorithm for the PARAFAC analysis of n × m × p three-way arrays is adapted to handle arrays in which n > rnp more efficiently. For such arrays, the adapted algorithm needs less memory space to store the data during the iterations, and uses less com- putation time than the original CANDECOMP algorithm. The size of the arrays that can be handled by the new algorithm is in no way limited by the number of observation units (n) in the data.
DOCUMENT
Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.
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