Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
How 3-MFA data can cause degenerate parafac solutions, among other relationships
Multiway data analysis
An alternating least squares algorithms for PARAFAC2 and three-way DEDICOM
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Product form approximations for communicating Markov processes
Performance Evaluation
PARAFAC2 receivers for orthogonal space-time block codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Approximate low-rank factorization with structured factors
Computational Statistics & Data Analysis
Acceleration of the alternating least squares algorithm for principal components analysis
Computational Statistics & Data Analysis
Approximate aggregation of Markovian models using alternating least squares
Performance Evaluation
| Hi-index | 0.03 |
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.