The Multilinear Engine: A Table-Driven, Least Squares Program for Solving Multilinear Problems, including the n-Way Parallel Factor Analysis Model

1999 ◽  
Vol 8 (4) ◽  
pp. 854 ◽  
Author(s):  
Pentti Paatero
Keyword(s):  
Factor Analysis ◽  
Least Squares ◽  
Parallel Factor Analysis ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Multilinear Engine ◽  
Parallel Factor

scholarly journals A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2058
Author(s):  
Carlos Martin-Barreiro ◽  
John A. Ramirez-Figueroa ◽  
Xavier Cabezas ◽  
Victor Leiva ◽  
Ana Martin-Casado ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Real World ◽  
Parallel Factor Analysis ◽  
Analysis Model ◽  
Real World Data ◽  
Factor Analysis Model ◽  
World Data ◽  
Orthogonality Constraints ◽  
Orthogonal Components ◽  
Parallel Factor

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

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