Initial value selection for the alternating least squares algorithm

The alternating least squares (ALS) algorithm is a popular computational algorithm for obtaining least squares solutions minimizing the loss functions in nonlinear multivariate analysis with optimal scaling (NMVA). The ALS algorithm is a simple computational procedure and has a stable convergence property, while the algorithm only guarantees local convergence. In order to avoid finding a local minimum of a loss function, the most commonly used method is to start the ALS algorithm with various random initial values. Such random initialization ALS algorithm tries to find the least squares solution that globally minimizes the loss function. However, the drawback of the random initialization ALS algorithm with multiple runs is to take a huge number of iterations and long computation time. For these problems, we consider initial value selection for selecting an initial value leading to a global minimum of the loss function. The proposed procedure enables efficiently selecting an initial value of the ALS algorithm. Furthermore, we can increase the computation speed when applying the vector ε acceleration for the ALS algorithm to the initial value selection procedure and the least squares estimation in NMVA.