A self-adaptive regularized alternating least squares method for tensor decomposition problems

Though the alternating least squares algorithm (ALS), as a classic and easily implemented algorithm, has been widely applied to tensor decomposition and approximation problems, it has some drawbacks: the convergence of ALS is not guaranteed, and the swamp phenomenon appears in some cases, causing the convergence rate to slow down dramatically. To overcome these shortcomings, the regularized-ALS algorithm (RALS) was proposed in the literature. By employing the optimal step-size selection rule, we develop a self-adaptive regularized alternating least squares method (SA-RALS) to accelerate RALS in this paper. Theoretically, we show that the step-size is always larger than unity, and can be larger than [Formula: see text], which is quite different from several optimization algorithms. Furthermore, under mild assumptions, we prove that the whole sequence generated by SA-RALS converges to a stationary point of the objective function. Numerical results verify that the SA-RALS performs better than RALS in terms of the number of iterations and the CPU time.

Tensorial Change Analysis Using Probabilistic Tensor Regression

This paper proposes a new method for change detection and analysis using tensor regression. Change detection in our setting is to detect changes in the relationship between the input tensor and the output scalar while change analysis is to compute the responsibility score of individual tensor modes and dimensions for the change detected. We develop a new probabilistic tensor regression method, which can be viewed as a probabilistic generalization of the alternating least squares algorithm. Thanks to the probabilistic formulation, the derived change scores have a clear information-theoretic interpretation. We apply our method to semiconductor manufacturing to demonstrate the utility. To the best of our knowledge, this is the first work of change analysis based on probabilistic tensor regression.