Tensor decompositions, alternating least squares and other tales - Comon, P.; Luciani, X.; de Almeida, A. L. F. (Journal of chemometrics, 2009)
This work was originally motivated by a classification of tensors proposed by Richard Harshman. In particular, we focus on simple and multiple ‘bottlenecks’, and on ‘swamps’. Existing theoretical results are surveyed, some numerical algorithms are described in details, and their numerical complexity is calculated. In particular, the interest in using the enhanced line search (ELS) enhancement in these algorithms is discussed. Computer simulations feed this discussion. Copyright © 2009 John Wiley & Sons, Ltd. Various aspects of tensor decompositions are addressed: existence, uniqueness and computation. The state of the art is surveyed, by making the difference between conjectures and proved results. Some numerical algorithms are described in details, and their numerical complexity is evaluated. The slowness of numerical algorithms is often due to a form of ill‐conditioning of the tensor to be decomposed. In particular, Richard Harshman called ‘bottleneck’ the fact that two or more factors in a mode are almost collinear.