Although alternating least squares algorithms have revealed extremely useful and flexible to solve multivariate curve resolution problems, other approaches based on non-linear optimization algorithms using non-linear constraints are possible. Once the subspaces defined by PCA solutions are identified, appropriate rotation and perturbation of these solutions can produce solutions fulfilling the ...

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...

The multiexponential analysis problem of fitting kinetic models to timeresolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard er...

The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important exception that best rank-one approximations always exists. The most popular approach to low-rank approximation is the alternating least squares (ALS) method...

Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gra...

Alternating minimization algorithms with a shrinkage step, derived within the Split Bregman (SB) or Alternating Direction Method of Multipliers (ADMM) frameworks, have become very popular for `-regularized problems, including Total Variation and Basis Pursuit Denoising. It appears to be generally assumed that they deliver much better computational performance than older methods such as Iterativ...