Fitting CANDECOMP-PARAFAC model for compositional data: a combined SWATLD-ALS algorithm

Multidimensional compositional arrays require special analytical tools to be modeled. Specifically, the variation of the data can be captured by linear combinations of a defined number of parameters, capable of describing the complexity of the data. Usually these models are described as generalizations of Principal Component Analysis (PCA) to higher order cases. Here the Candecomp/Parafac(CP) model is defined for compositional data contaminated with extreme observations by using a novel integrated SWATLD-ALS algorithm. Since the SWATLD proceduredoes not find a solution in the least square sense, it is expected to have a better performance in terms of sensitivity to outliers than ALS. However, due to the instability of its loss function, it should not be used alone: we suggest to combine SWATLD and ALS.