Fitting the CANDECOMP-PARAFAC model to 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 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 new procedure does 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.