Three–way compositional data: a multi–stage trilinear decomposition algorithm

The CANDECOMP/PARAFAC model is an extension of bilinear PCA and has been designed to model three-way data by preserving their multidimensional configuration. The Alternating Least Squares (ALS) procedure is the preferred estimating algorithm for this model because it guarantees stable results. It can, however, be slow at converging and sensitive to collinearity and over-factoring. Dealing with these issues is even more pressing when data are compositional and thus collinear by definition. In this talk the solution proposed is based on a multistage approach. Here parameters are optimized with procedures that work better for collinearity and over-factoring, namely ATLD and SWATLD, and then results are refined with ALS.