CP Decomposition - Other Decompositions

Other Decompositions

PARAFAC is one of several decomposition methods for multi-way data. The two main competitors are the Tucker3 method, and simply unfolding of the multi-way array to a matrix and then performing standard two-way methods as principal component analysis (PCA). The Tucker3 method should rightfully be called three-mode principal component analysis (or N-mode principal component analysis), but here the term Tucker3 or just Tucker decomposition will be used instead. PARAFAC, Tucker and two-way PCA are all multi- or bi-linear decomposition methods, which decompose the array into sets of "scores" and "loadings", that hopefully describe the data in a more condensed form than the original data array. There are advantages and disadvantages with all the methods, and often several methods must be tried to find the most appropriate.

In the field of chemometrics, a number of diagnostic tools and techniques exist to help a PARAFAC user determine the best fitting model. These include the core consistency diagnostic (CORCONDIA), split-half analyses, examination of the loadings, and residual analysis.